Keywords
 A1.2.4. QoS, performance evaluation
 A6.1.4. Multiscale modeling
 A6.2.3. Probabilistic methods
 A8.1. Discrete mathematics, combinatorics
 A8.2. Optimization
 A8.3. Geometry, Topology
 A8.6. Information theory
 A8.7. Graph theory
 A8.8. Network science
 A8.9. Performance evaluation
 A9.2. Machine learning
 A9.7. AI algorithmics
 B4.3. Renewable energy production
 B6.2.2. Radio technology
 B6.3.4. Social Networks
1 Team members, visitors, external collaborators
Research Scientists
 Bartlomiej Blaszczyszyn [Team leader, Inria, Senior Researcher, HDR]
 François Baccelli [Inria, Senior Researcher, In charge of ERC Nemo., HDR]
 Ana Busic [Inria, Researcher]
 Christine Fricker [Inria, Researcher, HDR]
 Ali Khezeli [Inria, Starting Research Position, from Oct 2020]
 Marc Lelarge [Inria, Senior Researcher, HDR]
 Laurent Massoulié [Inria, Researcher, HDR]
 Sean Meyn [INRIA, Chair, From May 2020 until Jul 2020]
PostDoctoral Fellows
 Simon Coste [Inria]
 Sanket Sanjay Kalamkar [Inria]
PhD Students
 Arnaud Cadas [Université Paris Sciences et Lettres]
 Michel Davydov [École Normale Supérieure de Paris]
 Bastien Dubail [École Normale Supérieure de Paris, from Sep 2020]
 Alexis Galland [Ministère des armées, until Nov 2020]
 Roman Gambelin [Inria, from Oct 2020]
 Luca Ganassali [Inria]
 Hadrien Hendrikx [Inria]
 Sayeh Khaniha [Inria]
 Quentin Le Gall [Orange, until Oct 2020]
 Maxime Leiber [Inria, from Feb 2020]
 Pierre Popineau [Inria, from Feb 2020]
 Bharath Roy Choudhury [Inria]
 Sébastien Samain [Inria]
 Ilia Shilov [Inria]
 Ludovic Stephan [Sorbonne Université]
Technical Staff
 Pierre Popineau [Inria, Engineer, until Jan 2020]
Interns and Apprentices
 Ahmad Alammouri [Inria, from Feb 2020 until Jul 2020]
 Bastien Dubail [École Normale Supérieure de Lyon, until Jan 2020]
 Mathieu Even [École Normale Supérieure de Paris, from Apr 2020]
 Teodora Popescu [Inria, from Mar 2020 until Jul 2020]
Administrative Assistants
 Helene Bessin Rousseau [Inria, until Nov 2020]
 Julien Guieu [Inria, in charge of ERC Nemo]
 Helene Milome [Inria]
 Scheherazade Rouag [Inria, from Nov 2020]
Visiting Scientist
 Holger Keeler [Weierstrass Institute, until Jan 2020]
External Collaborators
 Pierre Bremaud [École polytechnique fédérale de Lausanne]
 Antoine Brochard [Huawei]
 Marc Olivier Buob [Bell Labs (Alcatel)]
 Fabien Mathieu [Nokia, HDR]
2 Overall objectives
The general scientific focus of DYOGENE is on the development of network mathematics. The following theories lie within our research interest: dynamical systems, queuing theory, optimization and control, information theory, stochastic processes, random graphs, stochastic geometry.
Our theoretical developments are motivated by and applied in the context of communication networks (Internet, wireless, mobile, cellular, peertopeer), social and economic networks, power grids, and, recently, infectious diseases.
We collaborate with many industrial partners. Our current industrial relations involve EDF, Huawei, Microsoft, Nokia, Orange, Safran.
More specifically, the scientific focus of DYOGENE defined in 2013 was on geometric network dynamics arising in communications. By geometric networks we understand networks with a nontrivial, discrete or continuous, geometric definition of the existence of links between the nodes. In stochastic geometric networks, this definition leads to random graphs or stochastic geometric models.
A first type of geometric network dynamics is the one where the nodes or the links change over time according to an exogeneous dynamics (e.g. node motion and geometric definition of the links). We will refer to this as dynamics of geometric networks below. A second type is that where links and/or nodes are fixed but harbor local dynamical systems (in our case, stemming from e.g. information theory, queuing theory, social and economic sciences). This will be called dynamics on geometric networks. A third type is that where the dynamics of the network geometry and the local dynamics interplay. Our motivations for studying these systems stem from many fields of communications where they play a central role, and in particular: message passing algorithms; epidemic algorithms; wireless networks and information theory; device to device networking; distributed content delivery; social and economic networks, power grids.
3 Research program
3.1 Initial research axes
The following research axes have been defined in 2013 when the projectteam was created.
 Algorithms for network performance analysis, led by A. Bouillard and A. Busic.
 Stochastic geometry and information theory for wireless network, led by F. Baccelli and B. Blaszczyszyn.
 The cavity method for network algorithms, led by M. Lelarge.
Our scientific interests keep evolving. Research areas which received the most of our attention in 2020 are summarized in the following sections.
3.2 Models of infectious diseases
Over the past year, with several researchers and collaborations with the main players in the medical system, we have looked at mathematical models of the evolution of the Covid 19 epidemic.
3.3 Distributed network control and smartgrids
Theory and algorithms for distributed control of networks with applications to the stabilization of power grids subject to high volatility of renewable energy production are being developed by A. Busic in collaboration with Sean Meyn [Prof. at University of Florida and Inria International Chair].
3.4 Mathematics of wireless cellular networks
A comprehensive approach involving information theory, queueing and stochastic geometry to model and analyze the performance of large cellular networks, validated and implemented by Orange is being led by B. Blaszczyszyn in collaboration with F. Baccelli and M. K. Karray [Orange Labs]. A new collaboration between the Standardization and Research Lab at Nokia Bell Labs and ERC NEMO led by F. Baccelli has been started in 2019.
3.5 Highdimensional statistical inference and distributed learning
We computed information theoretic bounds for unsupervised and semisupervised learning and proved complexity bounds for distributed optimization of convex functions using a network of computing units.
3.6 Stochastic Geometry
Stochastic geometry offers a mathematical framework for the analysis of various random structures embedded in Euclidean space. This year we were studying a general fragmentationinteractionaggregation spatial processes, Nash equilibrium on point measures, an optimal stationary marking representing various specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications, particle gradient descent model for point process generations, a processes on Delaunay neighbors in the PoissonVoronoi tessellation, and Dirichlet measures. We collaborated with V. Anantharam (EECS at UC Berkeley), Ch. Hirsch (University of Groningen), S. Mallat (ENS/Flatiron Institute) and S. Zhang (IRITSC)
4 Application domains
4.1 Physical communication networks
Internet, wireless, mobile, cellular networks, transportation networks, distributed systems (cloud, call centers). In collaboration with Nokia Bell Labs and Orange Labs.
4.2 Abstract networks
Social interactions, human communities, economic networks.
4.3 Power grids
Energy networks. In collaboration with EDF and Vito (Belgium).
5 Highlights of the year
An exhaustive treatment of Random Measures Point Processes and Stochastic Geometry has just been proposed in a new book 21 (more than 500 pages) by F. Baccelli, B. Błaszczyszyn and M. K. Karray. The book contains two types of results: (1) structural results of stationary random measures and stochastic geometry objects, which do not rely on any parametric assumptions; (2) more computational results on the most important parametric classes of point processes, in particular Poisson or Determinantal point processes.
5.1 Awards
The paper 18 on "Stochastic Geometry for Beam Management in 5G Networks" by S. Kalamkar and F. Baccelli in collaboration with Luis G. Uzeda Garcia, Fuad Abinader and Andrea Marcano from Nokia Bell Labs Paris received a best paper award at IEEE Globecom in December 2020; see Section 7.4.
6 New software and platforms
6.1 New platforms
Cellular network dimensioning toolbox CapRadio is being developed by Orange in a longterm collaboration between TREC/DYOGENE represented by B. Błaszczyszyn, and Orange Labs, represented by M. K. Karray. This year we are working on taking into account the “massive MIMO” in 5G cellular networks; see 8.1.1.
7 New results
7.1 Models of infectious diseases
1. Initiative face au virus Observations sur la mobilité pendant l'épidémie de Covid19 25 This report analyzes human mobility patterns in France during the first lockdown of France in MarchMay 2020, based on mobility data made available by Facebook through its ‘Data for Good’ programme. It highlights the impact of lockdown on various indices capturing among other things urban mobility and interregional mobility.
2. Probabilistic and meanfield model of COVID19 epidemics with user mobility and contact tracing 24 We propose a detailed discretetime model of COVID19 epidemics coming in two flavours, meanfield and probabilistic. The main contribution lies in several extensions of the basic model that capture i) user mobility — distinguishing routing, i.e. change of residence, from commuting, i.e. daily mobility  and ii) contact tracing procedures. We confront this model to public data on daily hospitalizations, and discuss its application as well as underlying estimation procedures.
3. Understanding and monitoring the evolution of the Covid19 epidemic from medical emergency calls: the example of the Paris area 1 We portray the evolution of the Covid19 epidemic during the crisis of MarchApril 2020 inthe Paris area, by analyzing the medical emergency calls received by the EMS of the four central departmentsof this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between thesedepartments. We show that the logarithm of each epidemic observable can be approximated by a piecewiselinear function of time. This allows us to distinguish the different phases of the epidemic, and to identify thedelay between sanitary measures and their influence on the load of EMS. This also leads to an algorithm,allowing one to detect epidemic resurgences. We rely on a transport PDE epidemiological model, and weuse methods from PerronFrobenius theory and tropical geometry.
7.2 Distributed network control and smartgrids
4. Adaptive Matching for Expert Systems with Uncertain Task Types 3A matching in a twosided market often incurs an externality: a matched resource maybecome unavailable to the other side of the market, at least for a while. This is especiallyan issue in online platforms involving human experts as the expert resources are often scarce.The efficient utilization of experts in these platforms is made challenging by the fact that theinformation available about the parties involved is usually limited.To address this challenge, we develop a model of a taskexpert matching system where atask is matched to an expert using not only the prior information about the task but alsothe feedback obtained from the past matches. In our model the tasks arrive online while theexperts are fixed and constrained by a finite service capacity. For this model, we characterizethe maximum task resolution throughput a platform can achieve. We show that the naturalgreedy approaches where each expert is assigned a task most suitable to her skill is suboptimal,as it does not internalize the above externality. We develop a throughput optimal backpressurealgorithm which does so by accounting for the ‘congestion’ among different task types. Finally,we validate our model and confirm our theoretical findings with datadriven simulations vialogs of Math.StackExchange, a StackOverflow forum dedicated to mathematics.
5. Simultaneous Allocation and Control of Distributed Energy Resources via KullbackLeiblerQuadratic Optimal Control 8 There is enormous flexibility potential in the power consumption of the majority of electric loads. This flexibility can be harnessed to obtain services for managing the grid: with carefully designed decision rules in place, power consumption for the population of loads can be ramped up and down, just like charging and discharging a battery, without any significant impact to consumers' needs. The concept is called Demand Dispatch, and the grid resource obtained from this design virtual energy storage (VES). In order to deploy VES, a balancing authority is faced with two challenges: 1. how to design local decision rules for each load given the target aggregate power consumption (distributed control problem), and 2. how to coordinate a portfolio of resources to maintain grid balance, given a forecast of netload (resource allocation problem).Rather than separating resource allocation and distributed control, in this paper the two problems are solved simultaneously using a single convex program. The joint optimization model is cast as a finitehorizon optimal control problem in a meanfield setting, based on the new KLQ optimal control approach proposed recently by the authors.The simplicity of the proposed control architecture is remarkable: With a large portfolio of heterogeneous flexible resources, including loads such as residential water heaters, commercial water heaters, irrigation, and utilityscale batteries, the control architecture leads to a single scalar control signal broadcast to every resource in the domain of the balancing authority.
6. Energy Packet Networks with Finite Capacity Energy Queues 20 Energy Packet Network (EPN) consists of a queueing network formed by n blocks, where each of them is formed by one data queue, that handles the workload, and one energy queue, that handles packets of energy. We study an EPN model where the energy packets start the transfer. In this model, energy packets are sent to the data queue of the same block. An energy packet routes one workload packet to the next block if the data queue is not empty, and it is lost otherwise. We assume that the energy queues have a finite buffer size and if an energy packet arrives to the system when the buffer is full, jumpover blocking (JOB) is performed, and therefore with some probability it is sent to the data queue and it is lost otherwise. We first provide a value of this probability such that the steadystate probability distribution of packets in the queues admits a product form solution. Moreover, in the case of a single block, we show that the number of data packets in the system decreases as the JOB probability increases.
7. Energy Storage Optimization for Grid Reliability 14 Large scale renewable energy source (RES) integration planned for multiple power grids around the world will require additional resources/reserves to achieve secure and stable grid operations to mitigate the inherent intermittency of RES. In this paper, we present formulations to understand the effect of fast storage reserves in improving grid reliability under different cost functions. Our formulations not only aim to minimize imbalance but also maintain stateofcharge (SoC) of storage. The proposed approaches rely on a macroscopic supplydemand model of the grid with total power output of energy storage as the control variable. We show that accounting for system response due to inertia and local governor response enables a more realistic quantification of storage requirements for damping net load fluctuations. Simulation case studies are embedded in the paper by using datasets from the Elia TSO in Belgium and BPA in the USA. The numerical results benchmark the marginal effect on reliability due to increasing storage size under different system responses and associated cost functions. Further we observe myopic control of batteries proposed approximates deterministic control of batteries for faster time scale reserve operation.
8. Efficient distributed solutions for sharing energy resources at local level: a cooperative game approach 6 Local energy generation as well as local energy storage represent key opportunities for energy transition. Nevertheless , their massive deployment is being delayed mainly due to cost reasons. Sharing resources at the local level enables not only reducing these costs significantly, but also to further optimize the cost of the energy exchanged with providers external to the local community. A key question that arises while sharing resources is how to distribute the obtained benefits among the various local players that cooperate. In this paper we propose a cooperative game model, where the players are the holders of energy resources (generation and storage); they cooperate in order to reduce their individual electricity costs. We prove that the core of the game is nonempty; i.e., the proposed cooperative game has a stable solution (distribution of the payoffs among the players) for the case where all players participate in a unique community, and no strict subset of players can obtain a better gain by leaving the community. We propose a formulation of this game, based on the theory of linear production games, which lead us to the two main contributions of this paper. First, we propose an efficient (with linear complexity) centralized algorithm for finding a stable payoff. Second, we provide an efficient distributed algorithm that computes an allocation in the core of the game without any requirement for the players to share any private information. The distributed algorithm requires the exchange of intermediate solutions among players. The topology of the network that enables these exchanges is closely related to the performance of the distributed algorithm. We show, by way of simulations, which are the best topologies for these communication graphs.
9. Sizing and Profitability of Energy Storage for Prosumers in Madeira, Portugal 15 This paper proposes a framework to select the bestsuited battery for cooptimizing for peak demand shaving, energy arbitrage and increase selfsufficiency in the context of power network in Madeira, Portugal. Feedintariff for electricity network in Madeira is zero, which implies consumers with excess production should locally consume the excess generation rather than wasting it. Further, the power network operator applies a peak power contract for consumers which imposes an upper bound on the peak power seen by the power grid interfaced by energy meter. We investigate the value of storage in Madeira, using four different types of prosumers, categorized based on the relationship between their inelastic load and renewable generation. We observe that the marginal increase in the value of storage deteriorates with increase in size and ramping capabilities. We propose the use of profit per cycle per unit of battery capacity and expected payback period as indices for selecting the bestsuited storage parameters to ensure profitability. This mechanism takes into account the consumption and generation patterns, profit, storage degradation, and cycle and calendar life of the battery. We also propose the inclusion of a friction coefficient in the original cooptimization formulation to increase the value of storage by reducing the operational cycles and eliminate low returning transactions.
10. Privacy Impact on Generalized Nash Equilibrium in PeertoPeer Electricity Market 44 We consider a peertopeer electricity market, where agents hold private information that they might not want to share. The problem is modeled as a noncooperative communication game, which takes the form of a Generalized Nash Equilibrium Problem, where the agents determine their randomized reports to share with the other market players, while anticipating the form of the peertopeer market equilibrium. In the noncooperative game, each agent decides on the deterministic and random parts of the report, such that (a) the distance between the deterministic part of the report and the truthful private information is bounded and (b) the expectation of the privacy loss random variable is bounded. This allows each agent to change her privacy level. We characterize the equilibrium of the game, prove the uniqueness of the Variational Equilibria and provide a closed form expression of the privacy price. In addition, we provide a closed form expression to measure the impact of the privacy preservation caused by inclusion of random noise and deterministic deviation from agents' true values. Numerical illustrations are presented on the 14bus IEEE network.
11. A mean field analysis of a stochastic model for reservation in carsharing systems 12 Over the past decade, vehiclesharing systems have appeared as a new answer to mobility challenges, like reducing congestion or pollution for numerous cities. In this paper we analyze a simple homogeneous stochastic model for stationbased carsharing systems with oneway trips where users reserve the parking space when the car is picked up. In these systems, users arrive at a station, pick up a vehicle while reserve a parking space at a destination station, use it for a while and then return it at the reserved parking space. Each station has a finite capacity and cannot host more vehicles and reserved parking spaces than its capacity. If the user cannot pick up a car or reserve at destination, he leaves the system. For this model, the large scale behavior is investigated via mean field approach. We derive asymptotics of the empirical measure process when the number of cars and stations are large together, such that their ratio tends to a constant. This gives the limiting distribution of the state of a station as the solution of a differential equation, called the FokkerPlanck equation. Then the main result is that the equilibrium point, characterized using queuing theory, exists and is unique. The proof uses a monotonicity argument as for bikesharing systems, but also needs implicit function theorem and combinatorial arguments. It allows to study the system performance in terms of large scale stationary proportion of empty and full stations, especially the influence of the fleet size. For the optimal fleet size, we give asymptotics for this quantity in light and heavy traffic. We prove that, in light traffic case, reservation has little impact, unlike the heavy traffic case.
12. Optimal Control of Dynamic Bipartite Matching Models 32 A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost problem. We fully characterize the optimal matching policy for complete matching graphs and for the Nshaped matching graph. In the former case, the optimal policy consists of matching everything and, in the latter case, it prioritizes the matchings in the extreme edges and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. For more general graphs, we need to consider some assumptions on the cost of the nodes. For complete graphs minus one edge, we provide conditions on the cost of the nodes such that the optimal policy of the Nshaped matching graph extends to this case. For acyclic graphs, we show that, when the cost of the extreme edges is large, the optimal matching policy prioritizes the matchings in the extreme edges. We also study the Wshaped matching graph and, using simulations, we show that there are cases where it is not optimal to prioritize to matchings in the extreme edges.
13. RiskAverse Equilibrium Analysis and Computation 45 We consider two market designs for a network of prosumers, trading energy: (i) a centralized design which acts as a benchmark, and (ii) a peertopeer market design. High renewable energy penetration requires that the energy market design properly handles uncertainty. To that purpose, we consider risk neutral models for market designs (i), (ii), and their riskaverse interpretations in which prosumers are endowed with coherent risk measures reflecting heterogeneity in their risk attitudes. We characterize analytically riskneutral and riskaverse equilibrium in terms of existence and uniqueness , relying on Generalized Nash Equilibrium and Variational Equilibrium as solution concepts. To hedge their risk towards uncertainty and complete the market, prosumers can trade financial contracts. We provide closed form characterisations of the riskadjusted probabilities under different market regimes and a distributed algorithm for risk trading mechanism relying on the Generalized potential game structure of the problem. The impact of risk heterogeneity and financial contracts on the prosumers' expected costs are analysed numerically in a three node network and the IEEE 14bus network.
14. Control oriented modeling of TCLs 35 Thermostatically controlled loads (TCLs) have the potential to be a valuable resource for the Balancing Authority (BA) of the future. Examples of TCLs include household appliances such as air conditioners, water heaters, and refrigerators. Since the rated power of each TCL is on the order of kilowatts, to provide meaningful service for the BA, it is necessary to control large collections of TCLs. To perform design of a distributed coordination/control algorithm, the BA requires a control oriented model that describes the relevant dynamics of an ensemble. Works focusing on solely modeling the ensemble date back to the 1980's, while works focusing on control oriented modeling are more recent. In this work, we contribute to the control oriented modeling literature. We leverage techniques from computational fluid dynamics (CFD) to discretize a pair of FokkerPlanck equations derived in earlier work 51. The discretized equations are shown to admit a certain factorization, which makes the developed model useful for control design. In particular, the effects of weather and control are shown to independently effect the system dynamics.
15. KullbackLeiblerQuadratic Optimal Control 34 This paper presents advances in KullbackLeiblerQuadratic (KLQ) optimal control: a stochastic control framework for Markovian models. The motivation is distributed control of large networks. As in prior work, the objective function is composed of a state cost in the form of KullbackLeibler divergence plus a quadratic control cost. With this choice of objective function, the optimal probability distribution of a population of agents over a finite time horizon is shown to be an exponential tilting of the nominal probability distribution. The same is true for the controlled transition matrices that induce the optimal probability distribution. However, one limitation of the previous work is that randomness can only be introduced via the control policy; all uncontrolled (natural) processes must be modeled as deterministic to render them immutable under an exponential tilting. In this work, only the controlled dynamics are subject to tilting, allowing for more general probabilistic models. Another advancement is a reduction in complexity based on lossy compression using transform techniques. This is motivated by the need to consider time horizons that are much longer than the intersampling times required for reliable control. Numerical experiments are performed in a power network setting. The results show that the KLQ method enables the aggregate power consumption of a collection of flexible loads to track a timevarying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints.
16. Storage Optimal Control under Net Metering Policies 41 Electricity prices and the end user net load vary with time. Electricity consumers equipped with energy storage devices can perform energy arbitrage, i.e., buy when energy is cheap or when there is a deficit of energy, and sell it when it is expensive or in excess, taking into account future variations in price and net load. Net metering policies indicate that many of the utilities apply a customer selling rate lower than or equal to the retail customer buying rate in order to compensate excess energy generated by end users. In this paper, we formulate the optimal control problem for an end user energy storage device in presence of net metering. We propose a computationally efficient algorithm, with worst case run time complexity of quadratic in terms of number of samples in lookahead horizon, that computes the optimal energy ramping rates in a time horizon. The proposed algorithm exploits the problem's piecewise linear structure and convexity properties for the discretization of optimal Lagrange multipliers. The solution has a thresholdbased structure in which optimal control decisions are independent of past or future price as well as of net load values beyond a certain time horizon, defined as a subhorizon. Numerical results show the effectiveness of the proposed model and algorithm. Furthermore, we investigate the impact of forecasting errors on the proposed technique. We consider an AutoRegressive Moving Average (ARMA) based forecasting of net load together with the Model Predictive Control (MPC). We numerically show that adaptive forecasting and MPC significantly mitigate the effects of forecast error on energy arbitrage gains.
17. Flexibility can hurt dynamic matching system performance 33 We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one to the system according to a given probability distribution. Upon arrival, an item is matched with a compatible item according to the First Come First Served discipline and leave the system immediately, whereas it is enqueued with other items of the same class, if any. We show that such a model may exhibit a non intuitive behavior: increasing the services ability by adding new edges in the matching graph may lead to a larger average population. This is similar to a Braess paradox. We first consider a quasicomplete graph with four nodes and we provide values of the probability distribution of the arrivals such that when we add an edge the mean number of items is larger. Then, we consider an arbitrary matching graph and we show sufficient conditions for the existence or nonexistence of this paradox. We conclude that the analog to the Braess paradox in matching models is given when specific independent sets are in saturation, i.e., the system is close to the stability condition.
18. Asynchrony and Acceleration in Gossip Algorithms 42 This paper considers the minimization of a sum of smooth and strongly convex functions dispatched over the nodes of a communication network. Previous works on the subject either focus on synchronous algorithms, which can be heavily slowed down by a few slow nodes (the straggler problem), or consider a historical asynchronous setting (Boyd et al., 2006), which relies on a communication model that cannot be readily implemented in practice, as it does not capture important aspects of asynchronous communications such as noninstantaneous computations and communications. We have two main contributions. 1) We introduce a new communication scheme, based on LossNetworks, that is programmable in a fully asynchronous and decentralized fashion. We establish empirically and theoretically that it improves over existing synchronous algorithms by depending on local communication delays in the analysis instead of global worstones. 2) We provide an acceleration of the standard gossip algorithm in the historical asynchronous model without requiring any additional synchronization.
19. Arbitrage with Power Factor Correction using Energy Storage 2 The importance of reactive power compensation for power factor (PF) correction will significantly increase with the largescale integration of distributed generation interfaced via inverters producing only active power. In this work, we focus on cooptimizing energy storage for performing energy arbitrage as well as local power factor corrections. The joint optimization problem is nonconvex, but can be solved efficiently using a McCormick relaxation along with penaltybased schemes. Using numerical simulations on real data and realistic storage profiles, we show that energy storage can correct PF locally without reducing arbitrage gains. It is observed that active and reactive power control is largely decoupled in nature for performing arbitrage and PF correction (PFC). Furthermore, we consider a stochastic online formulation of the problem with uncertain load, renewable and pricing profiles. We develop a model predictive control based storage control policy using ARMA forecast for the uncertainty. Using numerical simulations we observe that PFC is primarily governed by the size of the converter and therefore, lookahead in time in the online setting does not affect PFC noticeably. However, arbitrage gains are more sensitive to uncertainty for batteries with faster ramp rates compared to slow ramping batteries.
7.3 Reinforcement learning
20. Explicit MeanSquare Error Bounds for MonteCarlo and Linear Stochastic Approximation 9 This paper concerns error bounds for recursive equations subject to Markovian disturbances.Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) andReinforcement Learning (RL), and many of these algorithms can be interpreted as special casesof stochastic approximation (SA). It is argued that it is not possible in general to obtain aHoeffding bound on the error sequence, even when the underlying Markov chain is reversibleand geometrically ergodic, such as the $M/M/1$ queue. This is motivation for the focus on meansquare error bounds for parameter estimates. It is shown that mean square error achieves theoptimal rate of $O(1/n)$, subject to conditions on the stepsize sequence. Moreover, the exactconstants in the rate are obtained, which is of great value in algorithm design.
21. Zap QLearning for Optimal Stopping 10 This paper concerns approximate solutions to the optimal stopping problem for a geometrically ergodic Markov chain on a continuous state space. The starting point is the Galerkin relaxation of the dynamic programming equations that was introduced by Tsitsikilis and Van Roy in the 1990s, which motivated their Qlearning algorithm for optimal stopping. It is known that the convergence rate of Qlearning is in many cases very slow. The reason for slow convergence is explained here, along with a variant of "ZapQlearning" algorithm, designed to achieve the optimal rate of convergence. The main contribution is to establish consistency of ZapQlearning algorithm for a linear function approximation setting. The theoretical results are illustrated using an example from finance.
22. Zap QLearning With Nonlinear Function Approximation 11 The Zap stochastic approximation (SA) algorithm was introduced recently as a means to accelerate convergence in reinforcement learning algorithms. While numerical results were impressive, stability (in the sense of boundedness of parameter estimates) was established in only a few special cases. This class of algorithms is generalized in this paper, and stability is established under very general conditions. This general result can be applied to a wide range of algorithms found in reinforcement learning. Two classes are considered in this paper: (i)The natural generalization of Watkins' algorithm is not always stable in function approximation settings. Parameter estimates may diverge to infinity even in the linear function approximation setting with a simple finite stateaction MDP. Under mild conditions, the Zap SA algorithm provides a stable algorithm, even in the case of nonlinear function approximation. (ii) The GQ algorithm of Maei et. al. 2010 is designed to address the stability challenge. Analysis is provided to explain why the algorithm may be very slow to converge in practice. The new Zap GQ algorithm is stable even for nonlinear function approximation.
7.4 Mathematics of wireless cellular networks
23. Bandwidth Allocation and Service Differentiation in D2D Wireless Networks 4 Inspired by a new feature in 5G NR called bandwidth part (BWP), this paper presents a bandwidth allocation (BA) model that allows one to adapt the bandwidth allocated to users depending on their data rate needs. Specifically, in adaptive BA, a wide bandwidth is divided into chunks of smaller bandwidths and the number of bandwidth chunks allocated to a user depends on its needs or type. Although BWP in 5G NR mandates allocation of a set of contiguous bandwidth chunks, our BA model also allows other assumptions on chunk allocation such as the allocation of any set of bandwidth chunks, as in, e.g., LTE resource allocation, where chunks are selected uniformly at random. The BA model studied here is probabilistic in that the user locations are assumed to form a realization of a Poisson point process and each user decides independently to be of a certain type with some probability. This model allows one to quantify spectrum sharing and service differentiation in this context, namely to predict what performance a user gets depending on its type as well as the overall performance. This is based on exact representations of key performance metrics for each user type, namely its success probability, the meta distribution of its signaltointerference ratio, and its Shannon throughput. We show that, surprisingly, the higher traffic variability stemming from adaptive BA is beneficial: when comparing two networks using adaptive BA and having the same mean signal and the same mean interference powers, the network with higher traffic variability performs better for all these performance metrics. With respect to Shannon throughput, we observe that our BA model is roughly egalitarian per Hertz and leads to a linear service differentiation in aggregated throughput value.
24. Coverage probability in wireless networks with determinantal scheduling 7We propose a new class of algorithms for randomly scheduling network transmissions. The idea is to use (discrete) determinantal point processes (subsets) to randomly assign medium access to various repulsive subsets of potential transmitters. This approach can be seen as a natural extension of (spatial) Aloha, which schedules transmissions independently. Under a general path loss model and Rayleigh fading, we show that, similarly to Aloha, they are also subject to elegant analysis of the coverage probabilities and transmission attempts (also known as local delay). This is mainly due to the explicit, determinantal form of the conditional (Palm) distribution and closedform expressions for the Laplace functional of determinantal processes. Interestingly, the derived performance characteristics of the network are amenable to various optimizations of the scheduling parameters, which are determinantal kernels, allowing the use of techniques developed for statistical learning with determinantal processes. Wellestablished sampling algorithms for determinantal processes can be used to cope with implementation issues, which is is beyond the scope of this paper, but it creates paths for further research.
25. Beam Management in 5G: A Stochastic Geometry Analysis 18 Beam management is central in the operation of beamformed wireless cellular systems such as 5G New Radio (NR) networks. Focusing the energy radiated to mobile terminals (MTs) by increasing the number of beams per cell increases signal power and decreases interference, and has hence the potential to bring major improvements on area spectral efficiency (ASE). This paper proposes a first systemlevel stochastic geometry model encompassing major aspects of the beam management problem: frequencies, antenna configurations, and propagation; physical layer, wireless links, and coding; network geometry, interference, and resource sharing; sensing, signaling, and mobility management. This model leads to a simple analytical expression for the effective rate that the typical user gets in this context. This in turn allows one to find the number of beams per cell and per MT that maximizes the effective ASE by offering the best tradeoff between beamforming gains and beam management operational overheads and costs, for a wide variety of 5G network scenarios including millimeter wave (mmWave) and sub6 GHz. As part of the systemlevel analysis, we define and analyze several underlying new and fundamental performance metrics that are of independent interest. The numerical results discuss the effects of different systemic tradeoffs and performance optimizations of mmWave and sub6 GHz 5G deployments.
26. Crowdnetworking: modelling DevicetoDevice connectivity on street systems using percolation theory, and economic consequences 23 The fifth generation of cellular networks is expected to provide coverage for an unprecedented number of devices over large areas. One of the main paradigms investigated to address this challenge, called DevicetoDevice (D2D) communication, consists in allowing for shortrange direct communications between network devices. An application of significant economic interest for operators is the one of the uberisation of networks, where an operator having no (or very few) network infrastructure could build a mobile network relying only on its enddevices (users). In this thesis, we study new mathematical models of D2D networks in urban environments. We see the street system of a city as a planar PoissonVoronoi tessellation (PVT). Network users are given by a Cox process supported by the edges of the PVT while additional network relays are given by a Bernoulli process on the vertices of the PVT. The network is then modelled by a connectivity graph as follows: vertices are the atoms of both these processes and fixedrange connections between them possible only along the PVT edges or between network nodes located on adjacent PVT edges. Percolation of this random graph (existence of an infinite connected component with positive probability) is interpreted as good connectivity of the network. Using renormalisation techniques, we prove the existence of phase transitions between different connectivity regimes, in particular those where percolation can be solely ensured by the relays or, on the contrary, where a sufficient density of users is essential. Performing numerical simulations with original pathfinding algorithms, we estimate critical parameters (e.g. the density of relays and users) allowing for good connectivity of the network. Finally, we also introduce appropriate cost models and use our numerical estimates to study the economic feasibility of uberisation scenarios of telecommunications networks.
27. Relayassisted DevicetoDevice Networks: Connectivity and Uberization Opportunities 19 It has been shown that deploying devicetodevice (D2D) networks in urban environments requires equipping a considerable proportion of crossroads with relays. This represents a necessary economic investment for an operator. In this work, we tackle the problem of the economic feasibility of such relayassisted D2D networks. First, we propose a stochastic model taking into account a positive surface for streets and crossroads, thus allowing for a more realistic estimation of the minimal number of needed relays. Secondly, we introduce a cost model for the deployment of relays, allowing one to study operators' D2D deployment strategies. We investigate the example of an uberizing neooperator willing to set up a network entirely relying on D2D and show that a return on the initial investment in relays is possible in a realistic period of time, even if the network is funded by a very low revenue per D2D user. Our results bring quantitative arguments to the discussion on possible uberization scenarios of telecommunications networks.
28. Randomised Geographic Caching and its Applications in Wireless Networks 40 The randomised (or probabilistic) geographic caching is a proactive content placement strategy that has attracted a lot of attention, because it can simplify a great deal cachemanagement problems at the wireless edge. It diversifies content placement over caches and applies to scenarios where a request can be possibly served by multiple cache memories. Its simplicity and strength is due to randomisation. It allows one to formulate continuous optimisation problems for content placement over large homogeneous geographic areas. These can be solved to optimality by standard convex methods, and can even provide closedform solutions for specific cases. This way the algorithmic obstacles from NPhardness are avoided and optimal solutions can be derived with low computational cost. Randomised caching has a large spectrum of applications in realworld wireless problems, including femtocaching, multitier networks, devicetodevice communications, mobility, mmwave, security, UAVs, and more. In this chapter we will formally present the main policy with its applications in various wireless scenarios. We will further introduce some very useful extensions related to unequal filesizes and content placement with neighbourhood dependence.
29. Characterizing the Energy TradeOffs of EndtoEnd Vehicular Communications using an Hyperfractal Urban Modelling 43 We characterize tradeoffs between the endtoend communication delay and the energy in urban vehicular communications with infrastructure assistance. Our study exploits the selfsimilarity of the location of communication entities in cities by modeling them with an innovative model called "hyperfractal". We show that the hyperfractal model can be extended to incorporate roadside infrastructure and provide stochastic geometry tools to allow a rigorous analysis. We compute theoretical bounds for the endtoend communication hop count considering two different energyminimizing goals: either total accumulated energy or maximum energy per node. We prove that the hop count for an endtoend transmission is bounded by $O\left({n}^{1\alpha /({d}_{F}1)}\right)$ where $\alpha <1$ and ${d}_{F}>2$ is the fractal dimension.
7.5 Highdimensional statistical inference
30. From tree matching to sparse graph alignment 13 In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated ErdősRényi random graphs, we prove that the algorithm returns – in polynomial time – a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. This result holds with average degree of the graphs in $O\left(1\right)$ and correlation parameter $s$ that can be bounded away from 1, conditions under which random graph alignment is particularly challenging. As a byproduct of the analysis we introduce a matching metric between trees and characterize it for several models of correlated random trees. These results may be of independent interest, yielding for instance efficient tests for determining whether two random trees are correlated or independent.
31. Sharp threshold for alignment of graph databases with Gaussian weights 39 We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs $G$, ${G}^{\text{'}}$, where $G$ and ${G}^{\text{'}}$ have correlated Gaussian edge weights, and then $G$ is relabeled according to a random uniform permutation. We prove that there is a sharp informationtheoretic threshold for exact recovery of the planted permutation. This threshold is the same as the one obtained for detection in a recent work by Y. Wu, J. Xu and S. Yu: in other words, for Gaussian weighted graph alignment, the problem of reconstruction is not more difficult than that of detection. The study is based on the analysis of the MAP estimator, and proofs rely on proper use of the correlation structure of energies of permutations.
32. Spectral alignment of correlated Gaussian random matrices 38 In this paper we analyze a simple method ($EIG1$) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given $A$ and $B$, we compute ${v}_{1}$ and ${v}_{1}^{\text{'}}$ two leading eigenvectors of $A$ and $B$. The algorithm returns a permutation $\widehat{\Pi}$ such that the rank of the coordinate $\widehat{\Pi}\left(i\right)$ in ${v}_{1}$ is the rank of the coordinate $i$ in ${v}_{1}^{\text{'}}$ (up to the sign of ${v}_{1}^{\text{'}}$). We consider a model where $A$ belongs to the Gaussian Orthogonal Ensemble (GOE), and $B={\Pi}^{T}(A+\sigma H)\Pi $, where $\Pi $ is a permutation matrix and $H$ is an independent copy of $A$. We show the following 01 law: under the condition $\sigma {N}^{7/6+\u03f5}\to 0$, the $EIG1$ method recovers all but a vanishing part of the underlying permutation $\Pi $. When $\sigma {N}^{7/6\u03f5}\to \infty $, this algorithm cannot recover more than $o\left(N\right)$ correct matches. This result gives an understanding of the simplest and fastest spectral method for matrix alignment (or complete weighted graph alignment), and involves proof methods and techniques which could be of independent interest.
34. A simpler spectral approach for clustering in directed network 36 We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD truncation, and works very well down to the very sparse regime where the edge density has constant order. This simple approach was largely unnoticed in the mathematics and network science communities. Our analysis is based on a Master Theorem describing sharp asymptotics for isolated eigenvalues/eigenvectors of sparse, nonsymmetric matrices with independent entries. We also describe the limiting distribution of the entries of these eigenvectors; in the task of digraph clustering with spectral embeddings, we provide numerical evidence for the superiority of Gaussian Mixture clustering over the widely used kmeans algorithm.
36. Who started this rumor? Quantifying the natural differential privacy guarantees of gossip protocols 5 Gossip protocols are widely used to disseminate information in massive peertopeer networks. These protocols are often claimed to guarantee privacy because of the uncertainty they introduce on the node that started the dissemination. But is that claim really true? Can the source of a gossip safely hide in the crowd? This paper examines, for the first time, gossip protocols through a rigorous mathematical framework based on differential privacy to determine the extent to which the source of a gossip can be traceable. Considering the case of a complete graph in which a subset of the nodes are curious, we study a family of gossip protocols parameterized by a “muting” parameter s: nodes stop emitting after each communication with a fixed probability $1s$. We first prove that the standard push protocol, corresponding to the case $s=1$, does not satisfy differential privacy for large graphs. In contrast, the protocol with $s=0$ achieves optimal privacy guarantees but at the cost of a drastic increase in the spreading time compared to standard push, revealing an interesting tension between privacy and spreading time. Yet, surprisingly, we show that some choices of the muting parameter s lead to protocols that achieve an optimal order of magnitude in both privacy and speed. We also confirm empirically that, with appropriate choices of s, we indeed obtain protocols that are very robust against concrete source location attacks while spreading the information almost as fast as the standard (and nonprivate) push protocol.
37. Nonbacktracking spectra of weighted inhomogeneous random graphs 46 We study a model of random graphs where each edge is drawn independently (but not necessarily identically distributed) from the others, and then assigned a random weight. When the mean degree of such a graph is low, it is known that the spectrum of the adjacency matrix $A$ deviates significantly from that of its expected value $\mathbb{E}A$. In contrast, we show that over a wide range of parameters the top eigenvalues of the nonbacktracking matrix $B$ – a matrix whose powers count the nonbacktracking walks between two edges – are close to those of $\mathbb{E}A$, and all other eigenvalues are confined in a bulk with known radius. We also obtain a precise characterization of the scalar product between the eigenvectors of $B$ and their deterministic counterparts derived from the model parameters. This result has many applications, in domains ranging from (noisy) matrix completion to community detection, as well as matrix perturbation theory. In particular, we establish as a corollary that a result known as the BaikBen ArousPéché phase transition, previously established only for rotationally invariant random matrices, holds more generally for matrices $A$ as above under a mild concentration hypothesis.
7.6 Distributed optimization for machine learning
38. Statistically Preconditioned Accelerated Gradient Method for Distributed Optimization 17 We consider the setting of distributed empirical risk minimization where multiple machines compute the gradients in parallel and a centralized server updates the model parameters. In order to reduce the number of communications required to reach a given accuracy, we propose a preconditioned accelerated gradient method where the preconditioning is done by solving a local optimization problem over a subsampled dataset at the server. The convergence rate of the method depends on the square root of the relative condition number between the global and local loss functions. We estimate the relative condition number for linear prediction models by studying uniform concentration of the Hessians over a bounded domain , which allows us to derive improved convergence rates for existing preconditioned gradient methods and our accelerated method. Experiments on realworld datasets illustrate the benefits of acceleration in the illconditioned regime.
39. DualFree Stochastic Decentralized Optimization with Variance Reduction 16 We consider the problem of training machine learning models on distributed data in a decentralized way. For finitesum problems, fast singlemachine algorithms for large datasets rely on stochastic updates combined with variance reduction. Yet, existing decentralized stochastic algorithms either do not obtain the full speedup allowed by stochastic updates, or require oracles that are more expensive than regular gradients. In this work, we introduce a Decentralized stochastic algorithm with Variance Reduction called DVR. DVR only requires computing stochastic gradients of the local functions, and is computationally as fast as a standard stochastic variancereduced algorithms run on a 1/n fraction of the dataset, where n is the number of nodes. To derive DVR, we use Bregman coordinate descent on a wellchosen dual problem, and obtain a dualfree algorithm using a specific Bregman divergence. We give an accelerated version of DVR based on the Catalyst framework, and illustrate its effectiveness with simulations on real data.
40. Concentration of NonIsotropic Random Tensors with Applications to Learning and Empirical Risk Minimization 37 Dimension is an inherent bottleneck to some modern learning tasks, where optimization methods suffer from the size of the data. In this paper, we study nonisotropic distributions of data and develop tools that aim at reducing these dimensional costs by a dependency on an effective dimension rather than the ambient one. Based on nonasymptotic estimates of the metric entropy of ellipsoidsthat prove to generalize to infinite dimensionsand on a chaining argument, our uniform concentration bounds involve an effective dimension instead of the global dimension, improving over existing results. We show the importance of taking advantage of nonisotropic properties in learning problems with the following applications: i) we improve stateoftheart results in statistical preconditioning for communicationefficient distributed optimization, ii) we introduce a nonisotropic randomized smoothing for nonsmooth optimization. Both applications cover a class of functions that encompasses empirical risk minization (ERM) for linear models.
41. Conditioned Text Generation with Transfer for ClosedDomain Dialogue Systems 22 Scarcity of training data for taskoriented dialogue systems is a well known problem that is usually tackled with costly and timeconsuming manual data annotation. An alternative solution is to rely on automatic text generation which, although less accurate than human supervision, has the advantage of being cheap and fast. Our contribution is two fold. First we show how to optimally train and control the generation of intentspecific sentences using a conditional variational auto encoder. Then we introduce a new protocol called query transfer that allows to leverage a large unlabelled dataset, possibly containing irrelevant queries, to extract relevant information. Comparison with two different baselines shows that this method, in the appropriate regime, consistently improves the diversity of the generated queries without compromising their quality. We also demonstrate the effectiveness of our generation method as a data augmentation technique for language modelling tasks.
7.7 Stochastic Geometry
42. Random Measures, Point Processes, and Stochastic Geometry 21 This book is centered on the mathematical analysis of random structures embedded in the Euclidean space or more general topological spaces, with a main focus on random measures, point processes, and stochastic geometry. Such random structures have been known to play a key role in several branches of natural sciences (cosmology, ecology, cell biology) and engineering (material sciences, networks) for several decades. Their use is currently expanding to new fields like data sciences. The book was designed to help researchers finding a direct path from the basic definitions and properties of these mathematical objects to their use in new and concrete stochastic models. The theory part of the book is structured to be selfcontained, with all proofs included, in particular on measurability questions, and at the same time comprehensive. In addition to the illustrative examples which one finds in all classical mathematical books, the document features sections on more elaborate examples which are referred to as models in the book. Special care is taken to express these models, which stem from the natural sciences and engineering domains listed above, in clear and selfcontained mathematical terms. This continuum from a comprehensive treatise on the theory of point processes and stochastic geometry to the collection of models that illustrate its representation power is probably the main originality of this book. The book contains two types of mathematical results: (1) structural results on stationary random measures and stochastic geometry objects, which do not rely on any parametric assumptions; (2) more computational results on the most important parametric classes of point processes, in particular Poisson or Determinantal point processes. These two types are used to structure the book. The material is organized as follows. Random measures and point processes are presented first, whereas stochastic geometry is discussed at the end of the book. For point processes and random measures, parametric models are discussed before nonparametric ones. For the stochastic geometry part, the objects as point processes are often considered in the space of random sets of the Euclidean space. Both general processes are discussed as, e.g., particle processes, and parametric ones like, e.g., Poisson Boolean models of Poisson hyperplane processes. We assume that the reader is acquainted with the basic results on measure and probability theories. We prove all technical auxiliary results when they are not easily available in the literature or when existing proofs appeared to us not sufficiently explicit. In all cases, the corresponding references will always be given.
43. ReplicaMeanField Limits of FragmentationInteractionAggregation Processes 26 Network dynamics with pointprocessbased interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replicameanfield approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas , these networks become analytically tractable under the socalled "Poisson Hypothesis". However, in most applications, this hypothesis is only conjectured. Here, we establish the Poisson Hypothesis for a general class of discretetime, pointprocessbased dynamics, that we propose to call fragmentationinteractionaggregation processes, and which are introduced in the present paper. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson Hypothesis for the replicameanfield version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete time GalvesLöcherbach neural networks are used as a basic instance and illustration of our analysis.
44. Nash equilibrium structure of Cox process Hotelling games 47 We study an Nplayer game where a pure action of each player is to select a nonnegative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the players, and the value to a player is the measure of the union of its open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and comprised of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem.
45. Optimal stationary markings 31 Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting particles. Using the framework of stationary point processes in the Euclidean space, we pose it as a problem of an optimal stationary marking of a given stationary point process. The quality of a given marking is evaluated in terms of scores calculated in a covariant manner for all points in function of the proposed marked configuration. In the absence of total order of the configurations of scores, we identify intensityoptimality and local optimality as two natural ways for defining optimal stationary marking. We derive tightness and integrability conditions under which intensityoptimal markings exist and further stabilization conditions making them equivalent to locally optimal ones. We present examples motivating the proposed, general framework. Finally, we discuss various possible approaches leading to uniqueness results.
46. Particle gradient descent model for point process generation 30 This paper introduces a generative model for planar point processes in a square window, built upon a single realization of a stationary, ergodic point process observed in this window. Inspired by recent advances in gradient descent methods for maximum entropy models, we propose a method to generate similar point patterns by jointly moving particles of an initial Poisson configuration towards a target counting measure. The target measure is generated via a deterministic gradient descent algorithm, so as to match a set of statistics of the given, observed realization. Our statistics are estimators of the multiscale wavelet phase harmonic covariance, recently proposed in image modeling. They allow one to capture geometric structures through multiscale interactions between wavelet coefficients. Both our statistics and the gradient descent algorithm scale better with the number of observed points than the classical knearest neighbour distances previously used in generative models for point processes, based on the rejection sampling or simulatedannealing. The overall quality of our model is evaluated on point processes with various geometric structures through spectral and topological data analysis.
47. On Point Processes Defined by Angular Conditions on Delaunay Neighbors in the PoissonVoronoi Tessellation 27 Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta $. The first one is the set of points that belong to some onedimensional facet of the Voronoi tessellation and are such that the angle with which they see the two nuclei defining the facet is $\theta $. The main question of interest on this first point process is its intensity. The second point process is that of the intersections of the said tessellation with a straight line having a random orientation. Its intensity is well known. The intersection points almost surely belong to onedimensional facets. The main question here is about the Palm distribution of the angle with which the points of this second point process see the two nuclei associated with the facet. The note gives answers to these two questions and briefly discusses their practical motivations. It also discusses natural extensions to dimension three.
48. A stochastic geometry characterization of PitmanYor processes 48 In this master's thesis, we give a new integral characterization of PitmanYor processes. It is inspired by a similar characterization for Dirichlet processes given by G. Last in 2019. The proof makes use of classical point processes theory arguments and is based on a key result found by T. Lehéricy in his 2015 master's thesis 50
8 Bilateral contracts and grants with industry
8.1 Bilateral contracts with industry
8.1.1 CRE with Orange
Two year contract titled Taking into account the “massive MIMO” in the assessment of QoS and the dimensioning of 5G cellularnetworks between Inria and Orange Labs started 2019. It is a part of a longterm collaboration between TREC/DYOGENE, represented by B. Błaszczyszyn and Orange Labs, represented by M. K. Karray on the development of analytic tools and methods allowing one to capture macroscopic relation between antennas rollout, frequency allocation, volume of traffic carried on the network and quality of service parameters such as the average and the variation of bandwidth available to end users. This work addresses crucial technical and economical issues related to the operator core business, particularly related to the current evolution of the cellular network technology (4G$\Rightarrow $5G). The developed solutions are implemented by Orange Labs in the internal toolbox CapRadio (see 6.1) and used by the Direction of Regulatory Affairs of Orange.
8.1.2 Contract with EDF
Collaborative research in the area of demand dispatch of flexible loads. PI : A. Busic.
8.1.3 CIFRE with Orange
Contract with Orange started in 2017 and finished in 2020 for the coadvising by B. Błaszczyszyn of a PhD student of Orange, Quentin Le Gall, who defended his thesis 23.
9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Inria international partners
Informal international partners
 University of Florida; Collaborations with Prof Sean Meyn (ECE), Associate Prof Prabir Barooah (MAE), and the PhD students: A. Devraj (ECE), A. Coffman (MAE), N. Cammardella (ECE), J. Mathias (ECE).
 Sharif University, Tehran; Collaborations with O. Mirsadeghi.
 UC Berkeley; Collaborations with V. Anantharam.
 Lehigh University; Collaborations with J. E. Yukich.
 University of Groningen; Collaborations with Ch. Hirsch.
 Polytechnique Montréal; Collaborations with Martin Trépanier.
9.1.2 Participation in other international programs
IndoFrench Center of Applied Mathematics
IFCAM Project “Geometric statistics of stationary point processes” B. Błaszczyszyn and Yogeshwaran D. from Indian Statistical Institute (ISI), Bangalore, have got in 2018 the approval from IndoFrench Centre for Applied Mathematics (IFCAM), for their joint project on “Geometric statistics of stationary point processes" for the period 2018–2021. B. Błaszczyszyn was visiting Indian Statistical Institute (ISI), Bangalore, in two weeks in January 2020. 2019.
Microsoft ResearchInria collaboration
Microsoft ResearchInria collaboration: Laurent Massoulié heads the Microsoft ResearchInria Joint Centre, and also participates to the “Distributed Machine Learning” project of the Joint Centre, together with Francis Bach (Inria), Sébastien Bubeck and Lin Xiao (MSR Redmond), and PhD student Hadrien Hendrikx.
Fall 2020 program Theory of Reinforcement Learning
At Simons Institute for the Theory of Computing, UC Berkeley, Aug. 19 – Dec. 18, 2020. https://
Inria International Chairs
 IIC MEYN Sean
 Title: Distributed Control and Smart Grid
 International Partner: University of Florida (United States)  Department of Electrical and Computer Engineering
 Sean Meyn
 University of Florida (United States)  Department of Electrical and Computer Engineering  Sean Meyn
 Duration: 2019 – 2023
 Start year: 2019

See also: https://
www. inria. fr/ sites/ default/ files/ 201912/ HoldersChairesInt_EN. pdf TOPIC: “Distributed Control and Smart Grid”
9.2 European initiatives
9.2.1 Collaborations in European programs, except FP7 and H2020
ERC NEMO
NEMO, NEtwork MOtion https://
This year we hired A. Khezeli at the Starting Research Position in DYOGENE in relation to ERCNEMO since October 1, 2020. Also, a PhD student P. Popineau was hired in February 2020.
9.2.2 Collaborations with major European organizations
Partner: VITO (Belgium); https://
9.3 National initiatives
9.3.1 GdR GeoSto
Members of Dyogene participate in Research Group GeoSto
(Groupement de recherche, GdR 3477)
http://
This is a collaboration framework for all French research teams working in the domain of spatial stochastic modeling, both on theory development and in applications.
9.3.2 GdR RO
Members of Dyogene participate in GdRRO (Recherche Opérationelle;
GdR CNRS 3002), http://
9.3.3 ANR JCJC PARI
Probabilistic Approach for Renewable Energy Integration: Virtual Storage from Flexible Loads. The project started in January 2017. PI — A. Bušić. This project is motivated by current and projected needs of a power grid with significant renewable energy integration. Renewable energy sources such as wind and solar have a high degree of unpredictability and time variation, which makes balancing demand and supply challenging. There is an increased need for ancillary services to smooth the volatility of renewable power. In the absence of large, expensive batteries, we may have to increase our inventory of responsive fossilfuel generators, negating the environmental benefits of renewable energy. The proposed approach addresses this challenge by harnessing the inherent flexibility in demand of many types of loads. The objective of the project is to develop decentralized control for automated demand dispatch, that can be used by grid operators as ancillary service to regulate demandsupply balance at low cost. We call the resource obtained from these techniques virtual energy storage (VES). Our goal is to create the necessary ancillary services for the grid that are environmentally friendly, that have low cost and that do not impact the quality of service (QoS) for the consumers. Besides respecting the needs of the loads, the aim of the project is to design local control solutions that require minimal communications from the loads to the centralized entity. This is possible through a systems architecture that includes the following elements: i) local control at each load based on local measurements combined with a gridlevel signal; ii) frequency decomposition of the regulation signal based on QoS and physical constraints for each class of loads.
9.4 Regional initiatives
9.4.1 Laboratory of Information, Networking and Communication Sciences (LINCS)
Dyogene participates in LINCS https://
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organisation
EPI seminar
A weekly seminar on Monday, 2.30 pm, organized by S. Coste.
Invited speakers:
Eliza O'Reilly, Benedikt Jahnel, Zakhar Kabluchko, David Dereudre, Pablo Ferrari, Georgina Hall, Viet Chi Tran, Romain Couillet, Frédéric Lavancier, Sixin Zhang, Michel Davydof, Kevin Scaman and Ali Khezeli.
10.1.2 Scientific events: selection
Member of the conference program committees
S. S. Kalambar:
IEEE Global Communications Conference (GLOBECOM) 2020;
The Workshop on Spatial Stochastic Models for Wireless Networks (SPASWIN) 2020.
Reviewer
H. Hendrikx :
Conferences: NeurIPS 2020, ICML2020, AISTATS2021;
Journals: SIOPT, IEEE Transactions on Signal Processing, Automatica.
10.1.3 Journal
Member of the editorial boards
S. S. Kalambar: Sensors  Topic editor, Sensors  Editor for the special issue on “EnergyEfficient Communications for beyond 5G Green Networks”
Reviewer  reviewing activities
All members of the team act as reviewers for numerous scientific journals.
10.1.4 Invited talks
 Invited series of lectures on Network Dynamics, Weierstrass Institute, Berlin, November 2020, F. Baccelli.
 Invited lecture at the Montevideo Probability Seminar, November 2020 (on SIS point process dynamics), F. Baccelli.
 Invited lecture at LINCS, Paris, on spatial game theory, Sept. 2020, F. Baccelli.
 Keynote lecture at IEEE WiOptSpaswin, June 2020 (talk on vehicular wireless networks), Volos, Greece, F. Baccelli.
 Invited lecture at IISC Bangalore, Symposium on Advances in Communication Networks, July 2020 (talk on the SIS point process dynamics), F. Baccelli.
 Invited lecture at the Indian Statistical Institute, (on the dimension of infinite graphs), January 2010, F. Baccelli.
 Invited lecture at the Indian Statistical Institute, (Optimal stationary markings), January 2010, B. Błaszczyszyn.
 Talk at SNAPP (Stochastic Networks, Applied Probability, and Performance) online seminar series, (Optimal Control in Dynamic Matching Systems), September 2020, A. Busic.
 Invited talk at the Math and Physics seminar at Université de Genève, 9/2/2021, S. Coste.
 Invited talk at the working group point processes and applications à Lille, 12/2/2021, S. Coste.
 Invited talk at MAP5, March 2020, S. Coste.
 Invited talk at Spectra, Algorithms and Random Walks on Random Networks, January 2020, CIRM, S. Coste.
 Talk at Ulm universität, February 2020, S. Coste.
 Short talk at Discussion meeting on Stochastic Analysis, Geometry, and Random Fields, Bangalore, January 2020, S. Coste.
 Invited talk at Federated Learning One World Seminar, online series, June 2020, (Statistical Preconditioning for Federated Learning), H. Hendrikx.
 Invited talk at EPFL, online seminar, October 2020, H. Hendrikx.
 Invited lecture at LINCS, Paris, on Beam Management in 5G, May 2020, S. S. Kalamkar.
 Seminar at GIPSA lab, May 2020, L. Massoulié.
 Talk at workshop on “Dynamics over networks: epidemics, opinions and information”, September 2020, L. Massoulié.
 Seminar at Georgia Tech, October 2020, L. Massoulié.
 talk on Covid19, at event for startups organized by ‘Challenges’ and ‘Sciences et Avenir’ newspapers, June 2020, L. Massoulié.
 Demiheure de science at Inria Paris, work on Covid19, November 2020, L. Massoulié.
 Keynote on Covid19 work at ‘France is AI’, November 2020, L. Massoulié.
 Presentation at COLT conference, Luca Ganassali (July 2020).
 Presentation at ICML, July 2020, and Neurips, December 2020, conferences, Hadrien Hendrikx.
 Invited talk at Polytechnique MontrealCommunauto workshop, July 2020, T. Popescu.
10.1.5 Leadership within the scientific community
A. Busic: colead (with E. Hyon, LIP 6) of the research group COSMOS (Stochastic optimization and control, modeling and simulation) of the GDRRO; http://
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 Licence: B. Błaszczyszyn (Cours) Théorie de l'information et du codage 24 heqTD, L3, ENS Paris.
 Licence: A. Busic (Cours) and S. Samain (TD) Structures et algorithmes aléatoires 60 heqTD, L3, ENS Paris.
 Licence: L. Massoulié (Cours) Social and Communication networks 60 heqTD, L3, l'X.
 Master: B. Błaszczyszyn (Cours) Modèles géométriques aléatoires 39heqTD, M2 Probabilités et Modèles Aléatoires, UPMC.
 Master: A. Busic (Cours) and L. Stephan (TD) Modèles et algorithmes de réseaux 60 heqTD, M1, ENS Paris.
 Master: A. Busic and L. Massoulié (Cours) Fondements de la modélisation des réseaux 7.5 heqTD, M2 MPRI.
 Master: M. Lelarge (Cours) Deep Learning Do it Yourself, M1, ENS Paris,
X, XHEC. https://
mlelarge. github. io/ dataflowrweb/  Master: L. Massoulié (Cours) Inference in large random graphs, M2 Université d'Orsay.
 Préparation à l'agrégation: S. Coste (Cours+TD) Cours de statistiques, agrégation de sciences sociales, ENS ParisSaclay.
 MPSI: S. Coste (Interrogations) maths.
10.2.2 Supervision
 PhD: Alexis Galland, Deep Learning on Graphs, since 2017, advised by M. Lelarge; defended in December 2020 http://
www. ; (In the Bibliography the dissertation is still missing due to the delay in the preparation of the manuscripts accepted by the doctoral school.)theses. fr/ s201830  PhD: Quentin Le Gall “Crowd networking : modélisation de la connectivité D2D” since October 2017; PhD CIFRE coadvised by B. Błaszczyszyn and E. Cali (Orange); defended in Octobre 2020; 23.
 PhD in progress: Antoine Brochard "Signal processing for point processes and statistical learning for telecommunications", since September 2018; PhD CIFRE coadvised by B. Błaszczyszyn and Georgios Paschos (Huawei).
 PhD in progress: Sébastien Samain, “Monte Carlo methods for performance evaluation and reinforcement learning”, since November 2016, advised by A. Busic.
 PhD in progress: Arnaud Cadas, “Dynamic matching models”, since October 2017, supervised by A. Busic.
 PhD in progress: Michel Davydov, since September 2019, F. Baccelli.
 PhD in progress: Luca Ganassali, since September 2019, supervised by L. Massoulié.
 PhD in progress: Hadrien Hendrikx, since 2019, supervised by L. Massoulié.
 PhD in progress: Sayeh Khaniha, since 2019, supervised by F. Baccelli.
 PhD in progress: Pierre Popineau, since 2019, supervised by F. Baccelli.
 PhD in progress: Bharath Roy, since 2019, supervised by F. Baccelli and B. Błaszczyszyn.
 PhD in progress: Ilia Shilov, since 2019, supervised by A. Busic.
 PhD in progress: Ludovic Stephan, since 2018 supervised by L. Massoulié.
 PhD in progress: Maxime Leiber, since 2020 CIFRE thesis with SAFRAN supervised by L. Massoulié.
 PhD in progress: Bastien Dubail, since 2020 comentored with Charles Bordenave (CNRS, Marseille).
 PhD in progress: Roman Gambelin, since 2020, supervised by B. Błaszczyszyn.
 Master 2: Roman Gambelin, Université Paris DauphinePSL; 48
 Master 2: Mathieu Even.
 Master 1: Teodora Popescu, Ecole Polytechnique.
 4th year at ENS : Mathieu Even supervised by L. Massoulié.
10.2.3 Juries
 F. Baccelli: member of PhD thesis committee of Mateo Sfragara, Leiden University, Oct. 20; member of PhD thesis committee of Patrick Lambein, Ecole Polytechnique, Dec. 20; HDR jury member of Anastasios Giovanidis, UPMC, Dec. 20.
 B. Błaszczyszyn: reviewer of HDR of Pawel Lorek, University of Wroclaw, Jun 2020; reviewer of HDR of Daniel Edward Clark, Université de Paris Saclay, October 2020.
 A. Busic: PhD jury member of Diego Kiedanski, Telecom Paris.
 C. Fricker: member of PhD thesis committee of Santi Duran, june 2020, Université de Toulouse.
 L. Massoulié: member of PhD thesis committee of Yann Issartel, Université de Paris Saclay.
10.3 Visit to international teams
 S. Coste: Ulm Universitat (one week, February 2020).
 B. Błaszczyszyn: Indian Statistical Institute (ISI), Bangalore (two weeks, January 2020).
11 Scientific production
11.1 Publications of the year
International journals
 1 article'Understanding and monitoring the evolution of the Covid19 epidemic from medical emergency calls: the example of the Paris area'.Comptes Rendus Mathématique3587November 2020, 843875
 2 article'Arbitrage with Power Factor Correction using Energy Storage'.IEEE Transactions on Power Systems3542020, 2693  2703
 3 article'Adaptive Matching for Expert Systems with Uncertain Task Types'.Operations Research685September 2020, 14031424
International peerreviewed conferences
 4 inproceedings'Bandwidth Allocation and Service Differentiation in D2D Wireless Networks'.IEEE INFOCOM 2020  IEEE Conference on Computer CommunicationsToronto / Virtual, CanadaJuly 2020, 21162125
 5 inproceedings 'Who started this rumor? Quantifying the natural differential privacy guarantees of gossip protocols'. DISC 2020  34th International Symposium on Distributed Computing Freiburg / Virtual, Germany Inria 2020
 6 inproceedings 'Efficient distributed solutions for sharing energy resources at local level: a cooperative game approach'. CDC 2020  59th IEEE Conference on Decision and Control Proceedings of the 59th IEEE Conference on Decision and Control Jeju Island / Virtual, South Korea December 2020
 7 inproceedings 'Coverage probability in wireless networks with determinantal scheduling'. WiOPT 2020  18th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks Volos / Virtual, Greece https://ieeexplore.ieee.org/document/9155329 June 2020
 8 inproceedings'Simultaneous Allocation and Control of Distributed Energy Resources via KullbackLeiblerQuadratic Optimal Control'.ACC 2020  American Control ConferenceProceedings of the 2020 American Control Conference (ACC)Denver / Virtual, United States2020, 514520
 9 inproceedings 'Explicit MeanSquare Error Bounds for MonteCarlo and Linear Stochastic Approximation'. AISTATS 2020: 23rd International Conference on Artificial Intelligence and Statistics Proceedings of the 23rdInternational Conference on Artificial Intelligence and Statistics (AISTATS) 2020, Palermo,Italy. PMLR: Volume 108. Palermo / Virtual, Italy 2020
 10 inproceedings'Zap QLearning for Optimal Stopping'.ACC 2020  American Control ConferenceProceedings of the 2020 American Control Conference (ACC)Denver / Virtual, United States2020, 39203925
 11 inproceedings 'Zap QLearning With Nonlinear Function Approximation'. NeurIPS 2020: Thirtyfourth Conference on Neural Information Processing Systems Proceedings of the 2020 Conference on Neural Information Processing Systems Vancouver / Virtual, Canada 2020
 12 inproceedings'A mean field analysis of a stochastic model for reservation in carsharing systems'.MAMA  ACM SIGMETRICS 2020 Workshop on MAthematical performance Modeling and Analysis482Boston / Virtual, United StatesACMNovember 2020, 1820
 13 inproceedings 'From tree matching to sparse graph alignment'. Conference on Learning Theory (COLT) 2020 Graz, Austria February 2020
 14 inproceedings'Energy Storage Optimization for Grid Reliability'.eEnergy '20: The Eleventh ACM International Conference on Future Energy SystemsProceedings of The Eleventh ACM International Conference on Future Energy SystemsMelbourne / Virtual, Australia2020, 516522
 15 inproceedings 'Sizing and Profitability of Energy Storage for Prosumers in Madeira, Portugal'. 2020 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) Proceedings of the 2020 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) Washington DC, United States February 2020
 16 inproceedings 'DualFree Stochastic Decentralized Optimization with Variance Reduction'. NeurIPS 2020  34th Conference on Neural Information Processing Systems Advances in Neural Information Processing Systems Proceedings Vancouver / Virtual, Canada 2020
 17 inproceedings 'Statistically Preconditioned Accelerated Gradient Method for Distributed Optimization'. ICML 2020  Thirtyseventh International Conference on Machine Learning Proceedings of Machine Learning Research Vienna / Virtual, Austria 2020
 18 inproceedings 'Beam Management in 5G: A Stochastic Geometry Analysis'. IEEE Globecom Proceedings IEEE Globecom Taipei, Taiwan December 2020
 19 inproceedings 'Relayassisted DevicetoDevice Networks: Connectivity and Uberization Opportunities'. WCNC 2020  IEEE Wireless Communications and Networking Conference Seoul / Virtual, South Korea June 2020
 20 inproceedings'Energy Packet Networks with Finite Capacity Energy Queues'.VALUETOOLS '20: 13th EAI International Conference on Performance Evaluation Methodologies and ToolsProceedings of the 13th EAI International Conference on Performance Evaluation Methodologies and ToolsTsukuba / Virtual, Japan2020, 142149
Scientific books
 21 book 'Random Measures, Point Processes, and Stochastic Geometry'. January 2020
Scientific book chapters
 22 inbook'Conditioned Text Generation with Transfer for ClosedDomain Dialogue Systems'.International Conference on Statistical Language and Speech ProcessingSeptember 2020, 2334
Doctoral dissertations and habilitation theses
 23 thesis 'Crowdnetworking : modelling DevicetoDevice connectivity on street systems using percolation theory, and economic consequences'. Université Paris sciences et lettres October 2020
Reports & preprints
 24 misc 'Probabilistic and meanfield model of COVID19 epidemics with user mobility and contact tracing'. September 2020
 25 report 'Initiative face au virus Observations sur la mobilité pendant l'épidémie de Covid19'. Université PSL May 2020
 26 misc 'ReplicaMeanField Limits of FragmentationInteractionAggregation Processes'. May 2020
 27 misc 'On Point Processes Defined by Angular Conditions on Delaunay Neighbors in the PoissonVoronoi Tessellation'. January 2021
 30 misc 'Particle gradient descent model for point process generation'. October 2020
 31 misc 'Optimal stationary markings'. January 2020
 32 misc 'Optimal Control of Dynamic Bipartite Matching Models'. September 2020
 33 misc 'Flexibility can hurt dynamic matching system performance'. September 2020
 34 misc 'KullbackLeiblerQuadratic Optimal Control'. 2020
 35 misc 'Control oriented modeling of TCLs'. September 2020
 36 misc 'A simpler spectral approach for clustering in directed networks'. February 2021
 37 misc 'Concentration of NonIsotropic Random Tensors with Applications to Learning and Empirical Risk Minimization'. February 2021
 38 misc 'Spectral alignment of correlated Gaussian random matrices'. September 2020
 39 misc 'Sharp threshold for alignment of graph databases with Gaussian weights'. February 2021
 40 misc 'Randomised Geographic Caching and its Applications in Wireless Networks'. September 2020
 41 misc 'Storage Optimal Control under Net Metering Policies'. February 2020
 42 misc 'Asynchrony and Acceleration in Gossip Algorithms'. February 2021
 43 misc 'Characterizing the Energy TradeOffs of EndtoEnd Vehicular Communications using an Hyperfractal Urban Modelling'. December 2020
 44 misc 'Privacy Impact on Generalized Nash Equilibrium in PeertoPeer Electricity Market'. January 2021
 45 misc 'RiskAverse Equilibrium Analysis and Computation'. April 2020
 46 misc 'Nonbacktracking spectra of weighted inhomogeneous random graphs'. February 2021
Other scientific publications
 47 misc 'Nash equilibrium structure of Cox process Hotelling games'. August 2020
 48 thesis 'A stochastic geometry characterization of PitmanYor processes'. Université Paris Dauphine  PSL September 2020
11.2 Other
Patents
 49 patent 'Using loads with discrete finite states of power to provide ancillary services for a power grid'. June 2020
11.3 Cited publications
 50 mastersthesis'Une propriété caractéristique des processus de PoissonDirichlet'.MA ThesisLPMA  Laboratoire de Probabilités et Modèles AléatoiresSeptember 2015, 37
 51 article'Electric load model synthesis by diffusion approximation of a highorder hybridstate stochastic system'.IEEE Transactions on Automatic Control3091985, 854860