## Section: New Results

### Uncertainty and provenance of data

We have a strong focus on the uncertainty and provenance in databases. See [20] for a high-level introduction to the area.

In [15], we investigate the use of knowledge compilation, i.e., obtaining compact circuit-based representations of functions, for (Boolean) provenance. Some width parameters of the circuit, such as bounded treewidth or pathwidth, can be leveraged to convert the circuit to structured classes, e.g., deterministic structured NNFs (d-SDNNFs) or OBDDs. In [14], we investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.

In previous work [39], [40]. we have shown that the only restrictions to database instances that make probabilistic query evaluation tractable for a large class of queries is that of having a small treewidth. In [28], [32], we provide the first large-scale experimental study of treewidth and tree decompositions of real-world database instances (25 datasets from 8 different domains, with sizes ranging from a few thousand to a few million vertices). The goal is to determine which data, if any, has reasonably low treewidth. We also show that, even when treewidth is high, using partial tree decompositions can result in data structures that can assist algorithms.

To conclude on provenance management, in [23], [24], after investigating the complexity of satisfiability and query answering for attributed DL-LiteR ontologies, we propose a new semantics, based on provenance semirings, for integrating provenance information with query answering. Finally, we establish complexity results for satisfiability and query answering under this semantics.

We also consider **other notions of incompleteness**, such as in
[13], where we study the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful fragment of SQL, namely positive relational algebra with aggregates, whose bag semantics we extend to the partially ordered setting. Our semantics leads to the study of two main computational problems: the possibility and certainty of query answers. We show that these problems are respectively NP-complete and coNP-complete, but identify tractable cases depending on the query operators or input partial orders.

Finally, we also consider uncertainty through another angle, that of
learning in a dynamic environment, using techniques from
**reinforcement learning** and the **multi-armed bandit**
field.

In [19], we tackle the problem of *influence
maximization*: finding influential users, or nodes, in a graph so as to maximize the spread of information. We study a highly generic version of influence maximization, one of optimizing influence campaigns by sequentially selecting “spread seeds” from a set of influencers, a small subset of the node population, under the hypothesis that, in a given campaign, previously activated nodes remain persistently active. We introduce an estimator on the influencers’ remaining potential – the expected number of nodes that can still be reached from a given influencer – and justify its strength to rapidly estimate the desired value, relying on real data gathered from Twitter. We then describe a novel algorithm, GT-UCB, relying on probabilistic upper confidence bounds on the remaining potential.

In [21], we propose a Bayesian information-geometric approach to the exploration-exploitation trade-off in stochastic multi-armed bandits. The uncertainty on reward generation and belief is represented using the manifold of joint distributions of rewards and beliefs. Accumulated information is summarised by the barycentre of joint distributions, the pseudobelief-reward. While the pseudobelief-reward facilitates information accumulation through exploration, another mechanism is needed to increase exploitation by gradually focusing on higher rewards, the pseudobelief-focal-reward. Our resulting algorithm, BelMan, alternates between projection of the pseudobelief-focal-reward onto belief-reward distributions to choose the arm to play, and projection of the updated belief-reward distributions onto the pseudobelief-focal-reward.

In [29], we consider another form of bandits,
*linear bandits*, in which the available actions correspond to
arbitrary context vectors whose associated rewards follow a
non-stationary
linear regression model. In this setting, the unknown regression
parameter is al-
lowed to vary in time. To address this problem, we propose D-LinUCB, a
novel
optimistic algorithm based on discounted linear regression, where
exponential
weights are used to smoothly forget the past.