## Section: Scientific Foundations

### Crossing the Chasm

Countless studies have underlined the fact that many a good scientific and algorithmic advances fail to make it outside research labs. Such failures are often blamed on the Knowledge Barrier, the entry ticket people have to pay in order to master new techniques because of their many options and parameters, because of their flexibility and versatility. Parameter adjustment is at the core of most if not all TAO applicative studies in Numerical Engineering [Oops!] .

Considerable efforts are deployed to anticipate this usage barrier when designing algorithms or devices. One approach aims at building “plug-and-play” variants, allowing naive users to benefit from 90% of the algorithm potentialities. It is generally deemed however that some form of adaptation to the problem at hand is required to deliver robust results; in most application domains, the search for “the” killer algorithm has been acknowledged to be hopeless. Alternatively, one might want to build a meta-layer topping a set of algorithms, selecting the best algorithm to use depending on the problem at hand (Meta- Learning project, ESPRIT project 26.357 (2002-2004).)the bottleneck along this line has been identified as the description of the problems at the meta-level.

The fourth research direction of TAO will investigate two approaches for Crossing the Chasm, respectively based on online and offline hyperparameter tuning/learning.

The online tuning approach includes both self-adaptation heuristics (dating back to the 90's
(See
[Oops!] and other chapters of
*Parameter Setting in Evolutionary Algorithms* , Springer Verlag 2007.)), and the original use of multi-armed bandit algorithms which has been discussed in section
3.3 . While self-adaptation and specifically Covariance-Matrix Adaptation ES is acknowledged a major breakthrough in
continuous evolutionary optimization
(Hansen, N. and A. Ostermeier (2001). Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation, 9(2), pp. 159-195), TAO has a world-wide theoretical and applicative expertise on CMA-ES. Several
extensions of self-adaptive evolution will be investigated, aiming at bridging the gap between convex optimisation and continuous evolutionary computation: the convergence of the CMA-ES algorithm, along the lines of that of the SA-ES algorithm
(Anne Auger. Convergence results for (1,
)-SA-ES using the theory of
-irreducible markov chains.
*Theoretical Computer Science* , 334(1-3):35–69, 2005.); a separable version of CMA-ES (can separability be detected – and taken advantage of?); the handling of different types of constraint (at the moment, only bound constraints can be set on the variables); an efficient
version of multi-objective CMA-ES (as the existing version does not really use multi-objective information, and poorly samples the Pareto Front). Surrogate versions of CMA-ES (and other stochastic optimization algorithms) will also be considered, in particular within the Digiteo PhD grant
“Simplified models in Numerical Engineering”, that has been allocated to be co-supervised by M. Sebag and J.-M. Martinez, SF2MS, CEA (2007-2010).

The second approach, concerned with offline learning, resumes the Phase-Transition studies pioneered by TAO in collaboration with L. Saitta and A. Giordana (Univ. del Piemonte Orientale), (see section
6.1 ). Based on the appropriate order parameters, the phase transition framework allows for building the “competence
map” describing the average algorithm behaviour. Clearly, such competence maps make it easy to achieve meta-learning
(**J. Maloberti and M. Sebag**. Fast theta-subsumption with constraint satisfaction algorithms.
*Machine Learning Journal* , 55:137–174, 2004.)and decide for each problem which algorithm/setting will be the most appropriate on average. Indeed similar approaches have been developed for CSP solvers
(F. Hutter, Y. Hamadi, H. Hoos, and K. L. Brown. Performance prediction and automated tuning of randomized and parametric algorithms. In CP'06, pp 213–228, 2006.), exploiting a range of indicators developed over the years as order
parameters.

The fundamental bottleneck, i.e. designing relevant order parameters, has been tackled empirically so far. Further studies will use the statistical physics tools
(M.Mézard, G.Parisi, and M.A. Virasoro,
*Spin glass theory and beyond* , World Scientific, 1987.)to construct phase diagrams (physics equivalent of competence maps). Recent results at the frontier of statistical physics and computer science
(J. S. Yedidia, W. T. Freeman, and Y. Weiss,
*Generalized belief propagation* , Advances in Neural Information Processing Systems (NIPS 2001).)have bridged together optimization (free energy optima, K-SAT solutions,...) and learning with message passing algorithms (belief propagation, affinity propagation
(B.J. Frey and D. Dueck. Clustering by Passing Messages Between Data Points Science (2007) Vol. 315. pp. 972 - 976.)). In addition
(M. Mézard and R. Zecchina, The Random K-satisfiability problem : from an analytic solution to an efficient algorithm, 2002
*Phys. Rev. Letters E* **66**)an algorithmic hierarchy (warning propagation, survey propagation) appears to be in correspondence to the hierarchy provided by the order parameter of the mean-field theory. These results are synthesized in a phase diagram; the purpose of new adaptive heuristics will be to
infer the position of the instance problem in the phase diagram.

This direction of research subsumes several on-going projects, specifically Evotest and
*Microsoft-TAO project* where the goal is to produce off-the-shelf algorithms and to enforce technology transfer. In contrast, many previous
[Oops!] or current projects (e.g. GENNETEC) have enforced technology transfer ... manually.