We are developing a general framework for using learned Bayesian models for decision-theoretic control of search and reasoningalgorithms. We illustrate the approach on the specific task of controlling both general and domain-specific solvers on a hard class of structured constraint satisfaction problems. A successful strategyfor reducing the high (and even infinite) variance in running time typically exhibited by backtracking search algorithms is to cut off and restart the search if a solution is not found within a certainamount of time. Previous work on restart strategies have employed fixed cut off values. We show how to create a dynamic cut off strategy by learning a Bayesian model that predicts the ultimate length of a trial based on observing the early behavior of the search algorithm. Furthermore, we describe the general conditions under which a dynamic restart strategy can outperform the theoretically optimal fixed strategy.

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems are frequently intractable, but there are several important set CSPs that are known to be polynomial-time tractable. We introduce a large class of set CSPs that can be solved in quadratic time. Our class, which we call EI, contains all previously known tractable set CSPs, but also some new ones that are of crucial importance for example in description logics. The class of EI set constraints has an elegant universal-algebraic characterization, which we use to show that every set constraint language that properly contains all EI set constraints already has a finite sublanguage with an NP-hard constraint satisfaction problem.

While finding the exact solution for the MAP inference problem is intractable for many real-world tasks, MAP LP relaxations have been shown to be very effective in practice. However, the most efficient methods that perform block coordinate descent can get stuck in sub-optimal points as they are not globally convergent. In this work we propose to augment these algorithms with an $\epsilon$-descent approach and present a method to efficiently optimize for a descent direction in the subdifferential using a margin-based extension of the Fenchel-Young duality theorem. Furthermore, the presented approach provides a methodology to construct a primal optimal solution from its dual optimal counterpart. We demonstrate the efficiency of the presented approach on spin glass models and protein interactions problems and show that our approach outperforms state-of-the-art solvers.

Inference on high-order graphical models has become increasingly important in recent years. We consider energies with simple 'sparse' high-order potentials. Previous work in this area uses either specialized message-passing or transforms each high-order potential to the pairwise case. We take a fundamentally different approach, transforming the entire original problem into a comparatively small instance of a submodular vertex-cover problem. These vertex-cover instances can then be attacked by standard pairwise methods, where they run much faster (4--15 times) and are often more effective than on the original problem. We evaluate our approach on synthetic data, and we show that our algorithm can be useful in a fast hierarchical clustering and model estimation framework.

We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve local subproblems and a controller node to combine these local solutions into a global update. The key characteristic of AD3 is that each local subproblem has a quadratic regularizer, leading to a faster consensus than subgradient-based dual decomposition, both theoretically and in practice. We provide closed-form solutions for these AD3 subproblems for binary pairwise factors and factors imposing first-order logic constraints. For arbitrary factors (large or combinatorial), we introduce an active set method which requires only an oracle for computing a local MAP configuration, making AD3 applicable to a wide range of problems. Experiments on synthetic and realworld problems show that AD3 compares favorably with the state-of-the-art.

We propose a probabilistic model for the parallel execution of Las Vegas algorithms, i.e., randomized algorithms whose runtime might vary from one execution to another, even with the same input. This model aims at predicting the parallel performances (i.e., speedups) by analysis the runtime distribution of the sequential runs of the algorithm. Then, we study in practice the case of a particular Las Vegas algorithm for combinatorial optimization, on three classical problems, and compare with an actual parallel implementation up to 256 cores. We show that the prediction can be quite accurate, matching the actual speedups very well up to 100 parallel cores and then with a deviation of about 20% up to 256 cores.

The ability to make decisions and to assess potential courses of action is a corner-stone of many AI applications, and usually this requires explicit information about the decision-maker s preferences. IN many applications, preference elicitation IS a serious bottleneck.The USER either does NOT have the time, the knowledge, OR the expert support required TO specify complex multi - attribute utility functions. IN such cases, a method that IS based ON intuitive, yet expressive, preference statements IS required. IN this paper we suggest the USE OF TCP - nets, an enhancement OF CP - nets, AS a tool FOR representing, AND reasoning about qualitative preference statements.We present AND motivate this framework, define its semantics, AND show how it can be used TO perform constrained optimization.

Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication applications. It proposes a constraint satisfaction approach using a combinatorial lower bound, a pruning component that removes infeasible and suboptimal edges, as well as a search strategy exploring the most uncertain edges first. The resulting algorithm is shown to produce very dramatic improvements over the mathematical programming approach of Yaman et al. and to enlarge considerably the class of problems amenable to effective solutions

Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree decomposition method, which is the most powerful decomposition method on graphs, and the (generalized) hypertree decomposition method, which is its natural counterpart on arbitrary hypergraphs. The paper analyzes this framework, by focusing in particular on "minimal" tree projections, that is, on tree projections without useless redundancies. First, it is shown that minimal tree projections enjoy a number of properties that are usually required for normal form decompositions in various structural decomposition methods. In particular, they enjoy the same kind of connection properties as (minimal) tree decompositions of graphs, with the result being tight in the light of the negative answer that is provided to the open question about whether they enjoy a slightly stronger notion of connection property, defined to speed-up the computation of hypertree decompositions. Second, it is shown that tree projections admit a natural game-theoretic characterization in terms of the Captain and Robber game. In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones. As a special case, the Captain and Robber game can be used to characterize the generalized hypertree decomposition method, where such a game-theoretic characterization was missing and asked for. Besides their theoretical interest, these results have immediate algorithmic applications both for the general setting and for structural decomposition methods that can be recast in terms of tree projections.

Soft Constraint Logic Programming is a natural and flexible declarative programming formalism, which allows to model and solve real-life problems involving constraints of different types. In this paper, after providing a slightly more general and elegant presentation of the framework, we show how we can apply it to the e-mobility problem of coordinating electric vehicles in order to overcome both energetic and temporal constraints and so to reduce their running cost. In particular, we focus on the journey optimization sub-problem, considering sequences of trips from a user's appointment to another one. Solutions provide the best alternatives in terms of time and energy consumption, including route sequences and possible charging events.