Kidney exchanges are organized markets where patients swap willing but incompatible donors. In the last decade, kidney exchanges grew from small and regional to large and national---and soon, international. This growth results in more lives saved, but exacerbates the empirical hardness of the $\mathcal{NP}$-complete problem of optimally matching patients to donors. State-of-the-art matching engines use integer programming techniques to clear fielded kidney exchanges, but these methods must be tailored to specific models and objective functions, and may fail to scale to larger exchanges. In this paper, we observe that if the kidney exchange compatibility graph can be encoded by a constant number of patient and donor attributes, the clearing problem is solvable in polynomial time. We give necessary and sufficient conditions for losslessly shrinking the representation of an arbitrary compatibility graph. Then, using real compatibility graphs from the UNOS nationwide kidney exchange, we show how many attributes are needed to encode real compatibility graphs. The experiments show that, indeed, small numbers of attributes suffice.

We introduce an Embarrassingly Parallel Search (EPS) method for solving constraint problems in parallel, and we show that this method matches or even outperforms state-of-the-art algorithms on a number of problems using various computing infrastructures. EPS is a simple method in which a master decomposes the problem into many disjoint subproblems which are then solved independently by workers. Our approach has three advantages: it is an efficient method; it involves almost no communication or synchronization between workers; and its implementation is made easy because the master and the workers rely on an underlying constraint solver, but does not require to modify it. This paper describes the method, and its applications to various constraint problems (satisfaction, enumeration, optimization). We show that our method can be adapted to different underlying solvers (Gecode, Choco2, OR-tools) on different computing infrastructures (multi-core, data centers, cloud computing). The experiments cover unsatisfiable, enumeration and optimization problems, but do not cover first solution search because it makes the results hard to analyze. The same variability can be observed for optimization problems, but at a lesser extent because the optimality proof is required. EPS offers good average performance, and matches or outperforms other available parallel implementations of Gecode as well as some solvers portfolios. Moreover, we perform an in-depth analysis of the various factors that make this approach efficient as well as the anomalies that can occur. Last, we show that the decomposition is a key component for efficiency and load balancing.

In this paper we extend the classical notion of strong and weak backdoor sets for SAT and CSP by allowing that different instantiations of the backdoor variables result in instances that belong to different base classes; the union of the base classes forms a heterogeneous base class. Backdoor sets to heterogeneous base classes can be much smaller than backdoor sets to homogeneous ones, hence they are much more desirable but possibly harder to find. We draw a detailed complexity landscape for the problem of detecting strong and weak backdoor sets into heterogeneous base classes for SAT and CSP.

In this work we consider adversarial contextual bandits with risk constraints. At each round, nature prepares a context, a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and then receives the corresponding cost and risk associated with the pulled arm. In addition to minimizing the cumulative cost, the learner also needs to satisfy long-term risk constraints -- the average of the cumulative risk from all pulled arms should not be larger than a pre-defined threshold. To address this problem, we first study the full information setting where in each round the learner receives an adversarial convex loss and a convex constraint. We develop a meta algorithm leveraging online mirror descent for the full information setting and extend it to contextual bandit with risk constraints setting using expert advice. Our algorithms can achieve near-optimal regret in terms of minimizing the total cost, while successfully maintaining a sublinear growth of cumulative risk constraint violation.

Answer set programming (ASP) has emerged as an approach to declarative problem solving based on the stable model semantics for logic programs. The basic idea is to represent a computational problem by a logic program, formulating constraints in terms of rules, such that its answer sets correspond to problem solutions. To this end, ASP combines an expressive language for high-level modeling with powerful low-level reasoning capacities, provided by off-the-shelf tools. Compact problem representations take advantage of genuine modeling features of ASP, including (first-order) variables, negation by default, and recursion. In this article, we demonstrate the ASP methodology on two example scenarios, illustrating basic as well as advanced modeling and solving concepts. We also discuss mechanisms to represent and implement extended kinds of preferences and optimization. An overview of further available extensions concludes the article.

This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional projection based online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the projection operation. In this paper, we relax the functional constraints by allowing them to be violated at each round but still requiring them to be satisfied in the long term. This type of relaxed online convex optimization (with long term constraints) was first considered in Mahdavi et al. (2012). That prior work proposes an algorithm to achieve $O(\sqrt{T})$ regret and $O(T^{3/4})$ constraint violations for general problems and another algorithm to achieve an $O(T^{2/3})$ bound for both regret and constraint violations when the constraint set can be described by a finite number of linear constraints. A recent extension in Jenatton et al. (2016) can achieve $O(T^{\max\{\beta,1-\beta\}})$ regret and $O(T^{1-\beta/2})$ constraint violations where $\beta\in (0,1)$. The current paper proposes a new simple algorithm that yields improved performance in comparison to prior works. The new algorithm achieves an $O(\sqrt{T})$ regret bound with finite constraint violations.

We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with decoupled constraints, in which subsets of the objective and constraint functions may be evaluated independently. For example, when the objective is evaluated on a CPU and the constraints are evaluated independently on a GPU. These problems require an acquisition function that can be separated into the contributions of the individual function evaluations. We develop one such acquisition function and call it Predictive Entropy Search with Constraints (PESC). PESC is an approximation to the expected information gain criterion and it compares favorably to alternative approaches based on improvement in several synthetic and real-world problems. In addition to this, we consider problems with a mix of functions that are fast and slow to evaluate. These problems require balancing the amount of time spent in the meta-computation of PESC and in the actual evaluation of the target objective. We take a bounded rationality approach and develop partial update for PESC which trades off accuracy against speed. We then propose a method for adaptively switching between the partial and full updates for PESC. This allows us to interpolate between versions of PESC that are efficient in terms of function evaluations and those that are efficient in terms of wall-clock time. Overall, we demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.

This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to significant errors about the system's causal structure if not properly taken into account. In this paper, we first consider the search for the system timescale causal structures that correspond to a given measurement timescale structure. We provide a constraint satisfaction procedure whose computational performance is several orders of magnitude better than previous approaches. We then consider finite-sample data as input, and propose the first constraint optimization approach for recovering the system timescale causal structure. This algorithm optimally recovers from possible conflicts due to statistical errors. More generally, these advances allow for a robust and non-parametric estimation of system timescale causal structures from subsampled time series data.

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods to get algorithms for calculating partition functions in these families. These techniques give new, non-trivial approximation guarantees for the partition function beyond the regime of correlation decay. They also generalize some classical results from statistical physics about the Curie-Weiss ferromagnetic Ising model, as well as provide a partition function counterpart of classical results about max-cut on dense graphs \cite{arora1995polynomial}. With this, we connect techniques from two apparently disparate research areas -- optimization and counting/partition function approximations. (i.e. \#-P type of problems). Furthermore, we design to the best of our knowledge the first provable, convex variational methods. Though in the literature there are a host of convex versions of variational methods \cite{wainwright2003tree, wainwright2005new, heskes2006convexity, meshi2009convexifying}, they come with no guarantees (apart from some extremely special cases, like e.g. the graph has a single cycle \cite{weiss2000correctness}). We consider dense and low threshold rank graphs, and interestingly, the reason our approach works on these types of graphs is because local correlations propagate to global correlations -- completely the opposite of algorithms based on correlation decay. In the process we design novel entropy approximations based on the low-order moments of a distribution. Our proof techniques are very simple and generic, and likely to be applicable to many other settings other than Ising models.