In this abstract, we present our study of exploring the SAT search space via random-sampling, with the goal of improving Conflict Directed Clause Learning (CDCL) SAT solvers. Our proposed CDCL SAT solving algorithm expSAT uses a novel branching heuristic expVSIDS. It combines the standard VSIDS scores with heuristic scores derived from exploration. Experiments with application benchmarks from recent SAT competitions demonstrate the potential of the expSAT approach for improving CDCL SAT solvers.

The state of the art in bidirectional search has changed significantly a very short time period; we now can answer questions about unidirectional and bidirectional search that until very recently we were unable to answer. This paper is designed to provide an accessible overview of the recent research in bidirectional search in the context of the broader efforts over the last 50 years. We give particular attention to new theoretical results and the algorithms they inspire for optimal and near-optimal node expansions when finding a shortest path.

We present for the first time an exhaustive enumeration of Williamson matrices of even order n < 65. The search method relies on the novel SAT+CAS paradigm of coupling SAT solvers with computer algebra systems so as to take advantage of the advances made in both the field of satisfiability checking and the field of symbolic computation. Additionally, we use a programmatic SAT solver which allows conflict clauses to be learned programmatically, through a piece of code specifically tailored to the domain area. Prior to our work, Williamson matrices had only been enumerated for odd orders n < 60, so our work increases the bounds that Williamson matrices have been enumerated up to and provides the first enumeration of Williamson matrices of even order. Our results show that Williamson matrices of even order tend to be much more abundant than those of odd orders. In particular, Williamson matrices exist for every even order n < 65 but do not exist in orders 35, 47, 53, and 59.

Marginal MAP is a key task in Bayesian inference and decision-making. It is known to be very difficult in general, particularly because the evaluation of each MAP assignment requires solving an internal summation problem. In this paper, we propose a best-first search algorithm that provides anytime upper bounds for marginal MAP in graphical models. It folds the computation of external maximization and internal summation into an AND/OR tree search framework, and solves them simultaneously using a unified best-first search algorithm. The algorithm avoids some unnecessary computation of summation sub-problems associated with MAP assignments, and thus yields significant time savings. Furthermore, our algorithm is able to operate within limited memory. Empirical evaluation on three challenging benchmarks demonstrates that our unified best-first search algorithm using pre-compiled variational heuristics often provides tighter anytime upper bounds compared to those state-of-the-art baselines.

Learning an optimal policy from a multi-modal reward function is a challenging problem in reinforcement learning (RL). Hierarchical RL (HRL) tackles this problem by learning a hierarchicalpolicy, where multiple option policies are in charge of different strategies corresponding to modes of a reward function and a gating policy selects the best option for a given context. Although HRL has been demonstrated to be promising, current state-of-the-art methods cannot still perform well in complex real-world problems due to the difficulty of identifying modes of the reward function. In this paper, we propose a novel method called hierarchical policy search via return-weighted density estimation (HPSDE), which can efficiently identify the modes through density estimation with return-weighted importance sampling. Our proposed method finds option policies corresponding to the modes of the return function and automatically determines the number and the location of option policies, which significantly reduces the burden of hyper-parameters tuning. Through experiments, we demonstrate that the proposed HPSDE successfully learns option policies corresponding to modes of the return function and that it can be successfully applied to a motion planning problem of a redundant robotic manipulator.

We introduce a novel model-agnostic system that explains the behavior of complex models with high-precision rules called anchors, representing local, "sufficient" conditions for predictions. We propose an algorithm to efficiently compute these explanations for any black-box model with high-probability guarantees. We demonstrate the flexibility of anchors by explaining a myriad of different models for different domains and tasks. In a user study, we show that anchors enable users to predict how a model would behave on unseen instances with less effort and higher precision, as compared to existing linear explanations or no explanations.

We address the problem of approximating a matrix by the linear combination of a column sparse matrix and a low rank matrix. Two variants of a heuristic search algorithm are described. The first produces an optimal solution but may be slow, as these problems are believed to be NP-hard. The second is much faster, but only guarantees a suboptimal solution. The quality of the approximation and the optimality criterion can be specified in terms of unitarily invariant norms.

The minimum weighted vertex cover (MWVC) problem is a well known combinatorial optimization problem with important applications. This paper introduces a novel local search algorithm called NuMWVC for MWVC based on three ideas. First, four reduction rules are introduced during the initial construction phase. Second, the configuration checking with aspiration is proposed to reduce cycling problem. Moreover, a self-adaptive vertex removing strategy is proposed to save time.

Many real-life problems require optimizing functions with expensive evaluations. Bayesian Optimization (BO) and Search-based Optimization (SO) are two broad families of algorithms that try to find the global optima of a function with the goal of minimizing the number of function evaluations. A large body of existing work deals with the single-fidelity setting, where function evaluations are very expensive but accurate. However, in many applications, we have access to multiple-fidelity functions that vary in their cost and accuracy of evaluation. In this paper, we propose a novel approach called Multi-fidelity Hybrid (MF-Hybrid) that combines the best attributes of both BO and SO methods to discover the global optima of a black-box function with minimal cost. Our experiments on multiple benchmark functions show that the MF-Hybrid algorithm outperforms existing single-fidelity and multi-fidelity optimization algorithms.

We present a new sampling scheme for approximating hard to compute queries over graphical models, such as computing the partition function. The scheme builds upon exact algorithms that traverse a weighted directed state-space graph representing a global function over a graphical model (e.g., probability distribution). With the aid of an abstraction function and randomization, the state space can be compacted (trimmed) to facilitate tractable computation, yielding a Monte Carlo estimate that is unbiased. We present the general idea and analyze its properties analytically and empirically.