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We present a novel hybrid algorithm for training Deep Neural Networks that combines the state-of-the-art Gradient Descent (GD) method with a Mixed Integer Linear Programming (MILP) solver, outperforming GD and variants in terms of accuracy, as well as resource and data efficiency for both regression and classification tasks. Our GD+Solver hybrid algorithm, called GDSolver, works as follows: given a DNN D as input, GDSolver invokes GD to partially train D until it gets stuck in a local minima, at which point GDSolver invokes an MILP solver to exhaustively search a region of the loss landscape around the weight assignments of D’s final layer parameters with the goal of tunnelling through and escaping the local minima. The process is repeated until desired accuracy is achieved. In our experiments, we find that GDSolver not only scales well to additional data and very large model sizes, but also outperforms all other competing methods in terms of rates of convergence and data efficiency. For regression tasks, GDSolver produced models that, on average, had 31.5% lower MSE in 48% less time, and for classification tasks on MNIST and CIFAR10, GDSolver was able to achieve the highest accuracy over all competing methods, using only 50% of the training data that GD baselines required.

There is a well-known approach to cope with NP-hard problems in practice: reduce the given problem to SAT or MAXSAT and run a SAT or a MaxSAT solver. This method is very efficient since SAT/MaxSAT solvers are extremely well-studied, as well as the complexity of these problems. At AAAI 2011, Li et al. proposed an alternative to this approach and suggested the Partial Minimum Satisfiability problem as a reduction target for NP-hard problems. They developed the MinSatz solver and showed that reducing to Partial Minimum Satisfiability and using MinSatz is in some cases more efficient than reductions to SAT or MaxSAT. Since then many results connected to the Partial Minimum Satisfiability problem were published. However, to the best of our knowledge, the worst-case complexity of Partial Minimum Satisfiability has not been studied up until now. Our goal is to fix the issue and show a O*((2-ɛ)^m) lower bound under the SETH assumption (here m is the total number of clauses), as well as several other lower bounds and parameterized exact algorithms with better-than-trivial running time.

Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving models via proof complexity techniques. Our results show that almost all of the QCDCL models are exponentially incomparable with respect to proof size (and hence solver running time), pointing towards different orthogonal ways how to practically implement QCDCL.

Application domains of Bayesian optimization include optimizing black-box functions or very complex functions. The functions we are interested in describe complex real-world systems applied in industrial settings. Even though they do have explicit representations, standard optimization techniques fail to provide validated solutions and correctness guarantees for them. In this paper we present a combination of Bayesian optimization and SMT-based constraint solving to achieve safe and stable solutions with optimality guarantees.

The problem of exact weighted sampling of solutions of Boolean formulas has applications in Bayesian inference, testing, and verification. The state-of-the-art approach to sampling involves carefully decomposing the input formula and compiling a data structure called d-DNNF in the process. Recent work in the closely connected field of model counting, however, has shown that smartly composing different subformulas using dynamic programming and Algebraic Decision Diagrams (ADDs) can outperform d-DNNF-style approaches on many benchmarks. In this work, we present a modular algorithm called DPSampler that extends such dynamic-programming techniques to the problem of exact weighted sampling. DPSampler operates in three phases. First, an execution plan in the form of a project-join tree is computed using tree decompositions. Second, the plan is used to compile the input formula into a succinct tree-of-ADDs representation. Third, this tree is traversed to generate a random sample. This decoupling of planning, compilation and sampling phases enables usage of specialized libraries for each purpose in a black-box fashion. Further, our novel ADD-sampling algorithm avoids the need for expensive dynamic memory allocation required in previous work. Extensive experiments over diverse sets of benchmarks show DPSampler is more scalable and versatile than existing approaches.

Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in 2^O(n*log n) time, but single-exponential running times 2^O(n) are currently far out of reach. In this paper we consider single-exponential algorithms via a multivariate analysis consisting of a fine-grained parameter n (e.g., the number of variables) and a coarse-grained parameter k expected to be relatively small. We introduce the classes FPE and XE of problems solvable in f(k)*2^O(n), respectively f(k)^n, time, and prove several fundamental properties of these classes. We proceed by studying temporal reasoning problems and (1) show that the partially ordered time problem of effective width k is solvable in 16^{kn} time and is thus included in XE, and (2) that the network consistency problem for Allen's interval algebra with no interval overlapping with more than k others is solvable in (2nk)^{2k}*2^n time and is included in FPE. Our multivariate approach is in no way limited to these to specific problems and may be a generally useful approach for obtaining single-exponential algorithms.

We consider nonconvex optimization problem with constraint that is a product of simplices. A commonly used algorithm in solving this type of problem is the Multiplicative Weights Update (MWU), an algorithm that is widely used in game theory, machine learning and multi agent systems. Despite it has been known that MWU avoids saddle points, there is a question that remains unaddressed: ``Is there an accelerated version of MWU that avoids saddle points provably?'' In this paper we provide a positive answer to above question. We provide an accelerated MWU based on Riemannian Accelerated Gradient Descent, and prove that the Riemannian Accelerated Gradient Descent, thus the accelerated MWU, avoid saddle points.

Large Neighbourhood Search (LNS) is an algorithmic framework for optimization problems that can yield good performance in many domains. In this paper, we present a method for applying LNS to improve anytime maximum satisfiability (MaxSAT) solving by introducing a neighbourhood selection policy that shows good empirical performance. We show that our LNS solver can often improve the suboptimal solutions produced by other anytime MaxSAT solvers. When starting with a suboptimal solution of reasonable quality, our approach often finds a better solution than the original anytime solver can achieve. We demonstrate that implementing our LNS solver on top of three different state-of-the-art anytime solvers improves the anytime performance of all three solvers within the standard time limit used in the incomplete tracks of the annual MaxSAT Evaluation.

Online bipartite matching has attracted much attention due to its importance in various applications such as advertising, ride-sharing, and crowdsourcing. In most online matching problems, the rewards and node arrival probabilities are given in advance and are not controllable. However, many real-world matching services require them to be controllable and the decision-maker faces a non-trivial problem of optimizing them. In this study, we formulate a new optimization problem, Online Matching with Controllable Rewards and Arrival probabilities (OM-CRA), to simultaneously determine not only the matching strategy but also the rewards and arrival probabilities. Even though our problem is more complex than the existing ones, we propose a fast 1/2-approximation algorithm for OM-CRA. The proposed approach transforms OM-CRA to a saddle-point problem by approximating the objective function, and then solves it by the Primal-Dual Hybrid Gradient (PDHG) method with acceleration through the use of the problem structure. In simulations on real data from crowdsourcing and ride-sharing platforms, we show that the proposed algorithm can find solutions with high total rewards in practical times.

Statistical inference is a powerful technique in various applications. Although many statistical inference tools are available, answering inference queries involving complex quantification structures remains challenging. Recently, solvers for Stochastic Boolean Satisfiability (SSAT), a powerful formalism allowing concise encodings of PSPACE decision problems under uncertainty, are under active development and applied in more and more applications. In this work, we exploit SSAT solvers for the inference of Probabilistic Graphical Models (PGMs), an essential representation for probabilistic reasoning. Specifically, we develop encoding methods to systematically convert PGM inference problems into SSAT formulas for effective solving. Experimental results demonstrate that, by using our encoding, SSAT-based solving can complement existing PGM tools, especially in answering complex queries.

Tensor completion aims at estimating missing values from an incomplete observation, playing a fundamental role for many applications. This work proposes a novel low-rank tensor completion model, in which the inherent low-rank prior and external degradation accordant data-driven prior are simultaneously utilized. Specifically, the tensor nuclear norm (TNN) is adopted to characterize the overall low-dimensionality of the tensor data. Meanwhile, an implicit regularizer is formulated and its related subproblem is solved via a deep convolutional neural network (CNN) under the plug-and-play framework. This CNN, pretrained for the inpainting task on a mass of natural images, is expected to express the external data-driven prior and this plugged inpainter is consistent with the original degradation process. Then, an efficient alternating direction method of multipliers (ADMM) is designed to solve the proposed optimization model. Extensive experiments are conducted on different types of tensor imaging data with the comparison with state-of-the-art methods, illustrating the effectiveness and the remarkable generalization ability of our method.

Modern software systems rely on mining insights from business sensitive data stored in public clouds. A data breach usually incurs significant (monetary) loss for a commercial organization. Conceptually, cloud security heavily relies on Identity Access Management (IAM) policies that IT admins need to properly configure and periodically update. Security negligence and human errors often lead to misconfiguring IAM policies which may open a backdoor for attackers. To address these challenges, first, we develop a novel framework that encodes generating optimal IAM policies using constraint programming (CP). We identify reducing dormant permissions of cloud users as an optimality criterion, which intuitively implies minimizing unnecessary datastore access permissions. Second, to make IAM policies interpretable, we use graph representation learning applied to historical access patterns of users to augment our CP model with similarity constraints: similar users should be grouped together and share common IAM policies. Third, we describe multiple attack models and show that our optimized IAM policies significantly reduce the impact of security attacks using real data from 8 commercial organizations, and synthetic instances.

In constraint satisfaction problems, the variable ordering heuristic takes a central place by selecting the variables to branch on during backtrack search. As many hand-crafted branching heuristics have been proposed in the literature, a key issue is to identify, from a pool of candidate heuristics, which one is the best for solving a given constraint satisfaction task. Based on the observation that modern constraint solvers are using restart sequences, the best heuristic identification problem can be cast in the context of multi-armed bandits as a non-stochastic best arm identification problem. Namely, during each run of some given restart sequence, the bandit algorithm selects a branching heuristic and receives a reward for this heuristic before proceeding to the next run. The goal is to identify the best heuristic using few runs, and without any stochastic assumption about the constraint solver. In this study, we propose an adaptive variant of Successive Halving that exploits Luby's universal restart sequence. We analyze the convergence of this bandit algorithm in the non-stochastic setting, and we demonstrate its empirical effectiveness on various constraint satisfaction benchmarks.

All Solution SAT (AllSAT) is a variant of Propositional Satisfiability, which aims to find all satisfying assignments for a given formula. AllSAT has significant applications in different domains, such as software testing, data mining, and network verification. In this paper, observing that the lack of component analysis may result in more work for algorithms with non-chronological backtracking, we propose a DPLL-based algorithm for solving AllSAT problem, named AllSATCC, which takes advantage of component analysis to reduce work repetition caused by non-chronological backtracking. The experimental results show that our algorithm outperforms the state-of-the-art algorithms on most instances.

Program annotations under the form of function pre/postconditions are crucial for many software engineering and program verification applications. Unfortunately, such annotations are rarely available and must be retrofit by hand. In this paper, we explore how Constraint Acquisition (CA), a learning framework from Constraint Programming, can be leveraged to automatically infer program preconditions in a black-box manner, from input-output observations. We propose PreCA, the first ever framework based on active constraint acquisition dedicated to infer memory-related preconditions. PreCA overpasses prior techniques based on program analysis and formal methods, offering well-identified guarantees and returning more precise results in practice.

Constraint-based pattern mining is at the core of numerous data mining tasks. Unfortunately, thresholds which are involved in these constraints cannot be easily chosen. This paper investigates a Multi-objective Optimization approach where several (often conflicting) functions need to be optimized at the same time. We introduce a new model for efficiently mining Pareto optimal patterns with constraint programming. Our model exploits condensed pattern representations to reduce the mining effort. To this end, we design a new global constraint for ensuring the closeness of patterns over a set of measures. We show how our approach can be applied to derive high-quality non redundant association rules without the use of thresholds whose added-value is studied on both UCI datasets and case study related to the analysis of genes expression data integrating multiple external genes annotations.

In the maximum satisfiability problem (MaxSAT), given a CNF formula with m clauses and n variables, we are asked to find an assignment of the variables to satisfy the maximum number of clauses. Chen and Kanj showed that this problem can be solved in O*(1.3248^m) time (DAM 2004) and the running time bound was improved to O*(1.2989^m) by Xu et al. (IJCAI 2019). In this paper, we further improve the result to O*(1.2886^m). By using some new reduction and branching techniques we can avoid several bottlenecks in previous algorithms and get the improvement on this important problem.

MD4 is a prominent cryptographic hash function proposed in 1990. The full version consists of 48 steps and produces a hash of size 128 bits given a message of an arbitrary finite size. In 2007, its truncated 39-step version was inverted via reducing to SAT and applying a CDCL solver. Since that time, several attempts have been made but the 40-step version still remains unbroken. In this study, 40-, 41-, 42-, and 43-step versions of MD4 are successfully inverted. The problems are reduced to SAT and solved via the Cube-and-Conquer approach. Two algorithms are proposed for this purpose. The first one generates inversion problems for MD4 by adding special constraints. The second one is aimed at finding a proper threshold for the cubing phase of Cube-and-Conquer. While the first algorithm is focused on inverting MD4 and similar cryptographic hash functions, the second one is not area specific and so is applicable to a variety of classes of hard SAT instances.

We address Partial MaxSAT (PMS) and Weighted PMS (WPMS), two practical generalizations of the MaxSAT problem, and propose a local search algorithm called BandMaxSAT, that applies a multi-armed bandit to guide the search direction, for these problems. The bandit in our method is associated with all the soft clauses in the input (W)PMS instance. Each arm corresponds to a soft clause. The bandit model can help BandMaxSAT to select a good direction to escape from local optima by selecting a soft clause to be satisfied in the current step, that is, selecting an arm to be pulled. We further propose an initialization method for (W)PMS that prioritizes both unit and binary clauses when producing the initial solutions. Extensive experiments demonstrate that BandMaxSAT significantly outperforms the state-of-the-art (W)PMS local search algorithm SATLike3.0. Specifically, the number of instances in which BandMaxSAT obtains better results is about twice that obtained by SATLike3.0. We further combine BandMaxSAT with the complete solver TT-Open-WBO-Inc. The resulting solver BandMaxSAT-c also outperforms some of the best state-of-the-art complete (W)PMS solvers, including SATLike-c, Loandra and TT-Open-WBO-Inc.

We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which we search for the maximum common (connected) induced subgraph, the first operator of LSM maintains a score for the branching node using the short-term reward of each vertex of the first graph and the long-term reward of each vertex pair of the two graphs. In this way, the BnB process learns to reduce the search tree size significantly and boost the algorithm performance. The second operator of LUM further improves the performance by simultaneously matching the leaf vertices connected to the current matched vertices, and allows the algorithm to match multiple vertex pairs without affecting the optimality of solution. We incorporate the two operators into the state-of-the-art BnB algorithm McSplit, and denote the resulting algorithm as McSplit+LL. Experiments show that McSplit+LL outperforms McSplit+RL, a more recent variant of McSplit using reinforcement learning that is superior than McSplit.