Total: 22
We introduce a state space search method that identifies dead-end states, analyzes the reasons for failure, and learns to avoid similar mistakes in the future. Our work is placed in classical planning. The key technique are critical-path heuristics hC, relative to a set C of conjunctions. These recognize a dead-end state s, returning hC(s) = infty, if s has no solution even when allowing to break up conjunctive subgoals into the elements of C. Our key idea is to learn C during search. Starting from a simple initial C, we augment search to identify unrecognized dead-ends s, where hC(s) < infinity. We design methods analyzing the situation at such s, adding new conjunctions into C to obtain hC(s) = infty, thus learning to recognize s as well as similar dead-ends search may encounter in the future. We furthermore learn clauses phi where s' not satisfying phi implies hC(s') = infty, to avoid the prohibitive overhead of computing hC on every search state. Arranging these techniques in a depth-first search, we obtain an algorithm approaching the elegance of clause learning in SAT, learning to refute search subtrees. Our experiments show that this can be quite powerful. On problems where dead-ends abound, the learning reliably reduces the search space by several orders of magnitude.
Rumor blocking is a serious problem in large-scale social networks. Malicious rumors could cause chaos in society and hence need to be blocked as soon as possible after being detected. In this paper, we propose a model of dynamic rumor influence minimization with user experience (DRIMUX). Our goal is to minimize the influence of the rumor (i.e., the number of users that have accepted and sent the rumor) by blocking a certain subset of nodes. A dynamic Ising propagation model considering both the global popularity and individual attraction of the rumor is presented based on realistic scenario. In addition, different from existing problems of influence minimization, we take into account the constraint of user experience utility. Specifically, each node is assigned a tolerance time threshold. If the blocking time of each user exceeds that threshold, the utility of the network will decrease. Under this constraint, we then formulate the problem as a network inference problem with survival theory, and propose solutions based on maximum likelihood principle. Experiments are implemented based on large-scale real world networks and validate the effectiveness of our method.
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective consists of a smooth part and a nonsmooth but simple part. We propose the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the convergence rate O(1/K2), compared with O(1/K) by the traditional PALM. In order to further reduce the per-iteration complexity and handle the multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting (Fast PL-ADMM-PS) method. It also partially improves the rate related to the smooth part of the objective function. Experimental results on both synthesized and real world data demonstrate that our fast methods significantly improve the previous PALM and ADMM
Hash Distributed A* (HDA*) is an efficient parallel best first algorithm that asynchronously distributes work among the processes using a global hash function. Although Zobrist hashing, the standard hash function used by HDA*, achieves good load balance for many domains, it incurs significant communication overhead since it requires many node transfers among threads. We propose Abstract Zobrist hashing, a new work distribution method for parallel search which reduces node transfers and mitigates communication overhead by using feature projection functions. We evaluate Abstract Zobrist hashing for multicore HDA*, and show that it significantly outperforms previous work distribution methods.
Submodular optimization, particularly under cardinality or cost constraints, has received considerable attention, stemming from its breadth of application, ranging from sensor placement to targeted marketing. However, the constraints faced in many real domains are more complex. We investigate an important and very general class of problems of maximizing a submodular function subject to general cost constraints, especially focusing on costs coming from route planning. Canoni- cal problems that motivate our framework include mobile robotic sensing, and door-to-door marketing. We propose a generalized cost-benefit (GCB) greedy al- gorithm for our problem, and prove bi-criterion approximation guarantees under significantly weaker assumptions than those in related literature. Experimental evaluation on realistic mobile sensing and door-to-door marketing problems, as well as using simulated networks, show that our algorithm achieves significantly higher utility than state-of-the-art alternatives, and has either lower or competitive running time.
The Maximum Weight Clique problem (MWCP) is an important generalization of the Maximum Clique problem with wide applications. This paper introduces two heuristics and develops two local search algorithms for MWCP. Firstly, we propose a heuristic called strong configuration checking (SCC), which is a new variant of a recent powerful strategy called configuration checking (CC) for reducing cycling in local search. Based on the SCC strategy, we develop a local search algorithm named LSCC. Moreover, to improve the performance on massive graphs, we apply a low-complexity heuristic called Best from Multiple Selection (BMS) to select the swapping vertex pair quickly and effectively. The BMS heuristic is used to improve LSCC, resulting in the LSCC+BMS algorithm. Experiments show that the proposed algorithms outperform the state-of-the-art local search algorithm MN/TS and its improved version MN/TS+BMS on the standard benchmarks namely DIMACS and BHOSLIB, as well as a wide range of real world massive graphs.
Being one of the most effective methods, Alternating Direction Method (ADM) has been extensively studied in numerical analysis for solving linearly constrained convex program. However, there are few studies focusing on the convergence property of ADM under nonconvex framework though it has already achieved well-performance on applying to various nonconvex tasks. In this paper, a linearized algorithm with penalization is proposed on the basis of ADM for solving nonconvex and nonsmooth optimization. We start from analyzing the convergence property for the classical constrained problem with two variables and then establish a similar result for multi-block case. To demonstrate the effectiveness of our proposed algorithm, experiments with synthetic and real-world data have been conducted on specific applications in signal and image processing.
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of convergence by automatically deciding the constraint penalty needed for parameter consensus in each iteration. In addition, we also propose an extension of the method that adaptively determines the maximum number of iterations to update the penalty. We show that this approach effectively leads to an adaptive, dynamic network topology underlying the distributed optimization. The utility of the new penalty update schemes is demonstrated on both synthetic and real data, including an instance of the probabilistic matrix factorization task known as the structure from motion problem.
Nowadays, brick-and-mortar stores are finding it extremely difficult to retain their customers due to the ever increasing competition from the online stores. One of the key reasons for this is the lack of personalized shopping experience offered by the brick-and-mortar stores. This work considers the problem of persona based shopping recommendation for such stores to maximize the value for money of the shoppers. For this problem, it proposes a non-polynomial time-complexity optimal dynamic program and a polynomial time-complexity non-optimal heuristic, for making top-k recommendations by taking into account shopper persona and her time and budget constraints. In our empirical evaluations with a mix of real-world data and simulated data, the performance of the heuristic in terms of the persona based recommendations (quantified by similarity scores and items recommended) closely matched (differed by only 8% each with) that of the dynamic program and at the same time heuristic ran at least twice faster compared to the dynamic program.
Despite recent improvements in search techniques for cost-optimal classical planning, the exponential growth of the size of the search frontier in A* is unavoidable. We investigate tiebreaking strategies for A*, experimentally analyzing the performance of standard tiebreaking strategies that break ties according to the heuristic value of the nodes. We find that tiebreaking has a significant impact on search algorithm performance when there are zero-cost operators that induce large plateau regions in the search space. We develop a new framework for tiebreaking based on a depth metric which measures distance from the entrance to the plateau, and propose a new, randomized strategy which significantly outperforms standard strategies on domains with zero-cost actions.
The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.
The use of the Monte Carlo playouts as an evaluation function has proved to be a viable, general technique for searching intractable game spaces. This facilitate the use of statistical techniques like Monte Carlo Tree Search (MCTS), but is also known to require significant processing overhead. We seek to improve the quality of information extracted from the Monte Carlo playout in three ways. Firstly, by nesting the evaluation function inside another evaluation function; secondly, by measuring and utilising the depth of the playout; and thirdly, by incorporating pruning strategies that eliminate unnecessary searches and avoid traps. Our experimental data, obtained on a variety of two-player games from past General Game Playing (GGP) competitions and others, demonstrate the usefulness of these techniques in a Nested Player when pitted against a standard, optimised UCT player.
We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between the directional derivatives of the objective function and its surrogate function vanishes when the number of iterations approaches infinity, which is a very weak condition. So our method can use a surrogate function that directly approximates the non-smooth objective function. In comparison, all the existing MM methods construct the surrogate function by approximating the smooth component of the objective function. We apply our relaxed MM methods to the robust matrix factorization (RMF) problem with different regularizations, where our locally majorant algorithm shows advantages over the state-of-the-art approaches for RMF. This is the first algorithm for RMF ensuring, without extra assumptions, that any limit point of the iterates is a stationary point.
Recent work has raised the challenge of efficient automated troubleshooting in domains where repairing a set of components in a single repair action is cheaper than repairing each of them separately. This corresponds to cases where there is a non-negligible overhead to initiating a repair action and to testing the system after a repair action. In this work we propose several algorithms for choosing which batch of components to repair, so as to minimize the overall repair costs. Experimentally, we show the benefit of these algorithms over repairing components one at a time.
Pathfinding is a common task across many domains and platforms, whether in games, robotics, or road maps. Given the breadth of domains, there are also a wide variety of representations used for pathfinding, and there are many techniques which have been shown to improve performance. In the last few years, the state-of-the-art in grid-based pathfinding has been significantly improved with domain-specific techniques such as Jump Point Search (JPS), Subgoal Graphs, and Compressed Path Databases. In this paper we look at a specific implementation of the general idea of Geometric Containers, showing that, while it is effective on grid maps, when combined with JPS+ it provides state-of-the-art performance.
We investigate the problem of repacking stations in the FCC's upcoming, multi-billion-dollar "incentive auction". Early efforts to solve this problem considered mixed-integer programming formulations, which we show are unable to reliably solve realistic, national-scale problem instances. We describe the result of a multi-year investigation of alternatives: a solver, SATFC, that has been adopted by the FCC for use in the incentive auction. SATFC is based on a SAT encoding paired with a wide range of techniques: constraint graph decomposition; novel caching mechanisms that allow for reuse of partial solutions from related, solved problems; algorithm configuration; algorithm portfolios; and the marriage of local-search and complete solver strategies. We show that our approach solves virtually all of a set of problems derived from auction simulations within the short time budget required in practice.
Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range of applications, only few tractable fragments of ILP are known, probably the most prominent of which is based on the notion of total unimodularity. Using entirely different techniques, we identify new tractable fragments of ILP by studying structural parameterizations of the constraint matrix within the framework of parameterized complexity. In particular, we show that ILP is fixed-parameter tractable when parameterized by the treedepth of the constraint matrix and the maximum absolute value of any coefficient occurring in the ILP instance. Together with matching hardness results for the more general parameter treewidth, we draw a detailed complexity landscape of ILP w.r.t. decompositional parameters defined on the constraint matrix.
Finding diverse solutions has become important in many combinatorial search domains, including Automated Planning, Path Planning and Constraint Programming. Much of the work in these directions has however focussed on coming up with appropriate diversity metrics and compiling those metrics in to the solvers/planners. Most approaches use linear-time greedy algorithms for exploring the state space of solution combinations for generating a diverse set of solutions, limiting not only their completeness but also their effectiveness within a time bound. In this paper, we take a combinatorial search perspective on generating diverse solutions. We present a generic bi-level optimization framework for finding cost-sensitive diverse solutions. We propose complete methods under this framework, which guarantee finding a set of cost sensitive diverse solutions satisficing the given criteria whenever there exists such a set. We identify various aspects that affect the performance of these exhaustive algorithms and propose techniques to improve them. Experimental results show the efficacy of the proposed framework compared to an existing greedy approach.
The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP.Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the MIP instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.
While suboptimal best-first search algorithms like Greedy Best-First Search are frequently used when building automated planning systems, their greedy nature can make them susceptible to being easily misled by flawed heuristics. This weakness has motivated the development of best-first search variants like epsilon-greedy node selection, type-based exploration, and diverse best-first search, which all use random exploration to mitigate the impact of heuristic error. In this paper, we provide a theoretical justification for this increased robustness by formally analyzing how these algorithms behave on infinite graphs. In particular, we show that when using these approaches on any infinite graph, the probability of not finding a solution can be made arbitrarily small given enough time. This result is shown to hold for a class of algorithms that includes the three mentioned above, regardless of how misleading the heuristic is.
Identifying a small number of features that can represent the data is a known problem that comes up in areas such as machine learning, knowledge representation, data mining, and numerical linear algebra. Computing an optimal solution is believed to be NP-hard, and there is extensive work on approximation algorithms. Classic approaches exploit the algebraic structure of the underlying matrix, while more recent approaches use randomization. An entirely different approach that uses the A* heuristic search algorithm to find an optimal solution was recently proposed. Not surprisingly it is limited to effectively selecting only a small number of features. We propose a similar approach related to the Weighted A* algorithm. This gives algorithms that are not guaranteed to find an optimal solution but run much faster than the A* approach, enabling effective selection of many features from large datasets. We demonstrate experimentally that these new algorithms are more accurate than the current state-of-the-art while still being practical. Furthermore, they come with an adjustable guarantee on how different their error may be from the smallest possible (optimal) error. Their accuracy can always be increased at the expense of a longer running time.
Random k-CNF formulas at the anticipated k-SAT phase-transition point are prototypical hard k-SAT instances. We develop a stochastic local search algorithm and study it both theoretically and through a large-scale experimental study. The algorithm comes as a result of a systematic study that contrasts rates at which a certain measure concentration phenomenon occurs. This study yields a new stochastic rule for local search. A strong point of our contribution is the conceptual simplicity of our algorithm. More importantly, the empirical results overwhelmingly indicate that our algorithm outperforms the state-of-the-art. This includes a number of winners and medalist solvers from the recent SAT Competitions.