Recent real-time heuristic search algorithms have demonstrated outstanding performance in video-game pathfinding. However, their applications have been thus far limited to that domain. We proceed with the aim of facilitating wider applications of real-time search by fostering a greater understanding of the performance of recent algorithms. We first introduce eight algorithm-independent complexity measures for search spaces and correlate their values with algorithm performance. The complexity measures are statistically shown to be significant predictors of algorithm performance across a set of commercial video-game maps. We then extend this analysis to a wider variety of search spaces in the first application of database-driven real-time search to domains outside of video-game pathfinding. In doing so, we gain insight into algorithm performance and possible enhancement as well as into search space complexity.
Previous work has been conducted to predict the performance of simpler real-time heuristic search algorithms. Citing important applications in planning (e.g., as part of the Heuristic Search Planner @cite_14 and the Fast-Forward Planner @cite_15 ), L o pez sought to model the efficiency of heuristic hill-climbing by modelling the algorithm as a Markov process @cite_33 . Using several sizes of the sliding tile puzzle, the model could reasonably predict the likelihood that a hill-climbing agent reaches a target state in a number of moves equal to the initial heuristic value. L o pez stated that this model is useful not only as a predictor of simple real-time search performance, but as a gauge of heuristic accuracy.
@cite_15 @cite_14 @cite_33
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The purpose of this paper is twofold: on one hand, modelling the hill-climbing heuristic search algorithm as a stochastic process serves for deriving interesting properties about its expected performance; on the other hand, the probability that a hill-climbing search algorithm ever fails when approaching the target node (i.e., it does not find a descendant with a heuristic value strictly lower than the current one) can be considered as a pesimistic measure of the accuracy of the heuristic function guiding it. Thus, in this work, it is suggested to model heuristic hill-climbing search algorithms with Markov chains in order to fulfill these goals. Empirical results obtained in various sizes of the (n,m)-Puzzle domain prove that this model leads to very accurate predictions. Real-time heuristic search algorithms are used for creating agents that rely on local information and move in a bounded amount of time making them an excellent candidate for video games as planning time can be controlled. Path finding on video game maps has become the de facto standard for evaluating real-time heuristic search algorithms. Over the years researchers have worked to identify areas where these algorithms perform poorly in an attempt to mitigate their weaknesses. Recent work illustrates the benefits of tailoring algorithms for a given problem as performance is heavily dependent on the search space. In order to determine which algorithm to select for solving the search problems on a map the developer would have to run all the algorithms in consideration to obtain the correct choice. Our work extends the previous algorithm selection approach to use a deep learning classifier to select the algorithm to use on new maps without having to evaluate the algorithms on the map. To do so we select a portfolio of algorithms and train a classifier to predict which portfolio member to use on a unseen new map. Our empirical results show that selecting algorithms dynamically can outperform the single best algorithm from the portfolio on new maps, as well provide the lower bound for potential improvements to motivate further work on this approach. In the recent AIPS98 Planning Competition, the hsp planner, based on a forward state search and a domain-independent heuristic, showed that heuristic search planners can be competitive with state of the art Graphplan and Satisfiability planners. hsp solved more problems than the other planners but it often took more time or produced longer plans. The main bottleneck in hsp is the computation of the heuristic for every new state. This computation may take up to 85 of the processing time. In this paper, we present a solution to this problem that uses a simple change in the direction of the search. The new planner, that we call hspr, is based on the same ideas and heuristic as hsp , but searches backward from the goal rather than forward from the initial state. This allows hspr to compute the heuristic estimates only once. As a result, hspr can produce better plans, often in less time. For example, hspr solves each of the 30 logistics problems from Kautz and Selman in less than 3 seconds. This is two orders of magnitude faster than blackbox. At the same time, in almost all cases, the plans are substantially smaller. hspr is also more robust than hsp as it visits a larger number of states, makes deterministic decisions, and relies on a single adjustable parameter than can be fixed for most domains. hspr, however, is not better than hsp accross all domains and in particular, in the blocks world, hspr fails on some large instances that hsp can solve. We discuss also the relation between hspr and Graphplan, and argue that Graphplan can also be understood as a heuristic search planner with a precise heuristic function and search algorithm. In the AIPS98 Planning Contest, the HSP planner showed that heuristic search planners can be competitive with state-of-the-art Graphplan and SAT planners. Heuristic search planners like HSP transform planning problems into problems of heuristic search by automatically extracting heuristics from Strips encodings. They differ from specialized problem solvers such as those developed for the 24-Puzzle and Rubik’s Cube in that they use a general declarative language for stating problems and a general mechanism for extracting heuristics from these representations. In this paper, we study a family of heuristic search planners that are based on a simple and general heuristic that assumes that action preconditions are independent. The heuristic is then used in the context of best-first and hill-climbing search algorithms, and is tested over a large collection of domains. We then consider variations and extensions such as reversing the direction of the search for speeding node evaluation, and extracting information about propositional invariants for avoiding dead-ends. We analyze the resulting planners, evaluate their performance, and explain when they do best. We also compare the performance of these planners with two state-of-the-art planners, and show that the simplest planner based on a pure best-first search yields the most solid performance over a large set of problems. We also discuss the strengths and limitations of this approach, establish a correspondence between heuristic search planning and Graphplan, and briefly survey recent ideas that can reduce the current gap in performance between general heuristic search planners and specialized solvers.  2001 Elsevier Science B.V. All rights reserved. We present a deterministic (1+o(1))-approximation O(n1 2+o(1)+D1+o(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here n is the number of nodes in the network and D is its (hop) diameter. This is the first non-trivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+o(1))-approximation O(n1 2D1 4+D)-time algorithm of Nanongkai [STOC 2014] by a factor of as large as n1 8, and (ii) the O(є−1logє−1)-approximation factor of Lenzen and Patt-Shamir’s O(n1 2+є+D)-time algorithm [STOC 2013] within the same running time. Our running time matches the known time lower bound of Ω(n1 2 logn + D) [Das STOC 2011] modulo some lower-order terms, thus essentially settling the status of this problem which was raised at least a decade ago [Elkin SIGACT News 2004]. It also implies a (2+o(1))-approximation O(n1 2+o(1)+D1+o(1))-time algorithm for approximating a network’s weighted diameter which almost matches the lower bound by [PODC 2012]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic, construction of an (no(1), o(1))-hop set of size O(n1+o(1)). We combine these techniques with many distributed algorithmic techniques, some of which from problems that are not directly related to shortest paths, e.g. ruling sets [ STOC 1987], source detection [Lenzen, Peleg PODC 2013], and partial distance estimation [Lenzen, Patt-Shamir PODC 2015]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+o(1))-approximation O(no(1))-time algorithm on congested cliques, and (ii) a (1+o(1))-approximation O(no(1)logW)-pass O(n1+o(1)logW)-space streaming algorithm, when edge weights are in 1, 2, …, W . The first result answers an open problem in [Nanongkai, STOC 2014]. The second result partially answers an open problem raised by McGregor in 2006 [ sublinear.info , Problem 14]. We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence controlled agents must react quickly to user commands and to other agents. actions. On the downside, real-time search algorithms employ learning methods that frequently lead to poor solution quality and cause the agent to appear irrational by re-visiting the same problem states repeatedly. The situation changed recently with a new algorithm, D LRTA*, which attempted to eliminate learning by automatically selecting subgoals. D LRTA* is well poised for video games, except it has a complex and memory-demanding pre-computation phase during which it builds a database of subgoals. In this paper, we propose a simpler and more memory-efficient way of pre-computering subgoals thereby eliminating the main obstacle to applying state-of-the-art real-time search methods in video games. The new algorithm solves a number of randomly chosen problems off-line, compresses the solutions into a series of subgoals and stores them in a database. When presented with a novel problem on-line, it queries the database for the most similar previously solved case and uses its subgoals to solve the problem. In the domain of pathfinding on four large video game maps, the new algorithm delivers solutions eight times better while using 57 times less memory and requiring 14 less pre-computation time. Evaluation of tracking algorithms in the absence of ground truth is a challenging problem. There exist a variety of approaches for this problem, ranging from formal model validation techniques to heuristics that look for mismatches between track properties and the observed data. However, few of these methods scale up to the task of visual tracking, where the models are usually nonlinear and complex and typically lie in a high-dimensional space. Further, scenarios that cause track failures and or poor tracking performance are also quite diverse for the visual tracking problem. In this paper, we propose an online performance evaluation strategy for tracking systems based on particle filters using a time-reversed Markov chain. The key intuition of our proposed methodology relies on the time-reversible nature of physical motion exhibited by most objects, which in turn should be possessed by a good tracker. In the presence of tracking failures due to occlusion, low SNR, or modeling errors, this reversible nature of the tracker is violated. We use this property for detection of track failures. To evaluate the performance of the tracker at time instant t, we use the posterior of the tracking algorithm to initialize a time-reversed Markov chain. We compute the posterior density of track parameters at the starting time t = 0 by filtering back in time to the initial time instant. The distance between the posterior density of the time-reversed chain (at t = 0) and the prior density used to initialize the tracking algorithm forms the decision statistic for evaluation. It is observed that when the data are generated by the underlying models, the decision statistic takes a low value. We provide a thorough experimental analysis of the evaluation methodology. Specifically, we demonstrate the effectiveness of our approach for tackling common challenges such as occlusion, pose, and illumination changes and provide the Receiver Operating Characteristic (ROC) curves. Finally, we also show the applicability of the core ideas of the paper to other tracking algorithms such as the Kanade-Lucas-Tomasi (KLT) feature tracker and the mean-shift tracker. Abstract Real-time heuristic search methods interleave planning and plan executions and plan only in the part of the domain around the current state of the agents. So far, real-time heuristic search methods have mostly been applied to deterministic planning tasks. In this article, we argue that real-time heuristic search methods can efficiently solve nondeterministic planning tasks. We introduce Min-Max Learning Real-Time A∗ (Min-Max LRTA∗), a real-time heuristic search method that generalizes Korf's LRTA∗ to nondeterministic domains, and apply it to robot-navigation tasks in mazes, where the robots know the maze but do not know their initial position and orientation (pose). These planning tasks can be modeled as planning tasks in nondeterministic domains whose states are sets of poses. We show that Min-Max LRTA∗ solves the robot-navigation tasks fast, converges quickly, and requires only a small amount of memory. We introduce an algorithm for tracking deformable objects from a sequence of point clouds. The proposed tracking algorithm is based on a probabilistic generative model that incorporates observations of the point cloud and the physical properties of the tracked object and its environment. We propose a modified expectation maximization algorithm to perform maximum a posteriori estimation to update the state estimate at each time step. Our modification makes it practical to perform the inference through calls to a physics simulation engine. This is significant because (i) it allows for the use of highly optimized physics simulation engines for the core computations of our tracking algorithm, and (ii) it makes it possible to naturally, and efficiently, account for physical constraints imposed by collisions, grasping actions, and material properties in the observation updates. Even in the presence of the relatively large occlusions that occur during manipulation tasks, our algorithm is able to robustly track a variety of types of deformable objects, including ones that are one-dimensional, such as ropes; two-dimensional, such as cloth; and three-dimensional, such as sponges. Our implementation can track these objects in real time. Real-time heuristic search methods are used by situated agents in applications that require the amount of planning per move to be independent of the problem size. Such agents plan only a few actions at a time in a local search space and avoid getting trapped in local minima by improving their heuristic function over time. We extend a wide class of real-time search algorithms with automatically-built state abstraction and prove completeness and convergence of the resulting family of algorithms. We then analyze the impact of abstraction in an extensive empirical study in real-time pathfinding. Abstraction is found to improve efficiency by providing better trading offs between planning time, learning speed and other negatively correlated performance measures. We analyze the behavior of hill-climbing algorithms for the minimum bisection problem on instances drawn from the “planted bisection” random graph model, G n,p,q , previously studied in [3, 4, 10, 11, 14, 9, 7]. This is one of the few problem distributions for which various popular heuristic methods, such as simulated annealing, have been proven to succeed. However, it has been open whether these sophisticated methods were necessary, or whether simpler heuristics would also work. Juels [14] made the first progress towards an answer by showing that simple hill-climbing does suffice for very wide separations between p and q. Here we give a more complete answer. A simple, polynomial-time, hill-climbing algorithm for this problem is given and shown to succeed in finding the planted bisection with high probability if p - q = O (n-½ln3n). For dense graphs, this matches the condition for optimality of the planted bisection to within a polylogarithmic factor. Furthermore, we show that a generic randomized hill-climbing algorithm succeeds in finding the planted bisection in polynomial time if p - q = O (n-¼ ln3 n), for any ∈ > 0. This algorithm, studied also by [14], is a degenerate case of both Metropolis and go-with-the-winners, and the range here properly includes those analyzed in [11, 9, 14]. So this result implies, extends, and unifies those from [11, 9, 14]. Thus, to get a provable distinction between simulated annealing and hill-climbing for natural problems will require considerable progress both on new positive results for SA and new negative results for hill-climbing methods. In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We nonasymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings. In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation as a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and re-configures it dynamically using a set of moves, which are mostly reversible Markov chain jumps. This computational framework integrates two popular inference approaches--generative (top-down) methods and discriminative (bottom-up) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottom-up tests filters. In our Markov chain algorithm design, the posterior probability, defined by the generative models, is the invariant (target) probability for the Markov chain, and the discriminative probabilities are used to construct proposal probabilities to drive the Markov chain. Intuitively, the bottom-up discriminative probabilities activate top-down generative models. In this paper, we focus on two types of visual patterns--generic visual patterns, such as texture and shading, and object patterns including human faces and text. These types of patterns compete and cooperate to explain the image and so image parsing unifies image segmentation, object detection, and recognition (if we use generic visual patterns only then image parsing will correspond to image segmentation (Tu and Zhu, 2002. IEEE Trans. PAMI, 24(5):657--673). We illustrate our algorithm on natural images of complex city scenes and show examples where image segmentation can be improved by allowing object specific knowledge to disambiguate low-level segmentation cues, and conversely where object detection can be improved by using generic visual patterns to explain away shadows and occlusions. In a seminal paper, Karp, Vazirani, and Vazirani show that a simple ranking algorithm achieves a competitive ratio of 1-1 e for the online bipartite matching problem in the standard adversarial model, where the ratio of 1-1 e is also shown to be optimal. Their result also implies that in the random arrivals model defined by Goel and Mehta, where the online nodes arrive in a random order, a simple greedy algorithm achieves a competitive ratio of 1-1 e. In this paper, we study the ranking algorithm in the random arrivals model, and show that it has a competitive ratio of at least 0.696, beating the 1-1 e ≈ 0.632 barrier in the adversarial model. Our result also extends to the i.i.d. distribution model of , removing the assumption that the distribution is known. Our analysis has two main steps. First, we exploit certain dominance and monotonicity properties of the ranking algorithm to derive a family of factor-revealing linear programs (LPs). In particular, by symmetry of the ranking algorithm in the random arrivals model, we have the monotonicity property on both sides of the bipartite graph, giving good "strength" to the LPs. Second, to obtain a good lower bound on the optimal values of all these LPs and hence on the competitive ratio of the algorithm, we introduce the technique of strongly factor-revealing LPs. In particular, we derive a family of modified LPs with similar strength such that the optimal value of any single one of these new LPs is a lower bound on the competitive ratio of the algorithm. This enables us to leverage the power of computer LP solvers to solve for large instances of the new LPs to establish bounds that would otherwise be difficult to attain by human analysis. Recent compilers offer a vast number of multilayered optimizations targeting different code segments of an application. Choosing among these optimizations can significantly impact the performance of the code being optimized. The selection of the right set of compiler optimizations for a particular code segment is a very hard problem, but finding the best ordering of these optimizations adds further complexity. Finding the best ordering represents a long standing problem in compilation research, named the phase-ordering problem. The traditional approach of constructing compiler heuristics to solve this problem simply cannot cope with the enormous complexity of choosing the right ordering of optimizations for every code segment in an application. This article proposes an automatic optimization framework we call MiCOMP, which Mi tigates the Com piler P hase-ordering problem. We perform phase ordering of the optimizations in LLVM’s highest optimization level using optimization sub-sequences and machine learning. The idea is to cluster the optimization passes of LLVM’s O3 setting into different clusters to predict the speedup of a complete sequence of all the optimization clusters instead of having to deal with the ordering of more than 60 different individual optimizations. The predictive model uses (1) dynamic features, (2) an encoded version of the compiler sequence, and (3) an exploration heuristic to tackle the problem. Experimental results using the LLVM compiler framework and the Cbench suite show the effectiveness of the proposed clustering and encoding techniques to application-based reordering of passes, while using a number of predictive models. We perform statistical analysis on the results and compare against (1) random iterative compilation, (2) standard optimization levels, and (3) two recent prediction approaches. We show that MiCOMP’s iterative compilation using its sub-sequences can reach an average performance speedup of 1.31 (up to 1.51). Additionally, we demonstrate that MiCOMP’s prediction model outperforms the -O1, -O2, and -O3 optimization levels within using just a few predictions and reduces the prediction error rate down to only 5 . Overall, it achieves 90 of the available speedup by exploring less than 0.001 of the optimization space. Sequential decision making problems, such as structured prediction, robotic control, and game playing, require a combination of planning policies and generalisation of those plans. In this paper, we present Expert Iteration (ExIt), a novel reinforcement learning algorithm which decomposes the problem into separate planning and generalisation tasks. Planning new policies is performed by tree search, while a deep neural network generalises those plans. Subsequently, tree search is improved by using the neural network policy to guide search, increasing the strength of new plans. In contrast, standard deep Reinforcement Learning algorithms rely on a neural network not only to generalise plans, but to discover them too. We show that ExIt outperforms REINFORCE for training a neural network to play the board game Hex, and our final tree search agent, trained tabula rasa, defeats MoHex1.0, the most recent Olympiad Champion player to be publicly released. We consider the problem of learning to act in partially observable, continuous-state-and-action worlds where we have abstract prior knowledge about the structure of the optimal policy in the form of a distribution over policies. Using ideas from planning-as-inference reductions and Bayesian unsupervised learning, we cast Markov Chain Monte Carlo as a stochastic, hill-climbing policy search algorithm. Importantly, this algorithm's search bias is directly tied to the prior and its MCMC proposal kernels, which means we can draw on the full Bayesian toolbox to express the search bias, including nonparametric priors and structured, recursive processes like grammars over action sequences. Furthermore, we can reason about uncertainty in the search bias itself by constructing a hierarchical prior and reasoning about latent variables that determine the abstract structure of the policy. This yields an adaptive search algorithm--our algorithm learns to learn a structured policy efficiently. We show how inference over the latent variables in these policy priors enables intra- and intertask transfer of abstract knowledge. We demonstrate the flexibility of this approach by learning meta search biases, by constructing a nonparametric finite state controller to model memory, by discovering motor primitives using a simple grammar over primitive actions, and by combining all three. Beck's early work [3] gave an efficient version of the Lovasz Local Lemma(LLL) with significant compromise in the parameters. Following several improvements [1,7,4,13], Moser [8], and Moser and Tardos [9] obtained asymptotically optimal results in terms of the maximal degree. For a fixed dependency graph G the exact criterion under which LLL applies is given by Shearer in [12]. For a dependency structure G, let LO(G) be the set of those probability assignments to the nodes of G for which the Lovasz Local Lemma holds. We show that: Both the sequential and parallel ersions of the Moser-Tardos algorithm are efficient up to the Shearer's bound, by giving a tighter analysis. We also prove that, whenever p ∈ LO(G) (1+e), the expected running times of the sequential and parallel versions are at most n e and O(1 e log n e), the later when e Recently sparse representation has been applied to visual tracker by modeling the target appearance using a sparse approximation over a template set, which leads to the so-called L1 trackers as it needs to solve an l 1 norm related minimization problem for many times. While these L1 trackers showed impressive tracking accuracies, they are very computationally demanding and the speed bottleneck is the solver to l 1 norm minimizations. This paper aims at developing an L1 tracker that not only runs in real time but also enjoys better robustness than other L1 trackers. In our proposed L1 tracker, a new l 1 norm related minimization model is proposed to improve the tracking accuracy by adding an l 1 norm regularization on the coefficients associated with the trivial templates. Moreover, based on the accelerated proximal gradient approach, a very fast numerical solver is developed to solve the resulting l 1 norm related minimization problem with guaranteed quadratic convergence. The great running time efficiency and tracking accuracy of the proposed tracker is validated with a comprehensive evaluation involving eight challenging sequences and five alternative state-of-the-art trackers.