We present a novel learning-based method for generating optimal motion plans for high-dimensional motion planning problems. In order to cope with the curse of dimensional- ity, our method proceeds in a fashion similar to block co- ordinate descent in finite-dimensional optimization: at each iteration, the motion is optimized over a lower dimensional subspace while leaving the path fixed along the other dimen- sions. Naive implementations of such an idea can produce vastly suboptimal results. In this work, we show how a prof- itable set of directions in which to perform this dimensional descent procedure can be learned efficiently. We provide suf- ficient conditions for global optimality of dimensional de- scent in this learned basis, based upon the low-dimensional structure of the planning cost function. We also show how this dimensional descent procedure can easily be used for problems that do not exhibit such structure with monotonic convergence. We illustrate the application of our method to high dimensional shape planning and arm trajectory planning problems.

Pathfinding in uniform-cost grid environments is a problem commonly found in application areas such as robotics and video games. The state-of-the-art is dominated by hierarchical pathfinding algorithms which are fast and have small memory overheads but usually return suboptimal paths. In this paper we present a novel search strategy, specific to grids, which is fast, optimal and requires no memory overhead. Our algorithm can be described as a macro operator which identifies and selectively expands only certain nodes in a grid map which we call jump points. Intermediate nodes on a path connecting two jump points are never expanded. We prove that this approach always computes optimal solutions and then undertake a thorough empirical analysis, comparing our method with related works from the literature. We find that searching with jump points can speed up A* by an order of magnitude and more and report significant improvement over the current state of the art.

We consider the problem of routing electric vehicles (EV) in the most energy-efficient way within a road network taking into account both their limited energy supply as well as their ability to recuperate energy. Employing a classical result by Johnson and an observation about Dijkstra under non-constant edge costs we obtain O(n log n +m) query time after a O(nm) preprocessing phase for any road network graph whose edge costs represent energy consumption or recuperation.If the energy recuperation is height induced in a very natural way,the preprocessing phase can even be omitted. We then adapt a technique for speeding-up (unconstrained) shortest path queries to our scenario to achieve a speed-up of another factor of around 20. Our results drastically improve upon the recent results in (Artmeier et al. 2010) and allow for route planning of EVs in an instant even on large networks.

Recently, there has been a significant interest in studying security games to provide tools for addressing resource allocation problems in security applications. Patrolling security games (PSGs) constitute a special class of security games wherein the resources are mobile. One of the most relevant open problems in security games is the design of scalable algorithms to tackle realistic scenarios. While the literature mainly focuses on heuristics and decomposition techniques (e.g., double oracle), in this paper we provide, to the best of our knowledge, the first study on the use of abstractions in security games (specifically for PSGs) to design scalable algorithms. We define some classes of abstractions and we provide parametric algorithms to automatically generate abstractions. We show that abstractions allow one to relax the constraint of patrolling strategies' Markovianity (customary in PSGs) and to solve large game instances. We additionally pose the problem to search for the optimal abstraction and we develop an anytime algorithm to find it.

The problem of multiagent patrol has gained considerable attention during the past decade, with the immediate applicability of the problem being one of its main sources of interest. In this paper we concentrate on frequency-based patrol, in which the agents' goal is to optimize a frequency criterion, namely, minimizing the time between visits to a set of interest points. We consider multiagent patrol in environments with complex environmental conditions that affect the cost of traveling from one point to another. For example, in marine environments, the travel time of ships depends on parameters such as wind, water currents, and waves. We demonstrate that in such environments there is a need to consider a new multiagent patrol strategy which divides the given area into parts in which more than one agent is active, for improving frequency. We show that in general graphs this problem is intractable, therefore we focus on simplified (yet realistic) cyclic graphs with possible inner edges. Although the problem remains generally intractable in such graphs, we provide a heuristic algorithm that is shown to significantly improve point-visit frequency compared to other patrol strategies. For evaluation of our work we used a custom developed ship simulator that realistically models ship movement constraints such as engine force and drag and reaction of the ship to environmental changes.

We present a novel approach for identifying exact and approximate behavioral equivalence between models of agents. This is significant because both decision making and game play in multiagent settings must contend with behavioral models of other agents in order to predict their actions. One approach that reduces the complexity of the model space is to group models that are behaviorally equivalent. Identifying equivalence between models requires solving them and comparing entire policy trees. Because the trees grow exponentially with the horizon, our approach is to focus on partial policy trees for comparison and determining the distance between updated beliefs at the leaves of the trees. We propose a principled way to determine how much of the policy trees to consider, which trades off solution quality for efficiency. We investigate this approach in the context of the interactive dynamic influence diagram and evaluate its performance.

Dual-decomposition (DD) methods are quickly becoming important tools for estimating the minimum energy state of a graphical model. DD methods decompose a complex model into a collection of simpler subproblems that can be solved exactly (such as trees), that in combination provide upper and lower bounds on the exact solution. Subproblem choice can play a major role: larger subproblems tend to improve the bound more per iteration, while smaller subproblems enable highly parallel solvers and can benefit from re-using past solutions when there are few changes between iterations. We propose an algorithm that can balance many of these aspects to speed up convergence. Our method uses a cluster tree data structure that has been proposed for adaptive exact inference tasks, and we apply it in this paper to dual-decomposition approximate inference. This approach allows us to process large subproblems to improve the bounds at each iteration, while allowing a high degree of parallelizability and taking advantage of subproblems with sparse updates. For both synthetic inputs and a real-world stereo matching problem, we demonstrate that our algorithm is able to achieve significant improvement in convergence time.

Plan recognition is a form of abductive reasoning that involves inferring plans that best explain sets of observed actions. Most existing approaches to plan recognition and other abductive tasks employ either purely logical methods that donot handle uncertainty, or purely probabilistic methods thatdo not handle structured representations. To overcome these limitations, this paper introduces an approach to abductive reasoning using a first-order probabilistic logic, specifically Markov Logic Networks (MLNs). It introduces several novel techniques for making MLNs efficient and effective for abduction. Experiments on three plan recognition datasets showthe benefit of our approach over existing methods.

When to make a decision is a key question in decision making problems characterized by uncertainty. In this paper we deal with decision making in environments where the information arrives dynamically. We address the tradeoff between waiting and stopping strategies. On the one hand, waiting to obtain more information reduces the uncertainty, but it comes with a cost. On the other hand, stopping and making a decision based on an expected utility, decreases the cost of waiting, but the decision is made based on uncertain information. In this paper, we prove that computing the optimal time to make a decision that guarantees the optimal utility is NP-hard. We propose a pessimistic approximation that guarantees an optimal decision when the recommendation is to wait. We empirically evaluate our algorithm and show that the quality of the decision is near-optimal and much faster than the optimal algorithm.

We describe a memory-efficient implementation of a dynamic programming algorithm for learning the optimal structure of a Bayesian network from training data. The algorithm leverages the layered structure of the dynamic programming graphs representing the recursive decomposition of the problem to reduce the memory requirements of the algorithm from O(n2 n ) to O(C(n, n/2)), where C(n, n/2) is the binomial coefficient. Experimental results show that the approach runs up to an order of magnitude faster and scales to datasets with more variables than previous approaches.