This paper investigates the concept of symmetry and its role in problem solving. It first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given precise definitions of problems, it is relatively straightforward to construct a search process for finding solutions. Finally this paper attempts to exploit the concept of symmetry in improving problem solving.

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making -- minimizing expected regret -- to obtain minimax weighted expected regret (MWER). We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

Inference algorithms for arbitrary belief networks are impractical for large, complex belief networks. Inference algorithms for specialized classes of belief networks have been shown to be more efficient. In this paper, we present a search-based algorithm for approximate inference on arbitrary, noisy-OR belief networks, generalizing earlier work on search-based inference for two-level, noisy-OR belief networks. Initial experimental results appear promising.

Cooperative pathfinding is a problem of finding a set of non-conflicting trajectories for a number of mobile agents. Its applications include planning for teams of mobile robots, such as autonomous aircrafts, cars, or underwater vehicles. The state-of-the-art algorithms for cooperative pathfinding typically rely on some heuristic forward-search pathfinding technique, where A* is often the algorithm of choice. Here, we propose MA-RRT*, a novel algorithm for multi-agent path planning that builds upon a recently proposed asymptotically-optimal sampling-based algorithm for finding single-agent shortest path called RRT*. We experimentally evaluate the performance of the algorithm and show that the sampling-based approach offers better scalability than the classical forward-search approach in relatively large, but sparse environments, which are typical in real-world applications such as multi-aircraft collision avoidance.

Stochastic algorithms are among the best for solving computationally hard search and reasoning problems. The runtime of such procedures is characterized by a random variable. Different algorithms give rise to different probability distributions. One can take advantage of such differences by combining several algorithms into a portfolio, and running them in parallel or interleaving them on a single processor. We provide a detailed evaluation of the portfolio approach on distributions of hard combinatorial search problems. We show under what conditions the portfolio approach can have a dramatic computational advantage over the best traditional methods.

This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief updating and finding the maximum a posteriori hypothesis. We identify regions of completeness and provide preliminary empirical evaluation on randomly generated networks.

This paper introduces a new algorithm for the induction of complex finite state automata from samples of behaviour. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of magnitude over what was previously thought possible. We compare the algorithm with some existing induction techniques for finite state automata and show that the algorithm is much superior in both run time and quality of inductions.

We previously designed Partial Order Conflict Driven Clause Learning (PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a partial order on decision levels, and showed that it can speed up the solving on problems with a high independence between decision levels. In this paper, we more thoroughly analyze the reasons of the efficiency of PO-CDCL. Of particular importance is that the partial order introduces several candidates for the assertion level. By evaluating different heuristics for this choice, we show that the assertion level selection has an important impact on solving and that a carefully designed heuristic can significantly improve performances on relevant benchmarks.

In the real world, insufficient information, limited computation resources, and complex problem structures often force an autonomous agent to make a decision in time less than that required to solve the problem at hand completely. Flexible and approximate computations are two approaches to decision making under limited computation resources. Flexible computation helps an agent to flexibly allocate limited computation resources so that the overall system utility is maximized. Approximate computation enables an agent to find the best satisfactory solution within a deadline. In this paper, we present two state-space reduction methods for flexible and approximate computation: quantitative reduction to deal with inaccurate heuristic information, and structural reduction to handle complex problem structures. These two methods can be applied successively to continuously improve solution quality if more computation is available. Our results show that these reduction methods are effective and efficient, finding better solutions with less computation than some existing well-known methods.

Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy explicitly as a finite-state controller and iteratively improves the controller by search in policy space. Two related algorithms illustrate this approach. The first is a policy iteration algorithm that can outperform value iteration in solving infinitehorizon POMDPs. It provides the foundation for a new heuristic search algorithm that promises further speedup by focusing computational effort on regions of the problem space that are reachable, or likely to be reached, from a start state.