Title:

Searching with Distributional Heuristics

Distributional heuristic search uses distributions rather than point values for its heuristic estimates of the cost to goal from any given state. Distributional heuristics are desirable as they provide search algorithms not only with a way to evaluate nodes, but also with a basis for rational decision making tailored to specific search settings. Bounded suboptimal, anytime, and contract searches have differing but related objectives that each lend themselves to probabilistic reasoning supported by distributional heuristics. In many applications, speed of planning can be more important than solution quality. Whether due to certain domains' inherent difficulty, where anything but a satisficing approach is infeasible due to time or memory constraints, or due to the limited planning time available in real-time robotics and other time-sensitive planning settings, important open questions are how best to find solutions as quickly as possible and how to find the best solution possible while subject to an explicit limit on planning time. Successful algorithms must reason not only about solution cost, possibly in relation to a suboptimality bound, but also about the relative likelihood of finding a solution under one node vs. under another, of finding a solution of a particular cost (such as in relation to that of an incumbent solution), or about the expected amount of search effort to find a goal under a given node. This dissertation takes up these issues in five parts. I (1) examine different methods for generating distributional heuristics in bounded cost heuristic search and classical planning; (2) study the contract search setting, which involves online estimation of several unknown values; (3) consider the bounded suboptimal setting; (4) address the anytime setting; and (5) introduce and advocate for the tunable suboptimal heuristic search setting.

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