A Stochastic Process Model of Classical Search

TL;DR

This paper models classical search as a decision process, deriving a new anytime search algorithm, SMIRI, that outperforms existing algorithms on stochastic tree models by optimizing solution improvement rate.

Contribution

It formalizes classical search as an Abstract Search MDP and introduces SMIRI, a novel algorithm for anytime search that improves performance on stochastic models.

Findings

SMIRI outperforms current state-of-the-art anytime algorithms in tests.

The Abstract Search MDP provides a theoretical framework for search algorithm design.

SMIRI is effective across various stochastic tree parameters.

Abstract

Among classical search algorithms with the same heuristic information, with sufficient memory A* is essentially as fast as possible in finding a proven optimal solution. However, in many situations optimal solutions are simply infeasible, and thus search algorithms that trade solution quality for speed are desirable. In this paper, we formalize the process of classical search as a metalevel decision problem, the Abstract Search MDP. For any given optimization criterion, this establishes a well-defined notion of the best possible behaviour for a search algorithm and offers a theoretical approach to the design of algorithms for that criterion. We proceed to approximately solve a version of the Abstract Search MDP for anytime algorithms and thus derive a novel search algorithm, Search by Maximizing the Incremental Rate of Improvement (SMIRI). SMIRI is shown to outperform current state-of-the-art anytime search algorithms on a parametrized stochastic tree model for most of the tested parameter values.