A Bayesian Approach to Tackling Hard Computational Problems

TL;DR

This paper introduces a Bayesian framework for controlling search algorithms in complex problems, using learned models to dynamically optimize restart strategies and improve efficiency over fixed cutoff methods.

Contribution

It presents a novel Bayesian approach for dynamic restart strategies in search algorithms, outperforming fixed cutoff methods by predicting search durations based on early behavior.

Findings

Dynamic restart strategies can outperform fixed strategies.

Bayesian models effectively predict search durations.

The approach reduces variance in search times.

Abstract

We are developing a general framework for using learned Bayesian models for decision-theoretic control of search and reasoningalgorithms. We illustrate the approach on the specific task of controlling both general and domain-specific solvers on a hard class of structured constraint satisfaction problems. A successful strategyfor reducing the high (and even infinite) variance in running time typically exhibited by backtracking search algorithms is to cut off and restart the search if a solution is not found within a certainamount of time. Previous work on restart strategies have employed fixed cut off values. We show how to create a dynamic cut off strategy by learning a Bayesian model that predicts the ultimate length of a trial based on observing the early behavior of the search algorithm. Furthermore, we describe the general conditions under which a dynamic restart strategy can outperform the theoretically optimal fixed strategy.