Breadth-First Search vs. Restarting Random Walks for Escaping Uninformed Heuristic Regions

TL;DR

This paper compares breadth-first search and restarting random walks for escaping uninformed heuristic regions in search algorithms, providing theoretical runtime analysis and empirical evaluations on planning benchmarks.

Contribution

It offers a theoretical comparison of BrFS and RRWs for escaping UHRs and introduces EHC-RRW as an effective variant with runtime guarantees.

Findings

EHC-RRW outperforms standard EHC in certain UHR scenarios.

Theoretical analysis identifies conditions where RRWs are faster than BrFS.

Experimental results validate the theoretical predictions on PDDL benchmarks.

Abstract

Greedy search methods like Greedy Best-First Search (GBFS) and Enforced Hill-Climbing (EHC) often struggle when faced with Uninformed Heuristic Regions (UHRs) like heuristic local minima or plateaus. In this work, we theoretically and empirically compare two popular methods for escaping UHRs in breadth-first search (BrFS) and restarting random walks (RRWs). We first derive the expected runtime of escaping a UHR using BrFS and RRWs, based on properties of the UHR and the random walk procedure, and then use these results to identify when RRWs will be faster in expectation than BrFS. We then evaluate these methods for escaping UHRs by comparing standard EHC, which uses BrFS to escape UHRs, to variants of EHC called EHC-RRW, which use RRWs for that purpose. EHC-RRW is shown to have strong expected runtime guarantees in cases where EHC has previously been shown to be effective. We also run experiments with these approaches on PDDL planning benchmarks to better understand their relative effectiveness for escaping UHRs.