Approximate Multi-Objective Search Under Rulebooks

2026-08-04

AI Summary

This work addresses the high computational cost of exactly computing all optimal solutions that satisfy the priority structure specified in a rulebook for multi-objective robotic planning. To overcome this challenge, the paper introduces, for the first time, the concept of ε-rule-dominance as an approximation criterion and proposes the RA*pex algorithm, which efficiently generates a compact set of near-optimal solutions via best-first search. By integrating dimensionality reduction, hierarchical closed-set maintenance, and residual rule-set dominance checks, RA*pex significantly reduces computational complexity while strictly preserving the semantic hierarchy of the rulebook. Experimental results demonstrate that RA*pex outperforms existing algorithms by over two orders of magnitude in speed, with theoretical guarantees that every solution in the returned set ε-rule-dominates some true rulebook-optimal solution.

Abstract

Robotic planning often involves multiple objectives with complex priority relationships, such as safety, efficiency, and regulatory compliance. Rulebooks formalize these relationships, allowing partial ordering of objectives that generalizes both Pareto and lexicographic dominance. Computing the full set of rulebook-optimal solutions, however, is computationally expensive. To address this challenge, we introduce the concept of epsilon-rule-dominance, a principled notion of approximate dominance under rulebooks, and propose RA*pex, a best-first search algorithm that efficiently computes a compact set of epsilon-approximate rulebook-optimal solutions. RA*pex leverages dimensionality reduction, a technique used to speed up existing multi-objective search algorithms, while respecting rule hierarchies by maintaining separate closed sets and performing dominance checks over truncated and residual rule sets. We provide a formal analysis of RA*pex, proving that every rulebook-optimal solution is epsilon-rule-dominated (a generalization of approximate dominance we introduce) by at least one solution in the returned set. Empirical results demonstrate that our approach achieves computation times over two orders of magnitude faster than existing methods.

Problem

• multi-objective search
• rulebooks
• computational complexity
• robotic planning
• approximate optimization

Innovation

• epsilon-rule-dominance
• rulebook
• multi-objective search
• RA*pex
• approximate optimality