Omar Muhammetkulyyev | Searcharxiv

arXiv2026

Approximate Multi-Objective Search Under Rulebooks

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.

cs.RO↗

arXiv2025

Lexicographic Multi-Objective Stochastic Shortest Path with Mixed Max-Sum Costs

We study the Stochastic Shortest Path (SSP) problem for autonomous systems with mixed max-sum cost aggregations under Linear Temporal Logic constraints. Classical SSP formulations rely on sum-aggregated costs, which are suitable for cumulative quantities such as time or energy but fail to capture bottleneck-style objectives such as avoiding high-risk transitions, where performance is determined by the worst single event along a trajectory. Such objectives are particularly important in safety-critical systems, where even one hazardous transition can be unacceptable. To address this limitation, we introduce max-aggregated objectives that minimize the bottleneck cost, i.e., the maximum one-step cost along a trajectory. We show that standard Bellman equations on the original state space do not apply in this setting and propose an augmented MDP with a state variable tracking the running maximum cost, together with a value iteration algorithm. We further identify a cyclic policy phenomenon, where zero-marginal-cost cycles prevent goal reaching under max-aggregation, and resolve it via a finite-horizon formulation. To handle richer task requirements, linear temporal logic specifications are translated into deterministic finite automata and combined with the system to construct a product MDP. We propose a lexicographic value iteration algorithm that handles mixed max-sum objectives under lexicographic ordering on this product MDP. Gridworld case studies demonstrate the effectiveness of the proposed framework.

eess.SY↗