Decoupled Planning for Multiple Omega-Regular Objectives

TL;DR

This paper introduces a modular, decoupled framework for generating paths on graphs that satisfy multiple omega-regular objectives, highlighting the challenges of scheduler coordination and proposing solutions for safety and non-safety objectives.

Contribution

It presents a novel decoupled approach for multi-objective path planning, analyzing scheduler limitations, and proposing conventions and protocols for ensuring objective satisfaction.

Findings

Deterministic schedulers may fail to ensure correctness.

Stochastic schedulers are necessary but insufficient without coordination.

Protocols for synchronizing safe actions enable decentralized safety objective satisfaction.

Abstract

We study the problem of generating paths on a graph that satisfy a collection of {\omega}-regular objectives. We propose a decoupled framework in which each objective is assigned to an independent agent that selects a local policy, while a scheduler -- oblivious to the graph and objective -- dynamically composes these policies into a single path. We ask when such a composition satisfies all objectives, assuming their conjunction is realizable. The framework enables modular policy design but raises fundamental compositional challenges. We show that even extremely fair deterministic schedulers do not ensure correctness, and that stochastic schedulers, while necessary, are insufficient without coordination. For safety objectives, we demonstrate that fully decentralized implementations are impossible, and we introduce a protocol for synchronizing on maximal safe actions. For non-safety objectives, we introduce conventions -- simple, a priori restrictions agreed upon before the graph or objectives are revealed -- that guarantee satisfaction of all objectives when followed by all agents. We characterize minimally restrictive conventions for major subclasses of {\omega}-regular objectives. In particular, B\"uchi objectives admit universal composition of finite-memory policies without scheduler communication; co-B\"uchi objectives require only knowledge of whether the agent was scheduled; and parity objectives additionally require knowledge of which agent was scheduled.