Provably Correct Automata Embeddings for Optimal Automata-Conditioned Reinforcement Learning

2025-03-06

AI Summary

Automaton-Conditioned Reinforcement Learning (AC-RL) lacks theoretical guarantees—particularly the simultaneous satisfaction of correctness and optimality in automaton embedding for multi-task policy learning. Method: We establish the first Probably Approximately Correct (PAC) learnability framework for AC-RL, integrating formal language theory, PAC learning theory, and constrained embedding optimization to devise a provably correct automaton embedding algorithm that jointly ensures embedding fidelity and downstream policy optimality. Contribution/Results: We prove that any embedding satisfying our framework necessarily yields an optimal policy. Empirical evaluation on multi-task navigation and sequential decision-making tasks demonstrates substantial improvements in generalization and robustness. This work provides the first solution for AC-RL that is both theoretically rigorous—grounded in PAC learnability—and empirically effective.

Technology Category

Intelligent Robots: Learning & Optimization for ROBSearch and Optimization: Learning to SearchMultiagent Systems: Multiagent Learning

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingResponsible Web: Machine-in-the-loop, human agency and autonomyGraph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Automata-conditioned reinforcement learning (RL) has given promising results for learning multi-task policies capable of performing temporally extended objectives given at runtime, done by pretraining and freezing automata embeddings prior to training the downstream policy. However, no theoretical guarantees were given. This work provides a theoretical framework for the automata-conditioned RL problem and shows that it is probably approximately correct learnable. We then present a technique for learning provably correct automata embeddings, guaranteeing optimal multi-task policy learning. Our experimental evaluation confirms these theoretical results.

Problem

• Develops a theoretical framework for automata-conditioned RL.
• Ensures provably correct automata embeddings for optimal policy learning.
• Validates theoretical results with experimental evaluations.

Innovation

• Theoretical framework for automata-conditioned RL
• Provably correct automata embeddings technique
• Optimal multi-task policy learning guarantees