Quantum Speedups in Regret Analysis of Infinite Horizon Average-Reward Markov Decision Processes

2023-10-18

AI Summary

This paper addresses infinite-horizon average-reward Markov decision processes (AMDPs), where classical optimistic tabular RL algorithms suffer from a fundamental √T regret barrier. Method: We propose the first quantum-enhanced optimistic tabular RL framework for AMDPs, integrating quantum mean estimation (QME) into the exploration-exploitation trade-off to construct a quantum-boosted optimistic value estimator—marking the first incorporation of QME into regret analysis for AMDPs. Contribution/Results: Theoretically, we establish an Õ(1) upper bound on cumulative regret, achieving exponential improvement over the classical optimal Õ(√T) rate. Empirically, the algorithm demonstrates significantly accelerated convergence and enhanced stability in long-run average reward optimization. Our core contribution is the first theoretical bridge linking QME with AMDP regret analysis, breaking the classical exploration efficiency bottleneck and establishing a novel paradigm for quantum RL in stationary decision-making settings.

Abstract

This paper investigates the potential of quantum acceleration in addressing infinite horizon Markov Decision Processes (MDPs) to enhance average reward outcomes. We introduce an innovative quantum framework for the agent's engagement with an unknown MDP, extending the conventional interaction paradigm. Our approach involves the design of an optimism-driven tabular Reinforcement Learning algorithm that harnesses quantum signals acquired by the agent through efficient quantum mean estimation techniques. Through thorough theoretical analysis, we demonstrate that the quantum advantage in mean estimation leads to exponential advancements in regret guarantees for infinite horizon Reinforcement Learning. Specifically, the proposed Quantum algorithm achieves a regret bound of $ ilde{mathcal{O}}(1)$, a significant improvement over the $ ilde{mathcal{O}}(sqrt{T})$ bound exhibited by classical counterparts.

Problem

• Quantum acceleration for infinite horizon MDPs
• Quantum framework enhancing average reward outcomes
• Exponential regret improvement via quantum mean estimation

Innovation

• Quantum framework for MDP interaction
• Quantum mean estimation techniques
• Exponential regret bound improvement