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

• URL: http://arxiv.org/abs/2310.11684v3
• Date: Sun, 28 Apr 2024 20:04:52 GMT
• Title: Quantum Speedups in Regret Analysis of Infinite Horizon Average-Reward Markov Decision Processes
• Authors: Bhargav Ganguly, Yang Xu, Vaneet Aggarwal,
• Abstract summary: We introduce an innovative quantum framework for the agent's engagement with an unknown MDP. We show that the quantum advantage in mean estimation leads to exponential advancements in regret guarantees for infinite horizon Reinforcement Learning.
• Score: 32.07657827173262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\tilde{\mathcal{O}}(1)$, a significant improvement over the $\tilde{\mathcal{O}}(\sqrt{T})$ bound exhibited by classical counterparts.

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