Order-Optimal Regret with Novel Policy Gradient Approaches in Infinite-Horizon Average Reward MDPs

• URL: http://arxiv.org/abs/2404.02108v2
• Date: Sun, 11 May 2025 01:27:57 GMT
• Title: Order-Optimal Regret with Novel Policy Gradient Approaches in Infinite-Horizon Average Reward MDPs
• Authors: Swetha Ganesh, Washim Uddin Mondal, Vaneet Aggarwal,
• Abstract summary: We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP)<n>The first one employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $tildemathcalO(T2/3)$.<n>The second approach, rooted in Hessian-based techniques, ensures an expected regret of the order $tildemathcalO(sqrtT)$.
• Score: 31.343919501963416
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP). The first one employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $\tilde{\mathcal{O}}(T^{2/3})$. The second approach, rooted in Hessian-based techniques, ensures an expected regret of the order $\tilde{\mathcal{O}}(\sqrt{T})$. These results significantly improve the state-of-the-art $\tilde{\mathcal{O}}(T^{3/4})$ regret and achieve the theoretical lower bound. We also show that the average-reward function is approximately $L$-smooth, a result that was previously assumed in earlier works.

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