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

Swetha Ganesh; Washim Uddin Mondal; Vaneet Aggarwal

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arXiv · 2404.02108

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

Swetha Ganesh·Washim Uddin Mondal·Vaneet Aggarwal

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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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Swetha Ganesh, Washim Uddin Mondal, Vaneet Aggarwal. 2024-04-02. Order-Optimal Regret with Novel Policy Gradient Approaches in Infinite-Horizon Average Reward MDPs. https://arxiv.org/abs/2404.02108

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