Fast Global Convergence of Policy Optimization for Constrained MDPs

• URL: http://arxiv.org/abs/2111.00552v1
• Date: Sun, 31 Oct 2021 17:46:26 GMT
• Title: Fast Global Convergence of Policy Optimization for Constrained MDPs
• Authors: Tao Liu, Ruida Zhou, Dileep Kalathil, P. R. Kumar, Chao Tian
• Abstract summary: We show that gradient-based methods can achieve an $mathcalO(log(T)/T)$ global convergence rate both for the optimality gap and the constraint violation. When Slater's condition is satisfied and known a priori, zero constraint violation can be further guaranteed for a sufficiently large $T$.
• Score: 17.825031573375725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the issue of safety in reinforcement learning. We pose the problem in a discounted infinite-horizon constrained Markov decision process framework. Existing results have shown that gradient-based methods are able to achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate both for the optimality gap and the constraint violation. We exhibit a natural policy gradient-based algorithm that has a faster convergence rate $\mathcal{O}(\log(T)/T)$ for both the optimality gap and the constraint violation. When Slater's condition is satisfied and known a priori, zero constraint violation can be further guaranteed for a sufficiently large $T$ while maintaining the same convergence rate.

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