Convergence of policy gradient methods for finite-horizon exploratory linear-quadratic control problems

• URL: http://arxiv.org/abs/2211.00617v3
• Date: Fri, 1 Mar 2024 20:42:36 GMT
• Title: Convergence of policy gradient methods for finite-horizon exploratory linear-quadratic control problems
• Authors: Michael Giegrich, Christoph Reisinger, Yufei Zhang
• Abstract summary: We study the global linear convergence of policy gradient (PG) methods for finite-horizon continuous-time exploratory linear-quadratic control (LQC) problems. We propose a novel PG method with discretetime policies. The algorithm leverages the continuous-time analysis, and achieves a robust linear convergence across different action frequencies.
• Score: 3.8661825615213012
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the global linear convergence of policy gradient (PG) methods for finite-horizon continuous-time exploratory linear-quadratic control (LQC) problems. The setting includes stochastic LQC problems with indefinite costs and allows additional entropy regularisers in the objective. We consider a continuous-time Gaussian policy whose mean is linear in the state variable and whose covariance is state-independent. Contrary to discrete-time problems, the cost is noncoercive in the policy and not all descent directions lead to bounded iterates. We propose geometry-aware gradient descents for the mean and covariance of the policy using the Fisher geometry and the Bures-Wasserstein geometry, respectively. The policy iterates are shown to satisfy an a-priori bound, and converge globally to the optimal policy with a linear rate. We further propose a novel PG method with discrete-time policies. The algorithm leverages the continuous-time analysis, and achieves a robust linear convergence across different action frequencies. A numerical experiment confirms the convergence and robustness of the proposed algorithm.

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