Wasserstein Policy Gradient for Entropy-Regularized Linear-Quadratic Control
Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space. We study entropy-regularized discounted linear-quadratic (LQ) control. A Bellman verification argument shows that the unrestricted problem has a linear-Gaussian optimal policy, and the discounted-occupancy-weighted statewise Wasserstein gradient is tangent to this policy class. WPG therefore reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance. We prove that this ODE is globally well posed and converges exponentially from every admissible initialization. For each fixed LQ problem, the exponent has a positive limit as the entropy temperature tends to ...
| Authors | Zhaoyu Zhu, Rui Gao, Shuang Li |
|---|---|
| Primary category | math.OC |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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