Wasserstein Policy Optimization

We introduce Wasserstein Policy Optimization (WPO), an actor-critic algorithm for reinforcement learning in continuous action spaces. WPO can be derived as an approximation to Wasserstein gradient flow over the space of all policies projected into a finite-dimensional parameter space (e.g., the weights of a neural network), leading to a simple and completely general closed-form update. The resulting algorithm combines many properties of deterministic and classic policy gradient methods. Like deterministic policy gradients, it exploits knowledge of the gradient of the action-value function with respect to the action. Like classic policy gradients, it can be applied to stochastic policies with arbitrary distributions over actions -- without using the reparameterization trick. We show results on the DeepMind Control Suite and a magnetic confinement fusion task which compare favorably with state-of-the-art continuous control methods.

@article{pfau2025_2505.00663,
  title={ Wasserstein Policy Optimization },
  author={ David Pfau and Ian Davies and Diana Borsa and Joao G. M. Araujo and Brendan Tracey and Hado van Hasselt },
  journal={arXiv preprint arXiv:2505.00663},
  year={ 2025 }
}