Volume 29, 2023
|Number of page(s)||26|
|Published online||07 March 2023|
Department of Mathematics and Halicioğlu Data Science Institute, University of California,
San Diego, La Jolla,
2 Department of Mathematics, Stanford University, Stanford, California, USA
*** Corresponding author: firstname.lastname@example.org
Accepted: 13 January 2023
We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.
Mathematics Subject Classification: 90C40 / 93E20
Key words: Markov decision process / reinforcement learning / policy gradient / optimal control
The work of Y.Z. and L.Y. is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program.
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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