Equivalence of stochastic and deterministic policy gradients

• URL: http://arxiv.org/abs/2505.23244v2
• Date: Tue, 10 Jun 2025 01:48:08 GMT
• Title: Equivalence of stochastic and deterministic policy gradients
• Authors: Emo Todorov,
• Abstract summary: We show that the gradient and deterministic policy gradients, natural gradients, and state value functions are identical.<n>We then develop a general procedure for constructing an MDP with deterministic policy that is equivalent to a given MDP with policy.<n>Our results suggest that policy methods can be unified by approxing state value functions rather than state-control value functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Policy gradients in continuous control have been derived for both stochastic and deterministic policies. Here we study the relationship between the two. In a widely-used family of MDPs involving Gaussian control noise and quadratic control costs, we show that the stochastic and deterministic policy gradients, natural gradients, and state value functions are identical; while the state-control value functions are different. We then develop a general procedure for constructing an MDP with deterministic policy that is equivalent to a given MDP with stochastic policy. The controls of this new MDP are the sufficient statistics of the stochastic policy in the original MDP. Our results suggest that policy gradient methods can be unified by approximating state value functions rather than state-control value functions.

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