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Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow

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arxiv 2402.17208 v2 pith:EXK4ICX4 submitted 2024-02-27 math.OC

Mo Zhou , Jianfeng Lu This is my paper · ORCID
classification math.OC
keywords actor-criticcontrolconvergenceflowmethodoptimalpolicystochastic
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We propose an actor-critic framework to solve the time-continuous stochastic optimal control problem. A least square temporal difference method is applied to compute the value function for the critic. The policy gradient method is implemented as policy improvement for the actor. Our key contribution lies in establishing a linear rate of convergence for our proposed actor-critic flow. Theoretical findings are further validated through numerical examples, showing the efficacy of our approach in practical applications.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration

    math.NA 2025-07 conditional novelty 6.0 of 10

    A PINN-based policy iteration method for nonconvex Hamilton-Jacobi-Isaacs equations with a convergence analysis and tests up to 10 dimensions.

  2. Simulating Fokker-Planck equations via mean field control of score-based normalizing flows

    math.OC 2025-06 conditional novelty 4.0 of 10

    A mean field control formulation using score-based normalizing flows simulates Fokker-Planck equations deterministically, with a convergence theorem for Ornstein-Uhlenbeck processes and experiments on Langevin and cha...

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