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This paper introduces a continuous-time, model-free reinforcement learning algorithm that reformulates time-inconsistent control problems into a two-stage framework to learn deterministic equilibrium policies. By combining deterministic policy gradients with fixed-point iterations, the authors theoretically establish convergence under mild assumptions and demonstrate effectiveness in financial applications like mean-variance portfolio management. The work advances the intersection of optimization, control theory, and machine learning by providing a unified approach to handling time-inconsistency without relying on specific discounting models.
Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problems
arXiv:2606.11798v1 Announce Type: cross Abstract: In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.
Abstract:In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.
Computational Finance (q-fin.CP); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2606.11798 [q-fin.CP]
(or arXiv:2606.11798v1 [q-fin.CP] for this version)
https://doi.org/10.48550/arXiv.2606.11798 arXiv-issued DOI via DataCite (pending registration)
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