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This paper presents Trajectory-Regularized Stochastic Optimal Control (TRSOC), a theoretical framework that integrates Kullback-Leibler divergence penalties into standard stochastic optimal control to balance performance with adherence to reference dynamics. By leveraging Girsanov's theorem, the method preserves dynamic programming structures while offering closed-form solutions in linear-quadratic settings and demonstrating utility for offline data-driven tasks. This advancement directly impacts machine learning applications requiring robust policy optimization under distributional constraints or safety guidelines.
Trajectory-Regularized Stochastic Optimal Control via KL Divergence
arXiv:2607.22201v1 Announce Type: cross Abstract: We introduce trajectory-regularized stochastic optimal control (TRSOC), which augments standard stochastic optimal control (SOC) with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions. Using Girsanov's theorem, the trajectory KL reduces to a quadratic drift mismatch penalty, yielding a modified running cost that preserves the dynamic programming (DP) structure. We derive the corresponding Hamilton--Jacobi--Bellman (HJB) equation and characterize the optimal policy. In the linear-quadratic (LQ) setting, the formulation admits a closed-form solution with an augmented control cost. Experiments show that the regularization parameter induces a trade-off between performance-driven and reference-preserving behavior, including cases with reference dynamics learned from offline data.
Abstract:We introduce trajectory-regularized stochastic optimal control (TRSOC), which augments standard stochastic optimal control (SOC) with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions. Using Girsanov's theorem, the trajectory KL reduces to a quadratic drift mismatch penalty, yielding a modified running cost that preserves the dynamic programming (DP) structure. We derive the corresponding Hamilton--Jacobi--Bellman (HJB) equation and characterize the optimal policy. In the linear-quadratic (LQ) setting, the formulation admits a closed-form solution with an augmented control cost. Experiments show that the regularization parameter induces a trade-off between performance-driven and reference-preserving behavior, including cases with reference dynamics learned from offline data.
Systems and Control (eess.SY); Machine Learning (cs.LG)
arXiv:2607.22201 [eess.SY]
(or arXiv:2607.22201v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2607.22201 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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