Trajectory-Regularized Stochastic Optimal Control via KL Divergence
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-...
| Authors | Mintae Kim, Koushil Sreenath |
|---|---|
| Primary category | eess.SY |
| Published | 24 July 2026 |
| Last updated at source | 19 September 2026 |
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