TRSOC is introduced, which augments standard stochastic optimal control with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions, and the regularization parameter induces a trade-off between performance-driven and reference-preserving behavior.
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.
This paper presents a data-driven stable manifold (DD-SM) method, which integrates Koopman operator representation learning with the geometric stable manifold approach to Hamilton-Jacobi-Bellman (HJB) equations, enabling end-to-end optimal feedback control synthesis from raw trajectory data without prior knowledge of s...
Empirical results demonstrate that PI-VM matches SOTA precision with an order-of-magnitude efficiency gain in low-dimensional settings, while effectively mitigating mode collapse in high-dimensional scenarios, and offers a scalable solution for solving complex SOC problems.
Bangyan Liao, Cheng-Lei Yu, Yuchen Yang et al.· 0 citations
On-policy and off-policy Q-learning algorithms that learn the optimal controller solely from online state trajectory data are developed, specifically developing on-policy and off-policy Q-learning algorithms that learn the optimal controller solely from online state trajectory data.
Wasserstein policy gradient (WPG) reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance and it is proved that this ODE is globally well posed and converges exponentially from every admissible initialization.
A hybrid policy combining time-independent affine feedback with finite-horizon steering over a terminal layer is constructed, proving that its worst-case cost gap decays exponentially with the terminal-layer length uniformly in the horizon, which helps reducing the computation cost for long-horizon robust controls.
The resulting characterization reveals how control-dependent noise, policy-evaluation sensitivity, and update ordering govern local error propagation, and yields explicit sufficient conditions for local linear convergence.
Karl Handwerker, Felix Thömmes, Lucas Günther et al.· 1 citation
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