Information-Theoretic Adaptive Cooling for Deterministic MPPI via Entropy Feedback
For researchers and practitioners using sampling-based optimal control methods, this work provides a principled, adaptive cooling mechanism that enhances the efficiency and robustness of deterministic MPPI without requiring derivative information.
The paper addresses the challenge of designing an effective cooling schedule for deterministic Model Predictive Path Integral (MPPI) control. It proposes an Information-Theoretic Adaptive Cooling (ITAC) framework that uses Shannon entropy of importance weights as feedback to regulate temperature, achieving faster convergence and improved sampling efficiency on nonsmooth motion-planning tasks compared to state-of-the-art baselines.
This paper investigates deterministic optimal control using Model Predictive Path Integral (MPPI) control, a sampling-based and derivative-free framework well suited for systems with complex dynamics and nonsmooth objectives. In deterministic MPPI, the temperature must be driven to zero to recover the true optimum, yet the design of an effective cooling schedule remains a fundamental challenge. Existing methods typically rely on predefined open-loop schedules, which limit the efficiency and robustness of the algorithm. To overcome this limitation, we propose an Information-Theoretic Adaptive Cooling (ITAC) framework that uses the Shannon entropy of the importance weights as an online feedback signal to regulate the temperature. The proposed mechanism adapts the cooling rate to the current sampling state, enabling fast progress when the weights are diffuse and cautious cooling when they become concentrated. We prove asymptotic convergence of the resulting scheme to the deterministic optimum, and further derive a critical entropy threshold that leads to a smooth barrier against premature weight collapse. Experiments on nonsmooth signal temporal logic motion-planning tasks show that ITAC improves sampling efficiency and achieves substantially faster convergence than state-of-the-art baselines without sacrificing the derivative-free nature of MPPI.