Information-Theoretic Adaptive Cooling for Deterministic MPPI via Entropy Feedback

2026-07-15

AI Summary

This work addresses the challenge that deterministic Model Predictive Path Integral (MPPI) control struggles to robustly converge to the true optimal solution due to the absence of an effective temperature cooling strategy. The paper introduces Shannon entropy as an online feedback signal and proposes a novel adaptive cooling mechanism that dynamically adjusts the temperature based on the distribution of importance weights, while enforcing a critical entropy threshold to prevent premature weight collapse. By integrating this approach with nonsmooth signal temporal logic task specifications, the method significantly enhances sampling efficiency and convergence speed—outperforming state-of-the-art alternatives—while preserving MPPI’s gradient-free nature. Theoretical analysis further establishes its asymptotic convergence to the deterministic optimal solution.

Abstract

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.

Problem

• deterministic MPPI
• cooling schedule
• optimal control
• sampling efficiency
• temperature regulation

Innovation

• adaptive cooling
• Model Predictive Path Integral (MPPI)
• Shannon entropy
• importance weights
• deterministic optimal control