Path Integral Value Matching for Linear Quadratic Stochastic Optimal Control

• URL: http://arxiv.org/abs/2608.10777v1
• Date: Tue, 11 Aug 2026 10:29:49 GMT
• Title: Path Integral Value Matching for Linear Quadratic Stochastic Optimal Control
• Abstract summary: Current state-of-the-art policy-based methods suffer from prohibitive computational costs and instability.<n>We propose a paradigm shift toward a value-based approach by revisiting Path Integral Control (PIC)<n>Building upon this theoretical foundation, we propose the Path Integral Value Matching (PI-VM) algorithm.
• Score: 26.034302137738127
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Linear Quadratic Stochastic Optimal Control (LQ-SOC) establishes a fundamental framework for steering noisy dynamical systems and has recently gained renewed interest in the machine learning community. However, current state-of-the-art policy-based methods suffer from prohibitive computational costs and instability due to their heavy reliance on full-trajectory simulation. To overcome these limitations, we propose a paradigm shift toward a value-based approach by revisiting Path Integral Control (PIC). Although standard PIC suffers from the same high-variance bottleneck as policy-based methods, we discover that by truncating and marginalizing the original path integral formulation, we can derive a temporal recursive form of the value function. Building upon this theoretical foundation, we propose the Path Integral Value Matching (PI-VM) algorithm. Specifically, we employ temporal-difference learning to approximate the recursive value dynamics, and further integrate the Girsanov theorem with experience replay to enable off-policy training. We benchmark PI-VM against SOTA policy-based methods across various SOC benchmarks and sampling tasks. 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. Consequently, PI-VM offers a scalable solution for solving complex SOC problems.

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