A Stochastic Gradient Descent Approach to Design Policy Gradient Methods for LQR

A team of researchers from multiple institutions has published a significant paper on arXiv titled 'A Stochastic Gradient Descent Approach to Design Policy Gradient Methods for LQR,' proposing a novel framework for data-driven policy optimization in control systems. The work addresses the Linear Quadratic Regulator (LQR) problem—a fundamental optimal control challenge—using stochastic gradient descent (SGD) methods that work directly with trajectory data rather than requiring perfect system knowledge.

The paper introduces two distinct approaches for estimating policy gradients from stochastic data: an indirect method that first estimates system matrices then constructs gradients, and a direct zeroth-order method that approximates gradients through empirical cost evaluations. Both approaches produce random gradient estimates, allowing the researchers to apply SGD theory to analyze convergence. A key technical contribution involves modeling these gradient estimates as suitable stochastic gradient oracles and deriving sufficient conditions under which SGD with biased oracles converges asymptotically to optimal policies.

This research matters because traditional policy gradient methods often assume perfect knowledge of system dynamics or access to exact gradients. In real-world control applications—from robotics to autonomous systems—such assumptions rarely hold. The proposed framework enables reinforcement learning agents to learn optimal control policies using only observed trajectory data, making it applicable to systems where models are unknown or partially observable. The numerical experiments validate that both approaches effectively converge to optimal policies, with the indirect method potentially offering better sample efficiency while the direct method provides more flexibility.

For practitioners in robotics, autonomous systems, and industrial control, this work provides mathematically grounded methods for implementing data-driven reinforcement learning where system identification is challenging. The convergence guarantees for biased gradient oracles represent an important theoretical advancement that could enable more robust learning in noisy, real-world environments.