Oracle Complexity Reduction for Model-free LQR: A Stochastic Variance-Reduced Policy Gradient Approach
This work addresses a computational bottleneck in reinforcement learning for control systems, offering an incremental improvement in oracle efficiency for applications where cost evaluations are expensive.
The paper tackles the high cost of two-point queries in model-free Linear Quadratic Regulator (LQR) problems by proposing a stochastic variance-reduced policy gradient method that reduces the requirement to O(log(1/ε)^β) two-point queries for an ε-approximate solution, with β in (0,1).
We investigate the problem of learning an $ε$-approximate solution for the discrete-time Linear Quadratic Regulator (LQR) problem via a Stochastic Variance-Reduced Policy Gradient (SVRPG) approach. Whilst policy gradient methods have proven to converge linearly to the optimal solution of the model-free LQR problem, the substantial requirement for two-point cost queries in gradient estimations may be intractable, particularly in applications where obtaining cost function evaluations at two distinct control input configurations is exceptionally costly. To this end, we propose an oracle-efficient approach. Our method combines both one-point and two-point estimations in a dual-loop variance-reduced algorithm. It achieves an approximate optimal solution with only $O\left(\log\left(1/ε\right)^β\right)$ two-point cost information for $β\in (0,1)$.