Robust Learning-Based Control via Bootstrapped Multiplicative Noise
This addresses robustness issues in control systems for applications like robotics or autonomous systems, but appears incremental as it builds on existing adaptive control and reinforcement learning methods.
The paper tackles the problem of designing controllers robust to non-asymptotic uncertainties from finite, noisy data by proposing a robust adaptive control algorithm that incorporates bootstrap resampling and multiplicative noise in LQR design, showing it significantly outperforms certainty equivalent controllers in expected regret and regret risk in numerical experiments.
Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties arising from models estimated with finite, noisy data. We propose a robust adaptive control algorithm that explicitly incorporates such non-asymptotic uncertainties into the control design. The algorithm has three components: (1) a least-squares nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method using an optimal linear quadratic regulator (LQR) with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. We show through numerical experiments that the proposed robust adaptive controller can significantly outperform the certainty equivalent controller on both expected regret and measures of regret risk.