Optimal Rates for Bandit Nonstochastic Control

• URL: http://arxiv.org/abs/2305.15352v3
• Date: Wed, 25 Oct 2023 01:26:40 GMT
• Title: Optimal Rates for Bandit Nonstochastic Control
• Authors: Y. Jennifer Sun, Stephen Newman, Elad Hazan
• Abstract summary: We give an algorithm for bandit LQR and LQG which attains optimal regret (up to logarithmic factors) for both known and unknown systems. A central component of our method is a new scheme for bandit convex optimization with memory, which is of independent interest.
• Score: 18.47192040293437
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) control are foundational and extensively researched problems in optimal control. We investigate LQR and LQG problems with semi-adversarial perturbations and time-varying adversarial bandit loss functions. The best-known sublinear regret algorithm of \cite{gradu2020non} has a $T^{\frac{3}{4}}$ time horizon dependence, and its authors posed an open question about whether a tight rate of $\sqrt{T}$ could be achieved. We answer in the affirmative, giving an algorithm for bandit LQR and LQG which attains optimal regret (up to logarithmic factors) for both known and unknown systems. A central component of our method is a new scheme for bandit convex optimization with memory, which is of independent interest.

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