Adversarially Robust Multitask Adaptive Control

Adaptive control seeks to design controllers that adapt to uncertain or unknown system dynamics. Rooted in early work on self-tuning regulators for flight and aerospace applications [ Astr om and Wittenmark, 1973, Astr om, 1983], it remains central to modern control. Among its formulations, the linear quadratic regulator (LQR) serves as a canonical benchmark due to its tractability and theoretical appeal. Extensive research over the last five or so years has established non-asymptotic performance guarantees for adaptive LQR through regret analysis [Abbasi-Yadkori and Szepesv ari, 2011, Dean et al., 2018, Cohen et al., 2019, Simchowitz and Foster, 2020, Hazan et al., 2020, Ziemann and Sandberg, 2022], proving that in the single-system setting the optimal expected regret scales as O( dT), with d = d