An SDP-based algorithm estimates both control gains and minimum dwell times online for switched LQR systems with unknown dynamics, achieving O(|M|^{1/4} n_s^{3/4} + n_m) expected regret while keeping state norms bounded.
Learning Linear-Quadratic Regulators Efficiently with only $\sqrt{T}$ Regret
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abstract
We present the first computationally-efficient algorithm with $\widetilde O(\sqrt{T})$ regret for learning in Linear Quadratic Control systems with unknown dynamics. By that, we resolve an open question of Abbasi-Yadkori and Szepesv\'ari (2011) and Dean, Mania, Matni, Recht, and Tu (2018).
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Regret-Guaranteed Safe Switching: LQR Setting with Unknown Dynamics
An SDP-based algorithm estimates both control gains and minimum dwell times online for switched LQR systems with unknown dynamics, achieving O(|M|^{1/4} n_s^{3/4} + n_m) expected regret while keeping state norms bounded.