Abstract:We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics At, Bt. The sequence of dynamics matrices can be arbitrary, but with a total variation, VT, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of Õ(V… Show more
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