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The Power of Predictions in Online Control

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Document pages: 24 pages

Abstract: We study the impact of predictions in online Linear Quadratic Regulatorcontrol with both stochastic and adversarial disturbances in the dynamics. Inboth settings, we characterize the optimal policy and derive tight bounds onthe minimum cost and dynamic regret. Perhaps surprisingly, our analysis showsthat the conventional greedy MPC approach is a near-optimal policy in bothstochastic and adversarial settings. Specifically, for length-$T$ problems, MPCrequires only $O( log T)$ predictions to reach $O(1)$ dynamic regret, whichmatches (up to lower-order terms) our lower bound on the required predictionhorizon for constant regret.

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