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The exploration/exploitation trade-off is an inherent challenge indata-driven adaptive control. Though this trade-off has been studied formulti-armed bandits (MAB's) and reinforcement learning for linear systems; itis less well-studied for learning-based control of nonlinear systems. Asignificant theoretical challenge in the nonlinear setting is that there is noexplicit characterization of an optimal controller for a given set of cost andsystem parameters. We propose the use of a finite-horizon oracle controllerwith full knowledge of parameters as a reasonable surrogate to optimalcontroller. This allows us to develop policies in the context of learning-basedMPC and MAB's and conduct a control-theoretic analysis using techniques fromMPC- and optimization-theory to show these policies achieve low regret withrespect to this finite-horizon oracle. Our simulations exhibit the low regretof our policy on a heating, ventilation, and air-conditioning model withpartially-unknown cost function.

Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function