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Poster
Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator
Sarah Dean · Horia Mania · Nikolai Matni · Benjamin Recht · Stephen Tu

Wed Dec 05 07:45 AM -- 09:45 AM (PST) @ Room 210 #81
in Wed Poster Session A »

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.

Keywords: Learning Theory · Online Learning · Control Theory
[ Paper] 

Author Information

Sarah Dean (Cornell University)
Horia Mania (UC Berkeley)
Nikolai Matni (UC Berkeley)
Benjamin Recht (UC Berkeley)
Stephen Tu (UC Berkeley)

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