Geometric Exploration for Online Control

• URL: http://arxiv.org/abs/2010.13178v2
• Date: Thu, 29 Oct 2020 12:19:11 GMT
• Title: Geometric Exploration for Online Control
• Authors: Orestis Plevrakis and Elad Hazan
• Abstract summary: We study the control of an emphunknown linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers.
• Score: 38.87811800375421
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the control of an \emph{unknown} linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers, which encompasses all stabilizing linear-dynamical-controllers. In this work, we first consider the case of known cost functions, for which we design the first polynomial-time algorithm with $n^3\sqrt{T}$-regret, where $n$ is the dimension of the state plus the dimension of control input. The $\sqrt{T}$-horizon dependence is optimal, and improves upon the previous best known bound of $T^{2/3}$. The main component of our algorithm is a novel geometric exploration strategy: we adaptively construct a sequence of barycentric spanners in the policy space. Second, we consider the case of bandit feedback, for which we give the first polynomial-time algorithm with $poly(n)\sqrt{T}$-regret, building on Stochastic Bandit Convex Optimization.

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