Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics

Abstract: We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal $\sqrt{T}$ regret-rate compared to the best stabilizing linear controller in hindsight. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.