Bandit Linear Control
This addresses the challenge of limited feedback in control systems for applications like robotics or autonomous systems, representing an incremental advance over full feedback settings.
The paper tackles the problem of controlling a known linear dynamical system with bandit feedback, where only the incurred cost is observed, and presents an efficient algorithm that achieves regret scaling with the square root of the time horizon T for strongly convex and smooth costs.
We consider the problem of controlling a known linear dynamical system under stochastic noise, adversarially chosen costs, and bandit feedback. Unlike the full feedback setting where the entire cost function is revealed after each decision, here only the cost incurred by the learner is observed. We present a new and efficient algorithm that, for strongly convex and smooth costs, obtains regret that grows with the square root of the time horizon $T$. We also give extensions of this result to general convex, possibly non-smooth costs, and to non-stochastic system noise. A key component of our algorithm is a new technique for addressing bandit optimization of loss functions with memory.