SCaLE: Switching Cost aware Learning and Exploration

This work addresses the fundamental problem of unbounded metric movement costs in bandit online convex optimization, by considering high-dimensional dynamic quadratic hitting costs and ${\mathrm{\ell }}_2$-norm switching costs in a noisy bandit feedback model. For a general class of stochastic environments, we provide the first algorithm SCaLE that provably achieves a distribution-agnostic sub-linear dynamic regret, without the knowledge of hitting cost structure. En-route, we present a novel spectral regret analysis that separately quantifies eigenvalue-error driven regret and eigenbasis-perturbation driven regret. Extensive numerical experiments, against online-learning baselines, corroborate our claims, and highlight statistical consistency of our algorithm.