Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation

Abstract

Online convex optimization with switching cost is considered under the frugal information setting where at time $t$, before action $x_t$ is taken, only a single function evaluation and a single gradient is available at the previously chosen action $x_{t-1}$ for either the current cost function $f_t$ or the most recent cost function $f_{t-1}$. When the switching cost is linear, online algorithms with optimal order-wise competitive ratios are derived for the frugal setting. When the gradient information is noisy, an online algorithm whose competitive ratio grows quadratically with the noise magnitude is derived.

arXiv comment9 pages, 2 figures