No-Regret Algorithms for Unconstrained Online Convex Optimization¶
Authors: Matthew Streeter, H. Brendan McMahan
Published: 2012 ()
Algorithm: No-Regret OCO
arXiv: 1211.2260
Summary¶
Abstract¶
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this setting unless constraints on the comparator point x^* are known in advance. We present algorithms that, without such prior knowledge, offer near-optimal regret bounds with respect to any choice of x^*. In particular, regret with respect to x^* = 0 is constant. We then prove lower bounds showing that our guarantees are near-optimal in this setting.