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Some of the most compelling applications of online convex optimization,including online prediction and classification, are unconstrained: the naturalfeasible set is R^n. Existing algorithms fail to achieve sub-linear regret inthis setting unless constraints on the comparator point x^* are known inadvance. We present algorithms that, without such prior knowledge, offernear-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 showingthat our guarantees are near-optimal in this setting.

No-Regret Algorithms for Unconstrained Online Convex Optimization