We study Online Lazy Gradient Descent for optimisation on a strongly convex domain. The algorithm is known to achieve $O(\sqrt N)$ regret against adversarial opponents; here we show it is universal in the sense that it also achieves $O(\log N)$ expected regret against i.i.d opponents.

We study Online Lazy Gradient Descent for optimisation on a strongly convex domain. The algorithm is known to achieve O(\sqrt N) regret against adversarial opponents; here we show it is universal in the sense that it also achieves O(\log N) expected regret against i.i.d opponents. In addition we show that, unlike for the simplex, order bounds for pseudo-regret and expected regret are equivalent for strongly convex domains.