Bandit smooth convex optimization: Improving the bias-variance tradeoff

Bandit convex optimization is one of the fundamental problems in the field of online learning. The best algorithm for the general bandit convex optimization problem guarantees a regret of Õ(T^5/6), while the best known lower bound is Ω(T^1/2). Many attempts have been made to bridge the huge gap between these bounds. A particularly interesting special case of this problem assumes that the loss functions are smooth. In this case, the best known algorithm guarantees a regret of Õ(T^2/3). We present an efficient algorithm for the bandit smooth convex optimization problem that guarantees a regret of Õ(T^5/8). Our result rules out an Ω(T^2/3) lower bound and takes a significant step towards the resolution of this open problem.