## Joint Probability / Computer Science Theory Seminar

A lot of progress has been made in recent years on extending classical multi-armed bandit strategies to very large set of actions. A particularly challenging setting is the one where the action set is continuous and the underlying cost function is convex, this is the so-called bandit convex optimization (BCO) problem. I will tell the story of BCO and explain some of the new ideas that we recently developed to solve it. I will focus on three new ideas from our recent work http://arxiv.org/abs/1607.03084 with Yin Tat Lee and Ronen Eldan: (i) a new connection between kernel methods and the popular multiplicative weights strategy; (ii) a new connection between kernel methods and one of Erdos’ favorite mathematical object, the Bernoulli convolution, and (iii) a new adaptive (and increasing!) learning rate for multiplicative weights. These ideas could be of broader interest in learning/algorithm’s design.