Abstract: The goal of Convex Bandit Optimization is to minimize a (stochastic/adversarial) sequence of convex functions, but in each round you are only allowed to query the function once. This is a challenging problem, as one has to build an estimator for an entire function based on single evaluations. In this talk, I will introduce this problem and some of the history that goes with it. I will also present a new algorithm reaching state-of-the-art high probability regret bound guarantees. This algorithm was developed in collaboration with Tor Lattimore, Jack Mayo and Dirk van der Hoeven.