Projection-Free Bandit Convex Optimization

In this paper, we propose the first computationally efficient projection-free algorithm for the bandit convex optimization (BCO). We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the dimension) for any bounded convex functions with uniformly bounded gradients. We also evaluate the performance of our algorithm against prior art on both synthetic and real data sets for portfolio selection and multiclass classification problems.