STOCHASTIC CONVEX OPTIMIZATION WITH BANDIT FEEDBACK

This paper addresses the problem of minimizing a convex, Lipschitz function f over a convex, compact set X under a stochastic bandit (i.e., noisy zeroth-order) feedback model. In this model, the algorithm is allowed to observe noisy realizations of the function value f(x) at any query point x is an element of X. The quantity of interest is the regret of the algorithm, which is the sum of the function values at algorithm's query points minus the optimal function value. We demonstrate a generalization of the ellipsoid algorithm that incurs (O) over tilde (poly(d)root T) regret. Since any algorithm has regret at least Omega(root T) on this problem, our algorithm is optimal in terms of the scaling with T.