Relative to the large literature on upper bounds on complexity of convex
optimization, lesser attention has been paid to the fundamental hardness of
these problems. Given the extensive use of convex optimization in machine
learning and statistics, gaining an understanding of these complexity-theoretic
issues is important. In this paper, we study the complexity of stochastic
convex optimization in an oracle model of computation. We improve upon known
results and obtain tight minimax complexity estimates for various function
classes
