Title: EE-Grad: Exploration and Exploitation for Cost-Efficient Mini-Batch SGD,
Abstract: We present a generic framework for trading off fidelity and cost in computing
stochastic gradients when the costs of acquiring stochastic gradients of
different quality are not known a priori. We consider a mini-batch oracle that
distributes a limited query budget over a number of stochastic gradients and
aggregates them to estimate the true gradient. Since the optimal mini-batch
size depends on the unknown cost-fidelity function, we propose an algorithm,
{\it EE-Grad}, that sequentially explores the performance of mini-batch oracles
and exploits the accumulated knowledge to estimate the one achieving the best
performance in terms of cost-efficiency. We provide performance guarantees for
EE-Grad with respect to the optimal mini-batch oracle, and illustrate these
results in the case of strongly convex objectives. We also provide a simple
numerical example that corroborates our theoretical findings.