# EE-Grad: Exploration and Exploitation for Cost-Efficient Mini-Batch SGD

## TL;DR

EE-Grad introduces a framework for balancing cost and fidelity in stochastic gradient computation, optimizing mini-batch size adaptively to improve cost-efficiency in stochastic gradient descent.

## Contribution

The paper proposes EE-Grad, an adaptive algorithm that explores and exploits mini-batch oracles to optimize cost-efficiency without prior knowledge of cost-fidelity relationships.

## Key findings

- EE-Grad achieves near-optimal cost-efficiency in gradient estimation.
- Theoretical guarantees are provided for strongly convex objectives.
- Numerical experiments validate the theoretical results.

## 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.