# Surrogate Losses for Online Learning of Stepsizes in Stochastic Non-Convex Optimization

## TL;DR

This paper introduces surrogate loss functions that enable online learning of adaptive stepsizes for stochastic gradient descent in non-convex optimization, improving convergence without manual tuning.

## Contribution

It proposes a novel surrogate loss framework that casts stepsize selection as an online convex optimization problem, allowing automatic, theoretically-guaranteed adaptation.

## Key findings

- Achieves convergence rates adaptive to noise levels.
- Provides a self-tuning SGD algorithm with theoretical guarantees.
- Reduces the need for manual stepsize tuning in practice.

## Abstract

Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate this problem. They have proved efficient in reducing the labor of tuning in practice, but many of them lack theoretic guarantees even in the convex setting. In this paper, we propose new surrogate losses to cast the problem of learning the optimal stepsizes for the stochastic optimization of a non-convex smooth objective function onto an online convex optimization problem. This allows the use of no-regret online algorithms to compute optimal stepsizes on the fly. In turn, this results in a SGD algorithm with self-tuned stepsizes that guarantees convergence rates that are automatically adaptive to the level of noise.