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

arXiv: https://arxiv.org/abs/1901.09068 · HTML: https://mlsanity.com/paper/1901.09068/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion](https://mlsanity.com/paper/2302.03775/) (2023)
- [Gradient Methods with Online Scaling Part I. Theoretical Foundations](https://mlsanity.com/paper/2505.23081/) (2025)
- [Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles](https://mlsanity.com/paper/2607.17607/) (2026)

## Abstract (arXiv)

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.