Towards Stability of Parameter-free Optimization

TL;DR

This paper introduces AdamG, a new parameter-free optimizer that automatically adapts to different problems, eliminating the need for manual learning rate tuning, and demonstrates superior or comparable performance to traditional optimizers.

Contribution

The paper proposes a novel parameter-free optimizer, AdamG, based on a golden step size derived for AdaGrad-Norm, and introduces a new evaluation criterion, reliability, for tuning-free optimization methods.

Findings

AdamG outperforms other parameter-free optimizers.

AdamG matches the performance of tuned Adam across tasks.

Reliability metric effectively assesses tuning-free optimizer efficacy.

Abstract

Hyperparameter tuning, particularly the selection of an appropriate learning rate in adaptive gradient training methods, remains a challenge. To tackle this challenge, in this paper, we propose a novel parameter-free optimizer, \textsc{AdamG} (Adam with the golden step size), designed to automatically adapt to diverse optimization problems without manual tuning. The core technique underlying \textsc{AdamG} is our golden step size derived for the AdaGrad-Norm algorithm, which is expected to help AdaGrad-Norm preserve the tuning-free convergence and approximate the optimal step size in expectation w.r.t. various optimization scenarios. To better evaluate tuning-free performance, we propose a novel evaluation criterion, \textit{reliability}, to comprehensively assess the efficacy of parameter-free optimizers in addition to classical performance criteria. Empirical results demonstrate that compared with other parameter-free baselines, \textsc{AdamG} achieves superior performance, which is consistently on par with Adam using a manually tuned learning rate across various optimization tasks.