Towards Stability of Parameter-Free Optimization

Abstract

Hyperparameter tuning, particularly the selection of an appropriate learning rate in adaptive gradient training methods, remains a challenge. To address this challenge, we propose a novel parameter-free optimizer, \textsc{AdamG} (Adam with the Golden step size), designed to automatically adapt to diverse optimization problems without task-specific learning-rate 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 tuning-free convergence and approximate the optimal step size in expectation across diverse 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 \textsc{AdamG} outperforms other parameter-free baselines and consistently performs on par with Adam using a manually tuned learning rate across various optimization tasks.