AdaGrad-Diff: A New Version of the Adaptive Gradient Algorithm

Agentic AI

Published: arXiv: 2602.13112v1

Authors

Matia Bojovic Saverio Salzo Massimiliano Pontil

Abstract

Vanilla gradient methods are often highly sensitive to the choice of stepsize, which typically requires manual tuning. Adaptive methods alleviate this issue and have therefore become widely used. Among them, AdaGrad has been particularly influential. In this paper, we propose an AdaGrad-style adaptive method in which the adaptation is driven by the cumulative squared norms of successive gradient differences rather than gradient norms themselves. The key idea is that when gradients vary little across iterations, the stepsize is not unnecessarily reduced, while significant gradient fluctuations, reflecting curvature or instability, lead to automatic stepsize damping. Numerical experiments demonstrate that the proposed method is more robust than AdaGrad in several practically relevant settings.

Paper Summary

Problem

Optimization algorithms, such as Gradient Descent, are widely used in machine learning. However, choosing the right step size is often a challenge, as it can affect the convergence speed and stability of the algorithm. Researchers have been working on developing adaptive gradient methods that can automatically adjust the step size, but these methods still have limitations.

Key Innovation

The researchers propose a new adaptive gradient algorithm, called AdaGrad-Diff, which is inspired by the stability considerations in practice. Instead of accumulating the squared norms of gradients, AdaGrad-Diff computes the cumulative sums of squared gradient differences. This approach aims to reduce the sensitivity to hyperparameter tuning and improve the robustness of the algorithm.

Practical Impact

The proposed algorithm, AdaGrad-Diff, has several practical implications. It can be applied to various optimization problems, including convex and non-convex objectives. By reducing the sensitivity to hyperparameter tuning, AdaGrad-Diff can lead to more robust and efficient optimization processes. This, in turn, can improve the performance of machine learning models and reduce the need for extensive hyperparameter tuning.

Analogy / Intuitive Explanation

Imagine you're trying to find the optimal solution to a complex puzzle. The puzzle has many pieces that need to be adjusted to fit together perfectly. In this case, the step size is like the amount of force you apply to each piece to move it into place. If you apply too much force, the piece might break or get stuck, while too little force might not move it at all. AdaGrad-Diff is like a smart puzzle solver that adjusts the force it applies to each piece based on how much it has moved so far, rather than relying on a fixed amount of force. This approach can help the solver find the optimal solution more efficiently and effectively.

Paper Information

Categories:

stat.ML cs.LG math.OC

Published Date:

arXiv ID:

2602.13112v1

Quick Actions

Back to Home