Optimizing Optimizers for Fast Gradient-Based Learning

2025-12-06

AI Summary

This work addresses the reliance on empirical design and poor generalizability of hand-crafted optimizers in gradient-based learning. Methodologically, it formulates the optimizer as a learnable functional mapping from gradients to parameter updates, and—novelty—systematically recasts this as a sequence of analytically solvable convex optimization problems. This unified framework yields closed-form derivations of mainstream optimizers (e.g., SGD, Adam) along with their theoretically optimal hyperparameters. Furthermore, it incorporates a runtime gradient statistics mechanism enabling dynamic, adaptive tuning during training. Experiments demonstrate substantial improvements in convergence speed and training stability, while preserving theoretical rigor and practical deployability.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

We lay the theoretical foundation for automating optimizer design in gradient-based learning. Based on the greedy principle, we formulate the problem of designing optimizers as maximizing the instantaneous decrease in loss. By treating an optimizer as a function that translates loss gradient signals into parameter motions, the problem reduces to a family of convex optimization problems over the space of optimizers. Solving these problems under various constraints not only recovers a wide range of popular optimizers as closed-form solutions, but also produces the optimal hyperparameters of these optimizers with respect to the problems at hand. This enables a systematic approach to design optimizers and tune their hyperparameters according to the gradient statistics that are collected during the training process. Furthermore, this optimization of optimization can be performed dynamically during training.

Problem

• Automating optimizer design in gradient-based learning
• Maximizing instantaneous loss decrease via optimizer formulation
• Dynamically tuning hyperparameters based on gradient statistics

Innovation

• Automating optimizer design via greedy principle
• Formulating optimizer design as convex optimization problems
• Dynamically tuning hyperparameters using gradient statistics