SILAGE: Memory-Efficient, Full-Gradient-Free Nonconvex Optimization for Nested Finite Sums

2026-06-14 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

SILAGE is a new variance-reduced algorithm designed for memory-efficient, full-gradient-free nonconvex optimization, specifically targeting empirical risk minimization on massive datasets with a nested double finite-sum structure. This structure involves N=nm total samples partitioned into n blocks of size m. Unlike recursive estimators such as PAGE, which demand computationally expensive periodic global full-gradient refreshes over all nm samples, SILAGE eliminates these refreshes by evaluating at most one local group gradient per iteration. Furthermore, it significantly reduces memory requirements to only ℮(n), contrasting with single-loop methods like SILVER that need an impractical ℮(nm) memory footprint. SILAGE's convergence analysis adapts to data geometry through across-group (δ₁) and within-group (δ₂) heterogeneity, yielding improved bounds over existing methods in several practical scenarios.

Key takeaway

For Machine Learning Engineers optimizing models on massive, nested datasets, SILAGE offers a compelling alternative to traditional variance-reduced methods. You can achieve efficient nonconvex optimization with only ℮(n) memory, avoiding costly global full-gradient refreshes. This allows you to scale training processes more effectively, especially with data partitioned into n blocks of size m, without the impractical ℮(nm) memory overhead of other single-loop approaches.

Key insights

SILAGE optimizes nested finite sums with ℮(n) memory and no global full-gradient refreshes, adapting to data heterogeneity.

Principles

• Exploiting nested data structure improves efficiency.
• Data geometry (heterogeneity) impacts convergence.
• Variance reduction can be memory-efficient.

Method

SILAGE is a variance-reduced algorithm that exploits a double-sum structure, evaluating at most one local group gradient per iteration to avoid global full-gradient refreshes while maintaining ℮(n) memory.

In practice

• Optimize large datasets with nested structures.
• Reduce memory footprint for nonconvex problems.
• Improve convergence in heterogeneous data.

Topics

• Nonconvex Optimization
• Variance Reduction
• Nested Finite Sums
• Memory Efficiency
• Empirical Risk Minimization
• Gradient-Free Optimization

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.