Fast Compute for ML Optimization

• URL: http://arxiv.org/abs/2602.14280v1
• Date: Sun, 15 Feb 2026 19:09:58 GMT
• Title: Fast Compute for ML Optimization
• Authors: Nick Polson, Vadim Sokolov,
• Abstract summary: We study optimization for losses that admit a variance-mean scale-mixture representation.<n>The resulting Scale Mixture EM (SM-EM) algorithm removes user-specified learning-rate and momentum schedules.<n>For the base (non-accelerated) algorithm, EM monotonicity guarantees nonincreasing objective values; adding Nesterov extrapolation trades this guarantee for faster empirical convergence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which latent variables determine observation and parameter weights; these play roles analogous to Adam's second-moment scaling and AdamW's weight decay, but are derived from the model. The resulting Scale Mixture EM (SM-EM) algorithm removes user-specified learning-rate and momentum schedules. On synthetic ill-conditioned logistic regression benchmarks with $p \in \{20, \ldots, 500\}$, SM-EM with Nesterov acceleration attains up to $13\times$ lower final loss than Adam tuned by learning-rate grid search. For a 40-point regularization path, sharing sufficient statistics across penalty values yields a $10\times$ runtime reduction relative to the same tuned-Adam protocol. For the base (non-accelerated) algorithm, EM monotonicity guarantees nonincreasing objective values; adding Nesterov extrapolation trades this guarantee for faster empirical convergence.

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