Exact Instance Compression for Convex Empirical Risk Minimization via Color Refinement

• URL: http://arxiv.org/abs/2602.00437v1
• Date: Sat, 31 Jan 2026 01:17:08 GMT
• Title: Exact Instance Compression for Convex Empirical Risk Minimization via Color Refinement
• Authors: Bryan Zhu, Ziang Chen,
• Abstract summary: Empirical quadratic risk ERM (ERM) can be computationally expensive.<n>We propose a novel compression framework for convex minimization based on color refinement.
• Score: 12.6630190876621
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior work from linear programs and convex quadratic programs to a broad class of differentiable convex optimization problems. We develop concrete algorithms for a range of models, including linear and polynomial regression, binary and multiclass logistic regression, regression with elastic-net regularization, and kernel methods such as kernel ridge regression and kernel logistic regression. Numerical experiments on representative datasets demonstrate the effectiveness of the proposed approach.

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