用颜色精炼方法无损压缩凸风险最小化问题，提升求解效率。
Exact Instance Compression for Convex Empirical Risk Minimization via Color Refinement
- 基于颜色精炼实现凸ERM问题的无损压缩，适用于多种可微凸优化。
- 在多个回归与分类模型上验证，压缩后求解速度显著提升。
- 适合需要高效求解凸优化的机器学习研究者和工程师。
经验风险最小化（ERM）在计算上可能非常昂贵，即使在凸情况下，标准求解器的扩展性也较差。本文提出一种基于颜色精炼的新型无损压缩框架，将先前针对线性规划和凸二次规划的工作拓展至广泛的可微凸优化问题。我们为多种模型开发了具体算法，包括线性与多项式回归、二分类与多分类逻辑回归、带弹性网络正则化的回归，以及核方法如核岭回归和核逻辑回归。在代表性数据集上的数值实验表明该方法有效。
原文摘要 · Abstract (English)
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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