arXiv:2602.23360cs.LGcs.AI2026-02

通过锚定平均模型,统一证明四种算法可让模型分歧趋近于零。

Model Agreement via Anchoring

  • 用两模型平均作为锚点,推导独立训练模型的预测差异上限。
  • 在四种常见算法中,分歧随模型数量、迭代次数、架构规模或树深增加而趋于零。
  • 方法适用于多维回归与强凸损失,适合研究模型稳定性的学者参考。

针对机器学习中模型分歧问题,本文提出一种基于锚定(anchoring)的通用分析技术,用于控制两个独立训练模型在实值预测任务中的期望平方预测差异。该方法通过将分析锚定在两模型平均上,可统一推导出四类常见算法的分歧界:(1) 任意模型类的堆叠聚合(分歧随堆叠模型数k增加趋近0);(2) 梯度提升(分歧随迭代次数k增加趋近0);(3) 带架构搜索的神经网络训练(分歧随优化架构大小n增加趋近0);(4) 固定深度回归树的训练(分歧随树深d增加趋近0)。分析初始设定为一维回归与平方损失,但结果可推广至多维回归及任意强凸损失函数。

原文摘要 · Abstract (English)

Numerous lines of aim to control $\textit{model disagreement}$ -- the extent to which two machine learning models disagree in their predictions. We adopt a simple and standard notion of model disagreement in real-valued prediction problems, namely the expected squared difference in predictions between two models trained on independent samples, without any coordination of the training processes. We would like to be able to drive disagreement to zero with some natural parameter(s) of the training procedure using analyses that can be applied to existing training methodologies. We develop a simple general technique for proving bounds on independent model disagreement based on $\textit{anchoring}$ to the average of two models within the analysis. We then apply this technique to prove disagreement bounds for four commonly used machine learning algorithms: (1) stacked aggregation over an arbitrary model class (where disagreement is driven to 0 with the number of models $k$ being stacked) (2) gradient boosting (where disagreement is driven to 0 with the number of iterations $k$) (3) neural network training with architecture search (where disagreement is driven to 0 with the size $n$ of the architecture being optimized over) and (4) regression tree training over all regression trees of fixed depth (where disagreement is driven to 0 with the depth $d$ of the tree architecture). For clarity, we work out our initial bounds in the setting of one-dimensional regression with squared error loss -- but then show that all of our results generalize to multi-dimensional regression with any strongly convex loss.

模型分歧理论分析集成学习梯度提升

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