Dangerous Liaisons of Convex Learning and Non-Affine Aggregation

arXiv:2606.28123v1 Announce Type: new Abstract: Last-iterate convergence and generalization guarantees in first-order convex learning hinge on the monotonicity of the update operator. While linear averaging preserves the monotonicity of gradient updates, this property is often violated when gradients are aggregated non-affinely, as in modern pipelines enforcing constraints like adaptivity, privacy, robustness or fairness. Whether it is possible to design non-affine aggregation rules that maintain monotonicity has remained an open question. We answer this question negatively: we prove that the

Source: arXiv cs.LG — read the full report at the original publisher.

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