Spectral risk-based learning using unbounded losses

TL;DR

This paper introduces a spectral risk-based learning framework that effectively handles unbounded heavy-tailed losses, providing theoretical guarantees and an efficient implementation that improves risk management and classification accuracy.

Contribution

It develops excess risk guarantees for derivative-free learning under heavy-tailed losses and proposes a computationally efficient method that outperforms traditional risk minimizers.

Findings

Empirical results show improved balance between spectral risk and misclassification error.

Theoretical guarantees establish excess risk bounds for the proposed method.

Efficient implementation demonstrates practical viability in heavy-tailed loss scenarios.

Abstract

In this work, we consider the setting of learning problems under a wide class of spectral risk (or "L-risk") functions, where a Lipschitz-continuous spectral density is used to flexibly assign weight to extreme loss values. We obtain excess risk guarantees for a derivative-free learning procedure under unbounded heavy-tailed loss distributions, and propose a computationally efficient implementation which empirically outperforms traditional risk minimizers in terms of balancing spectral risk and misclassification error.