Feasible Learning

TL;DR

Feasible Learning (FL) is a new training paradigm that ensures models meet performance thresholds on every sample, leading to improved tail behavior and robustness compared to traditional ERM, with practical applications across various domains.

Contribution

The paper introduces Feasible Learning, a novel sample-centric training framework that emphasizes individual sample performance and proposes a primal-dual optimization approach with slack variables.

Findings

Models trained with FL show improved tail behavior.

FL achieves comparable average performance to ERM.

Empirical results across multiple tasks validate FL's effectiveness.

Abstract

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.