We present a framework to train a structured prediction model by performing smoothing ontheinference algorithm itbuilds upon.

But despite its wide applicability (see 2.2) and elegance, convergence theory for CCCP is quite limited.

W = 2for = 10 2and = 10 4, omitted architectures.

In 1weintroduce ourmotivations, ourmain results and discuss the related work.

Owing to their stability and convergence speed, extragradient methods have become astaple forsolving large-scale saddle-point problems inmachine learning.

Inthis methods families optimization 71], etc. canbe between Non-nested In variables stochastic are x/ p

However, there are relatively few results outside of these settings.

Thank you for your suggestion of comparing against other methods.

Thank you for your suggestion of comparing against other methods.

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.