"Feasible Learning"

Feasible Learning: where every data point gets its fair share of performance.

This paper addresses the limitation of Empirical Risk Minimization (ERM) which optimizes for average performance and may neglect individual data points. Feasible Learning (FL) is introduced to ensure satisfactory performance across all training samples, offering a sample-centric alternative to ERM.

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Paper - arxiv. org/abs/2501.14912

Original Problem 😕:

→ Empirical Risk Minimization (ERM) aims for best average performance.

→ ERM can overlook poor performance on individual data samples.

→ In scenarios like personalized recommendations, consistent performance for each user is crucial, not just average performance.

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Solution in this Paper 💡:

→ Feasible Learning (FL) is proposed as a new learning framework.

→ FL formulates learning as a feasibility problem.

→ FL seeks a predictor that achieves a bounded loss for every training sample.

→ Resilient Feasible Learning (RFL) is introduced to handle cases where FL constraints are too strict and no feasible solution exists.

→ RFL relaxes constraints using slack variables and minimizes the magnitude of these relaxations.

→ Both FL and RFL are solved using a primal-dual optimization approach with Lagrange multipliers, dynamically weighting each sample's importance during training.

→ The method uses gradient descent ascent on a Lagrangian formulation, making it computationally efficient, similar to ERM.

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Key Insights from this Paper 🧐:

→ FL is inherently sample-centric, ensuring a minimum performance level for each data point, unlike ERM's average-centric approach.

→ FL introduces functional regularization by bounding the loss itself, preventing over-minimization of loss beyond a threshold.

→ RFL enhances FL's robustness by handling infeasible constraint settings, making it more practical.

→ Lagrange multipliers in FL and RFL dynamically re-weight data points, highlighting difficult samples and reducing the influence of easy samples.

→ FL yields a more concentrated loss distribution compared to ERM, reducing the occurrence of very high losses, especially in the tail distribution.

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Results 📊:

→ FL and RFL achieve comparable average performance to ERM on CIFAR10, UTKFace, and Direct Preference Optimization (DPO) tasks.

→ RFL outperforms FL in scenarios where FL constraints are infeasible, like in UTKFace age regression with strict constraints.

→ FL and RFL show improved tail behavior in loss distribution compared to ERM, reducing the frequency of high losses, as shown in DPO experiments with Llama3-8B.