# Avoiding Structural Failure Modes in Tabular Fair SSL: Online Primal-Dual Allocation under Confidence Gating

arXiv: https://arxiv.org/abs/2605.16446 · HTML: https://mlsanity.com/paper/2605.16446/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 18 of 18)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [SoftMatch: Addressing the Quantity-Quality Trade-off in Semi-supervised Learning](https://mlsanity.com/paper/2301.10921/) (2023)
- [Online Learning Rate Adaptation with Hypergradient Descent](https://mlsanity.com/paper/1703.04782/) (2017)
- [Fairness, Semi-Supervised Learning, and More: A General Framework for Clustering with Stochastic Pairwise Constraints](https://mlsanity.com/paper/2103.02013/) (2021)
- [YellowFin and the Art of Momentum Tuning](https://mlsanity.com/paper/1706.03471/) (2017)
- [Don't fear the unlabelled: safe semi-supervised learning via simple debiasing](https://mlsanity.com/paper/2203.07512/) (2022)
- [SimFair: A Unified Framework for Fairness-Aware Multi-Label Classification](https://mlsanity.com/paper/2302.09683/) (2023)

## Abstract (arXiv)

Semi-supervised learning (SSL) enables prediction with limited labels, but high-stakes tabular applications (medical, credit, recidivism) require statistical fairness guarantees. We identify a structural conflict in tabular fair SSL through a diagnostic stress test: under confidence-gated pseudo-labeling, moment-matching fairness regularizers can trigger two failure modes -- Masking Collapse (fairness erodes confidence, starving pseudo-labels) and Trivial Saturation (drift to constant predictors). We propose Online Primal-Dual Allocation (OPDA), an online controller that schedules fairness and entropy-based stability penalties using violation, risk, and pseudo-label health signals, avoiding per-dataset selection of a fixed fairness weight within this diagnostic regime. On the evaluated tabular benchmarks (Adult, ACSIncome, COMPAS), OPDA mitigates the degenerate regimes observed under static weighting and simple single-signal adaptive baselines. On Adult and COMPAS, it yields non-degenerate operating points competitive with the empirical static-λ frontier; on ACSIncome, it preserves utility with a wider fairness-utility spread. Relative to OPDA-lite, the full controller mainly shifts the operating point toward higher utility on ACSIncome, while Adult highlights the fairness-utility trade-off between the two variants. These results position OPDA as a calibration-free controller for non-degenerate operating points in tabular fair SSL without per-dataset tuning.