Fairness-Aware Meta-Learning via Nash Bargaining

TL;DR

This work addresses group-level fairness in meta-learning by identifying hypergradient conflicts that destabilize one-stage fairness optimization. It introduces a two-stage framework, Nash-Meta-Learning, where an early Nash Bargaining Solution (NBS) aggregates hypergradients to steer updates toward the Pareto front, followed by stage-specific optimization for a chosen fairness objective. The authors provide an independence-free derivation of the NBS for gradient aggregation, prove Pareto improvement and monotonic validation-loss improvement, and demonstrate empirical gains across six fairness datasets and two image tasks, with improvements up to 10% in overall performance and up to 67% in disparity reduction. The approach offers a principled, game-theoretic mechanism to reconcile competing subgroup objectives in fairness-aware learning and shows robustness to varying fairness notions and data conditions, while highlighting the importance of validation-set quality.

Abstract

To address issues of group-level fairness in machine learning, it is natural to adjust model parameters based on specific fairness objectives over a sensitive-attributed validation set. Such an adjustment procedure can be cast within a meta-learning framework. However, naive integration of fairness goals via meta-learning can cause hypergradient conflicts for subgroups, resulting in unstable convergence and compromising model performance and fairness. To navigate this issue, we frame the resolution of hypergradient conflicts as a multi-player cooperative bargaining game. We introduce a two-stage meta-learning framework in which the first stage involves the use of a Nash Bargaining Solution (NBS) to resolve hypergradient conflicts and steer the model toward the Pareto front, and the second stage optimizes with respect to specific fairness goals. Our method is supported by theoretical results, notably a proof of the NBS for gradient aggregation free from linear independence assumptions, a proof of Pareto improvement, and a proof of monotonic improvement in validation loss. We also show empirical effects across various fairness objectives in six key fairness datasets and two image classification tasks.

Figures (7)

• Figure 1: Overview: We illustrate the problem of hypergradient conflicts in conventional one-stage fairness-aware meta-learning, which we find can lead to erratic performance and/or convergence at suboptimal, unfair local minima. Left: Graphical depiction of group-wise hypergradient conflicts (I, II) showing different scenarios where conflicts arise in one-stage meta-learning, affecting performance stability; (III) provides a depiction of the contrast case where the aggregated direction is not conflicting with any of the groups, which leads to a more stable, fair, and performant model. Right: (a, b) Comparison of traditional one-stage meta-learning (Vanilla, highlighted in HTML]e8e8e8gray) with our proposed two-stage meta-learning approach, which resolves inter-group hypergradient conflicts through a bargaining process (Ours, highlighted in HTML]dfecc3green). In our evaluation, we show the efficacy of our method in enhancing fairness-aware meta-learning, with improvements in performance by up to 10% and fairness by up to 67%, by initially focusing on conflict resolution in Stage 1 to steer the model towards the Pareto front followed by focusing on fairness goals in Stage 2.
• Figure 2: The unreliable performance of conventional one-stage fairness-aware meta-learning.
• Figure 3: Synthetic illustration of the bargaining's effects. "➜": final point not close to the fairness goal (x=y). "➜": final point not at the Pareto front. (a) Bargaining across all 1000 steps; (b) Bargaining only included in the first 100 steps (two-stage method).
• Figure 4: Effects on hypergradient alignment (Bank Telemarketing). (a) Smallest $g_i^\top \nabla L_\beta$. Portion of positive values (Align. Rate) at the bottom. (b) Hypergradient alignment rate per epoch.
• Figure 5: Synthetic illustration of each gradient aggregation method in resolving gradient conflicts and their implication in converging to Pareto front. Red circles imply the nodes that cannot converge to the Pareto front after 1000 steps of updates.

Theorems & Definitions (23)

• Theorem 3.1
• Theorem 3.2
• Corollary 3.3
• Corollary 3.4
• Theorem 3.5
• Theorem 3.6
• Theorem 3.7
• Theorem
• proof
• Theorem