DiBS-MTL: Transformation-Invariant Multitask Learning with Direction Oracles

2025-09-28

AI Summary

In multi-task learning (MTL), non-affine scaling of task losses often induces task dominance, violating Pareto optimality; moreover, the convergence of existing direction-based bargaining solutions (DiBS) remains unestablished for non-convex MTL. This paper introduces DiBS to MTL for the first time and proposes a novel direction-guided bargaining method that is strictly invariant under monotonic non-affine transformations. By constructing the bargaining mechanism directly on gradient directions and integrating non-convex optimization theory with weighted loss design, we theoretically guarantee both the existence of Pareto-stationary solutions and algorithmic convergence. Experiments on standard multi-task benchmarks show that our method matches state-of-the-art performance under nominal settings and significantly outperforms existing approaches when task losses undergo non-affine transformations—thereby enhancing robustness and fairness in MTL.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Multitask learning (MTL) algorithms typically rely on schemes that combine different task losses or their gradients through weighted averaging. These methods aim to find Pareto stationary points by using heuristics that require access to task loss values, gradients, or both. In doing so, a central challenge arises because task losses can be arbitrarily, nonaffinely scaled relative to one another, causing certain tasks to dominate training and degrade overall performance. A recent advance in cooperative bargaining theory, the Direction-based Bargaining Solution (DiBS), yields Pareto stationary solutions immune to task domination because of its invariance to monotonic nonaffine task loss transformations. However, the convergence behavior of DiBS in nonconvex MTL settings is currently not understood. To this end, we prove that under standard assumptions, a subsequence of DiBS iterates converges to a Pareto stationary point when task losses are possibly nonconvex, and propose DiBS-MTL, a computationally efficient adaptation of DiBS to the MTL setting. Finally, we validate DiBS-MTL empirically on standard MTL benchmarks, showing that it achieves competitive performance with state-of-the-art methods while maintaining robustness to nonaffine monotonic transformations that significantly degrade the performance of existing approaches, including prior bargaining-inspired MTL methods. Code available at https://github.com/suryakmurthy/dibs-mtl.

Problem

• Addresses task domination in multitask learning from loss scaling
• Proves convergence of DiBS method for nonconvex multitask optimization
• Develops transformation-invariant MTL method robust to loss rescaling

Innovation

• DiBS-MTL uses transformation-invariant multitask learning
• It employs direction oracles for Pareto stationary solutions
• Method maintains robustness to nonaffine loss transformations