[Paper Review] Pareto Multi-Task Learning

Xi Lin, Hui‐Ling Zhen+3 more|arXiv (Cornell University)|Dec 30, 2019

Advanced Multi-Objective Optimization AlgorithmsComputer Science52 citations

TL;DR

Pareto MTL decomposes a multi-task learning problem into multiple subproblems with different trade-off preferences to generate a diverse set of Pareto-optimal solutions that represent different task trade-offs.

ABSTRACT

Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with good trade-off among different tasks by casting multi-task learning as multiobjective optimization. In this paper, we generalize this idea and propose a novel Pareto multi-task learning algorithm (Pareto MTL) to find a set of well-distributed Pareto solutions which can represent different trade-offs among different tasks. The proposed algorithm first formulates a multi-task learning problem as a multiobjective optimization problem, and then decomposes the multiobjective optimization problem into a set of constrained subproblems with different trade-off preferences. By solving these subproblems in parallel, Pareto MTL can find a set of well-representative Pareto optimal solutions with different trade-off among all tasks. Practitioners can easily select their preferred solution from these Pareto solutions, or use different trade-off solutions for different situations. Experimental results confirm that the proposed algorithm can generate well-representative solutions and outperform some state-of-the-art algorithms on many multi-task learning applications.

Motivation & Objective

• Motivate the need for trade-off-aware multi-task learning due to conflicts between tasks.
• Address the limitation of a single optimal solution by generating a diverse Pareto set.
• Propose Pareto MTL to obtain well-representative Pareto solutions across trade-offs.
• Demonstrate applicability and performance gains on various multi-task learning problems.

Proposed method

• Formulate MTL as a multiobjective optimization and decompose it into K subproblems using a set of unit preference vectors.
• Define subregions in the objective space so each subproblem targets a different trade-off (Omega_k).
• Apply gradient-based methods to solve constrained multiobjective subproblems with a scalable dual formulation.
• Derive a scalable optimization approach by solving a reduced dual problem (in terms of Lagrange multipliers) rather than the full parameter space.
• Solve all subproblems in parallel to obtain a diverse set of Pareto-optimal solutions.
• Show that Pareto MTL corresponds to an adaptive linear scalarization with dynamic weights."],
• research_questions':['How can a MTL problem be decomposed into subproblems to cover diverse trade-offs among tasks?','Can we obtain a well-distributed set of Pareto solutions that represent different preferences without exhaustively searching weights?','How scalable is Pareto MTL when applied to large models and datasets?','How does Pareto MTL compare to state-of-the-art MTL approaches in terms of solution diversity and performance?'],
• key_findings':['Pareto MTL successfully generates a set of well-distributed Pareto-optimal solutions that represent different task trade-offs.','The method outperforms some state-of-the-art MTL algorithms on multiple applications.','Extreme-preference subproblems yield best performance for the corresponding task.','Experiments on MultiMNIST, MultiFashionMNIST, and self-driving localization demonstrate robust gains across tasks.','Subproblems can be solved in parallel, enabling scalable optimization for deep models.','The approach can be viewed as adaptive linear scalarization with weights determined by solving a dual constrained problem.'],
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Experimental results

Research questions

• RQ1 How can a MTL problem be decomposed into subproblems to cover diverse trade-offs among tasks?
• RQ2 Can a well-distributed set of Pareto solutions be obtained without exhaustive weight search?
• RQ3 How scalable is Pareto MTL for large models and datasets?
• RQ4 How does Pareto MTL compare to state-of-the-art MTL methods in terms of diversity and performance?

Key findings

• Pareto MTL yields a set of well-distributed Pareto-optimal solutions representing different task trade-offs.
• The method outperforms some state-of-the-art MTL approaches on multiple applications.
• Extreme-preference subproblems achieve best performance for their respective tasks.
• Experiments on MultiMNIST, MultiFashionMNIST, and autonomous driving localization show robust gains across tasks.
• Subproblems can be solved in parallel, enabling scalability for deep models.
• Pareto MTL can be viewed as an adaptive linear scalarization with dynamic weights determined by a dual formulation.