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Exact Pareto Optimal Search for Multi-Task Learning: Touring the Pareto Front

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 Added by Debabrata Mahapatra
 Publication date 2021
and research's language is English




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Multi-Task Learning (MTL) is a well-established paradigm for training deep neural network models for multiple correlated tasks. Often the task objectives conflict, requiring trade-offs between them during model building. In such cases, MTL models can use gradient-based multi-objective optimization (MOO) to find one or more Pareto optimal solutions. A common requirement in MTL applications is to find an {it Exact} Pareto optimal (EPO) solution, which satisfies user preferences with respect to task-specific objective functions. Further, to improve model generalization, various constraints on the weights may need to be enforced during training. Addressing these requirements is challenging because it requires a search direction that allows descent not only towards the Pareto front but also towards the input preference, within the constraints imposed and in a manner that scales to high-dimensional gradients. We design and theoretically analyze such search directions and develop the first scalable algorithm, with theoretical guarantees of convergence, to find an EPO solution, including when box and equality constraints are imposed. Our unique method combines multiple gradient descent with carefully controlled ascent to traverse the Pareto front in a principled manner, making it robust to initialization. This also facilitates systematic exploration of the Pareto front, that we utilize to approximate the Pareto front for multi-criteria decision-making. Empirical results show that our algorithm outperforms competing methods on benchmark MTL datasets and MOO problems.



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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.
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