Poster
Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms
Peiyao Xiao · Hao Ban · Hao Ban · Kaiyi Ji
Great Hall & Hall B1+B2 (level 1) #1118
Abstract:
Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new direction-oriented multi-objective formulation by regularizing the common descent direction within a neighborhood of a direction that optimizes a linear combination of objectives such as the average loss in MTL or a weighted loss that places higher emphasis on some tasks than the others. This formulation includes GD and MGDA as special cases, enjoys the direction-oriented benefit as in CAGrad, and facilitates the design of stochastic algorithms. To solve this problem, we propose Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad) with simple SGD type of updates, and its variant SDMGrad-OS with an efficient objective sampling. We develop a comprehensive convergence analysis for the proposed methods with different loop sizes and regularization coefficients. We show that both SDMGrad and SDMGrad-OS achieve improved sample complexities to find an -accurate Pareto stationary point while achieving a small -level distance toward a conflict-avoidant (CA) direction. For a constant-level CA distance, their sample complexities match the best known without bounded function value assumption. Extensive experiments show that our methods achieve competitive or improved performance compared to existing gradient manipulation approaches in a series of tasks on multi-task supervised learning and reinforcement learning. Code is available at https://github.com/ml-opt-lab/sdmgrad.
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