Title: RobGrad: Robustness-driven gradient descent for stochastic multi-objective optimization
Primary area: optimization
Keywords: Stochastic multi-objective optimization, Multi-task learning, Pareto stationarity

Abstract: Stochastic multi-objective optimization (SMOO) has become an influential framework for many machine learning problems with multiple objectives, where the gradient conflict problem is a fundamental bottleneck for effective training of models. Most existing methods address this problem with gradient-based approaches, which find an optimization direction that improves each objective through gradient manipulation techniques. However, these methods are based on instantaneous gradients and lack a global optimization perspective, which may lead to suboptimal solutions. In this paper, we consider minimizing the worst-case objective value from a global optimization perspective and transform the SMOO problem into a min-max optimization problem. Further, theoretical correspondences between this min-max problem and the SMOO problem are established. Based on this, we propose a robustness-driven gradient descent (RobGrad) algorithm. RobGrad guarantees that each objective performs not badly from a global perspective without introducing additional a priori parameters. Furthermore, we establish non-asymptotic convergence upper bounds for RobGrad in both convex and non-convex settings, which portray the expected performance gap under the worst weight assignment and the rate of RobGrad's decision approaching a Pareto stationary solution. Extensive experiments show that RobGrad has competitive or improved performance compared to state-of-the-art SMOO methods in a series of tasks on multi-task learning.