PMGDA: A Preference-based Multiple Gradient Descent Algorithm

It is desirable in many multi-objective machine learning applications, such as multi-task learning and multi-objective reinforcement learning, to find a Pareto optimal solution that can exactly match a given preference of decision-makers. These problems are often large-scale with available gradient information but cannot be handled very well by the existing algorithms. To tackle this critical issue, this paper proposes a novel predict-and-correct framework for locating the exact Pareto optimal solutions required by a decision maker. In the proposed framework, a constraint function is introduced in the search progress to align the solution with a user-specific preference, which can be optimized simultaneously with multiple objective functions. Experimental results show that our proposed method can efficiently find exact Pareto optimal solutions for standard benchmarks, multi-task, and multi-objective reinforcement learning problems with more than thousands of decision variables. Code is available at: \url{https://github.com/xzhang2523/pmgda}.