PMGDA: A Preference-based Multiple Gradient Descent Algorithm

TL;DR

PMGDA is a novel algorithm that efficiently finds Pareto solutions aligned with specific preferences in large-scale multi-objective problems, improving upon existing methods by incorporating a predict-and-correct framework with a constraint-based search.

Contribution

The paper introduces a new predict-and-correct framework with a preference-aligned constraint function for locating Pareto solutions in large-scale multi-objective optimization.

Findings

Successfully applied to multi-task learning and reinforcement learning problems

Handles problems with over a thousand decision variables

Outperforms existing algorithms in preference-based Pareto solution finding

Abstract

It is desirable in many multi-objective machine learning applications, such as multi-task learning with conflicting objectives and multi-objective reinforcement learning, to find a Pareto solution that can match a given preference of a decision maker. 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 a Pareto solution that fits the preference of 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 a particular Pareto solution under the demand of a decision maker for standard multiobjective benchmark, multi-task learning, and multi-objective reinforcement learning problems with more than thousands of decision variables. Code is available at: https://github.com/xzhang2523/pmgda. Our code is current provided in the pgmda.rar attached file and will be open-sourced after publication.}