Multi-Objective Bilevel Learning

TL;DR

This paper introduces a novel algorithmic framework for multi-objective bilevel learning, enabling efficient Pareto front exploration and convergence guarantees in complex ML problems with conflicting objectives.

Contribution

It develops the WC-MHGD framework for MOBL, providing convergence guarantees and systematic Pareto front exploration in both deterministic and stochastic settings.

Findings

The proposed WC-MHGD algorithm achieves low oracle complexity.

The framework guarantees finite-time Pareto-stationarity convergence.

Experiments confirm theoretical convergence and Pareto front exploration capabilities.

Abstract

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.