提出高效算法解决多目标分层优化问题，可精准探索最优权衡解。
Multi-Objective Bilevel Learning
- 基于加权切比雪夫法设计多梯度下降框架，统一处理确定与随机场景。
- 在有限步内实现帕累托平稳收敛，且对解集探索具有系统性。
- 适合需权衡多个冲突目标的复杂模型训练，如公平性与性能平衡。
近年来，机器学习应用日趋复杂，现代框架常需在多层耦合决策变量下处理多个可能冲突的目标，这催生了多目标分层学习（MOBL）的需求。然而，该领域仍处于萌芽阶段，诸多关键问题尚未被深入研究。为此，本文系统地建立MOBL的理论与算法基础：考虑上层偏好引导、下层解影响输入的多目标分层问题，目标是开发高效算法，实现(1)低查询复杂度的偏好引导帕累托平稳解；(2)系统的帕累托前沿探索。我们提出统一算法框架——加权-切比雪夫多超梯度下降（WC-MHGD），适用于确定与随机情形，并提供有限时间帕累托平稳收敛速率保证，不仅降低查询复杂度，还促进帕累托前沿的系统探索。大量实验验证了理论结果的有效性。
原文摘要 · Abstract (English)
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.
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