提出自适应惩罚方法，实现约束下多目标优化的高效学习。
A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions
- 设计双阶段可行性优先训练策略，动态调整梯度权重。
- 在5个基准上验证，可行性从36%-49%提升至87%-100%，性能提升2.3倍。
- 适用于多任务学习中的约束优化问题，尤其适合需高可行性场景。
针对分裂可行性条件下超网络训练中可控帕累托前沿学习（CPFL）的开放问题，本文将约束帕累托问题重构为双层标量化分裂问题（BSSP），提出自适应平衡惩罚（ABP）算法。该算法通过可计算的下界驱动自适应指示器，融合最优性、集合可行性和像可行性三类梯度分量。借助新颖的凸代理技术，在标准凸性与Robbins-Monro步长假设下证明了全序列收敛性。进一步将ABP惩罚结构转化为超MLP与超Trans架构的两阶段可行性优先训练策略（ABP-HyperNet）。为评估约束下的CPFL，引入期望可行超体积（EFHV），综合衡量解的质量与约束满足程度。在五个多目标基准测试中，ABP求解器逼近真实帕累托前沿；在三个多任务学习数据集上，ABP-HyperNet相较无约束基线，使EFHV最高提升2.3倍，可行性从36%-49%提升至87%-100%。
原文摘要 · Abstract (English)
We address the open problem of training hypernetworks for Controllable Pareto Front Learning (CPFL) under split feasibility conditions with rigorous theoretical guarantees. We reformulate the constrained Pareto problem as a Bi-Level Scalarized Split Problem (BSSP) and propose the Adaptive Balanced Penalty (ABP) algorithm, whose three gradient components -- optimality, set feasibility, and image feasibility -- are blended through an adaptive indicator driven by a computable lower bound. Using a novel convex surrogate technique, we prove full-sequence convergence under standard convexity and Robbins-Monro step-size assumptions. The ABP penalty structure is then translated into a two-phase, feasibility-first training strategy for Hyper-MLP and HyperTrans architectures (ABP-HyperNet). To evaluate constrained CPFL, we introduce the Expected Feasible Hypervolume (EFHV), which jointly captures solution quality and constraint satisfaction. Experiments on five multi-objective benchmarks validate the ABP solver against ground truth, while three multi-task learning datasets demonstrate that ABP-HyperNet achieves up to 2.3x higher EFHV than unconstrained baselines by raising feasibility from 36-49% to 87-100%.
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