A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions

• URL: http://arxiv.org/abs/2605.19306v1
• Date: Tue, 19 May 2026 03:37:22 GMT
• Title: A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions
• Abstract summary: We address the open problem of training hypernetworks under split feasibility conditions with rigorous theoretical guarantees.<n>We 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.<n>ABP-HyperNet achieves up to 2.3x higher Expected Feasible Hypervolume (EFHV) than unconstrained baselines by raising feasibility from 36-49% to 87-100%.
• Score: 5.297898316219452
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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