A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions
For researchers in multi-objective optimization and multi-task learning, this work provides a theoretically grounded method to enforce constraints in Pareto front learning, addressing a key limitation of existing approaches.
The paper tackles the open problem of training hypernetworks for Controllable Pareto Front Learning under split feasibility conditions, proposing the Adaptive Balanced Penalty (ABP) algorithm with theoretical convergence guarantees. Experiments show ABP-HyperNet achieves up to 2.3x higher Expected Feasible Hypervolume than unconstrained baselines, raising feasibility from 36-49% to 87-100%.
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%.