Beyond the Reference Trap: Adaptive Reverse Tchebycheff Scalarization for Pareto Set Learning in Expensive Multi-Objective Optimization

Pareto set learning (PSL) learns a continuous mapping from preference vectors to Pareto-optimal solutions, providing an appealing approach to expensive multi-objective optimization under limited evaluation budgets. Most existing scalarization-based PSL methods typically estimate reference points from the evaluated archive. We show that this simple design choice can induce an initialization-dependent reference geometry that restricts Pareto-front exploration: when the archive covers only a local portion of the front, the resulting scalarization can bias the learned solutions toward the observed region and make unexplored trade-offs difficult to reach. We refer to this failure as the reference trap. To address it, we propose Adaptive Reference Geometry for PSL, instantiated through Adaptive Reverse Tchebycheff (AdaRevTche). Instead treating the reference as a fixed archive statistic, AdaRevTche jointly learns the Pareto-set mapping and a bounded worse-side reference, allowing the scalarization geometry to adapt as optimization proceeds. We establish an exact result showing how the reference point restricts the reachable region in two-objective Tchebycheff scalarization, and analyze the corresponding geometric behavior for problems with more objectives. Results on 12 real-world and synthetic problems demonstrate the effectiveness of our AdaRevTche. Notably, compared with the SoTA PSL baseline, CDM-PSL, AdaRevTche reduces the hypervolume difference on RE41 by 51.8%.