SURF: Steering the Scalarization Weight to Uniformly Traverse the Pareto Front

Scalarization is widely used in multi-objective optimization for its simplicity and scalability. Many applications seek solutions that span diverse preferences and uniformly cover the Pareto front (PF), yet uniform scalarization weights generally produce non-uniform coverage. We explain this mismatch geometrically: as the weight varies, scalarized solutions traverse the PF at non-uniform speed. This speed induces an arc-length cumulative distribution function (CDF), whose inverse provides a principled rule for selecting weights with uniform PF coverage. Building on this insight, we propose SURF (Sampling Uniformly along the Pareto Front). For structured problems, including bi-objective bandits, we derive closed-form CDF expressions and PF-aware weights; for general problems, SURF alternates CDF reconstruction and weight sampling while retaining the underlying solver. Under standard regularity conditions, we prove linear convergence to an unavoidable finite-sampling floor. Experiments on bandits, MO-Gymnasium, and multi-objective LLM alignment show that SURF improves PF uniformity and approximation quality over representative baselines.