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

NeurIPS 2026 · Learning theory and algorithms › Combinatorial and search optimization · approach: Multi-objective optimization · 0 citations (OpenAlex)

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Proposes SURF, a wrapper that resamples scalarization weights through the inverse of the normalized PF arc-length CDF, iteratively estimated for general problems, to achieve uniform Pareto front coverage.

Problem

Scalarization with uniformly spaced weights yields non-uniform coverage of the Pareto front; the goal is to obtain solutions uniformly spaced along the PF efficiently.

Approach

Treat the scalarization weight as a dial that traverses the PF at non-uniform speed; the normalized cumulative arc length defines a CDF on weights whose inverse yields equal-arc-length PF points. For general problems the CDF is reconstructed iteratively from chord lengths of warm-started scalarized solves.

Key results

• On DST, SURF improves HV by 2.11x over uniform weighting (3.87e-3 vs 1.83e-3) and reduces CV from 10.91e-1 to 0.81e-1 and Gap Ratio from 17.16 to 1.45.
• On Reddit summarization with Qwen2.5-0.5B, SURF gives HV 4.03 vs 3.76 for Uniform-w, and CV 0.30 vs 0.65 (2.2x lower).
• On Fishwood, CV drops from best baseline 0.194 to 0.026 while HV and IGD remain nearly identical to baselines.

Surprising findings

• Reward soup yields evenly spaced weights and low CV on DST but its solutions are suboptimal and off the PF, so spacing must be assessed alongside approximation quality.

Limitations

• Convergence guarantee is proven only for bi-objective linear scalarization under strong convexity-type and constraint regularity assumptions.
• Experiments are limited to bi-objective problems; extension to higher-dimensional fronts is future work.
• LLM experiments use a small 0.5B model and limited budget; UMOD, OLS and IGD omitted for LLM due to cost.

Experimental setup

Datasets: Reddit summarization DST Fishwood MO-Mountaincar

Benchmarks: DST Fishwood MO-Mountaincar Reddit summarization

Metrics: hypervolume IGD coefficient of variation gap ratio

Baselines: Uniform-w OLS UMOD Reward soup

Builds on: linear scalarization optimistic linear support UMOD PPO LoRA

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