Beyond Scalar Leaderboards: Adaptive Sampling for Pareto Frontier Identification in Multi-Objective LLM Arenas

The evaluation of large language models (LLMs) is inherently multi-objective, as different models may offer different tradeoffs across performance dimensions such as math, code, and writing. Because such evaluations are often based on costly and time-consuming human feedback, it is important to draw reliable conclusions using as few comparisons as possible. In this paper, we present Vector-Borda Empirical-Gap Elimination (VB-EGE), a fixed-confidence adaptive sampling algorithm for efficiently identifying models on the Pareto frontier in arena-style evaluation, where each comparison evaluates a pair of models on a prompt with respect to a selected performance dimension. VB-EGE progressively eliminates models from an active set once sufficient statistical evidence has been accumulated to certify their Pareto status. Under a multi-objective Bradley-Terry model, we show that VB-EGE returns the correct Pareto frontier with high probability and derive an instance-dependent upper bound on its sample complexity. We further establish a worst-case lower bound showing that VB-EGE is minimax-optimal up to logarithmic factors. Simulations and experiments on three real-world Arena datasets (Arena, SearchArena, and VisionArena) demonstrate VB-EGE's empirical effectiveness.