BAMBO: Construct Ability and Efficiency LLM Pareto Set via Bayesian Adaptive Multi-objective Block-wise Optimization

Constructing a Pareto set is pivotal for navigating the capability-efficiency trade-offs in Large Language Models (LLMs); however, existing merging techniques remain inadequate for this task. Coarse-grained, model-level methods yield only a sparse set of suboptimal solutions, while fine-grained, layer-wise approaches suffer from the "curse of dimensionality," rendering the search space computationally intractable. To resolve this dichotomy, we propose BAMBO (Bayesian Adaptive Multi-objective Block-wise Optimization), a novel framework that automatically constructs the LLM Pareto set. BAMBO renders the search tractable by introducing a Hybrid Optimal Block Partitioning strategy. Formulated as a 1D clustering problem, this strategy leverages a dynamic programming approach to optimally balance intra-block homogeneity and inter-block information distribution, thereby dramatically reducing dimensionality without sacrificing critical granularity. The entire process is automated within an evolutionary loop driven by the q-Expected Hypervolume Improvement (qEHVI) acquisition function. Experiments demonstrate that BAMBO discovers a superior and more comprehensive Pareto frontier than baselines, enabling agile model selection tailored to diverse operational constraints. Code is available at: https://github.com/xin8coder/BAMBO.