ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design

TL;DR

ARCO-BO tackles multi-agent Bayesian optimization under heterogeneity in objectives, budgets, and input spaces. It introduces three core components—similarity- and optima-aware dynamic consensus, budget-aware asynchronous sampling, and partial input space sharing—built atop Gaussian Process surrogates to enable selective, resource-aware collaboration. Empirical results on synthetic and high-dimensional engineering benchmarks show ARCO-BO achieving faster convergence and lower regret than independent BO and static consensus baselines, particularly when budgets are uneven or inputs are only partially shared. The framework supports distributed, privacy-conscious design settings and has potential extensions to adaptive budgeting, learned consensus policies, and federated optimization. Overall, ARCO-BO demonstrates that targeted information sharing and asynchronous participation can substantially improve efficiency in heterogeneous multi-agent design tasks.

Abstract

Modern scientific and engineering design increasingly involves distributed optimization, where agents such as laboratories, simulations, or industrial partners pursue related goals under differing conditions. These agents often face heterogeneities in objectives, evaluation budgets, and accessible design variables, which complicates coordination and can lead to redundancy, poor resource use, and ineffective information sharing. Bayesian Optimization (BO) is a widely used decision-making framework for expensive black box functions, but its single-agent formulation assumes centralized control and full data sharing. Recent collaborative BO methods relax these assumptions, yet they often require uniform resources, fully shared input spaces, and fixed task alignment, conditions rarely satisfied in practice. To address these challenges, we introduce Adaptive Resource Aware Collaborative Bayesian Optimization (ARCO-BO), a framework that explicitly accounts for heterogeneity in multi-agent optimization. ARCO-BO combines three components: a similarity and optima-aware consensus mechanism for adaptive information sharing, a budget-aware asynchronous sampling strategy for resource coordination, and a partial input space sharing for heterogeneous design spaces. Experiments on synthetic and high-dimensional engineering problems show that ARCO-BO consistently outperforms independent BO and existing collaborative BO via consensus approach, achieving robust and efficient performance in complex multi-agent settings.

Figures (9)

• Figure 1: Conceptual illustration of multi-agent system. (a) Without collaboration, agents operate independently. (b) With collaboration, agents share information through consensus.
• Figure 2: Consensus operation in collaborative Bayesian optimization. Agents first propose samples independently, then update their decisions via a weighted consensus based on the matrix $\mathbf{W}^{(t)}$.
• Figure 3: Illustration of function heterogeneity in a three-agent system. (a) Agent-specific objective functions $f_i(x)$, whose global minima lie in different regions of the domain. (b) Pairwise similarity shown as a correlation matrix.
• Figure 4: Illustration of function transformations and their impact on similarity. Each panel compares a base function $f(x)$ (solid black) with a transformed variant (dashed gray). (a) Vertical shift: $f(x) + b$ preserves both shape and minimizer location. (b) Amplitude scaling: $af(x)$ changes magnitude but keeps the same shape and minimizer. (c) Sign flip: $-f(x)$ inverts the shape and shifts the minimizer. (d) Small input shift: $f(x + \varepsilon)$ retains high similarity in both shape and minimizer location. (e) Moderate input shift: $f(x + c)$ preserves shape but misaligns the minimizer. (f) Large input shift: $f(x + d)$ leads to low shape and proximity similarity. Pearson correlation measures shape similarity, while proximity reflects alignment between minimizers.
• Figure 5: Comparison of surrogate model predictions across three optimization strategies at iteration 20 for three agents optimizing distinct variants of the Sasena function. (a) separate BO, (b) benchmark collaborative BO and (c) our proposed ARCO-BO.