ARCO-BO: Adaptive Collaborative Bayesian Optimization

• The paper introduces ARCO-BO, a novel framework for distributed Bayesian optimization that adapts collaboration to diverse agents’ objectives, budgets, and design spaces.
• It integrates a time-varying consensus matrix using Pearson and proximity similarities to guide asynchronous, budget-aware sampling among heterogeneous agents.
• Experimental results on synthetic and real-world benchmarks demonstrate faster convergence and lower regrets compared to independent and static collaborative approaches.

Adaptive Resource Aware Collaborative Bayesian Optimization (ARCO-BO) is a framework for distributed optimization among heterogeneous agents—such as laboratories, simulators, or industrial design partners—operating under distinct objectives, variable evaluation budgets, and partially overlapping design spaces. Unlike traditional centralized or naive consensus-based approaches, ARCO-BO explicitly accounts for these heterogeneities by integrating adaptive information sharing, asynchronous budget coordination, and selective subspace communication to achieve robust and efficient performance in complex multi-agent settings (Wang et al., 18 Oct 2025).

1. Problem Formulation and Core Challenges

ARCO-BO addresses the limitations of single-agent Bayesian Optimization (BO) frameworks, which assume full data sharing and uniform problem setups. In practice, agents typically encounter differences in:

• Objective functions: Each agent may be optimizing for distinct, though related, goals.
• Resource constraints: Evaluation budgets (the number of queries permitted) vary across agents.
• Accessible design variables: Input spaces may overlap only partially due to proprietary restrictions or differing experimental setups.

Coordinating optimization under these conditions requires dynamic, resource-aware collaboration without inducing negative transfer from unrelated agents, and without bottlenecking high-budget participants by the slowest ones.

2. Similarity- and Optima-Aware Consensus Mechanism

ARCO-BO advances collaborative BO by introducing a time-varying, feature-driven consensus matrix. Each agent maintains a Gaussian Process (GP) surrogate for its local objective and computes predictive means over a shared test grid. Two similarities between agents $i$ and $j$ are leveraged:

1. Pearson similarity: $s_{ij}^{(\text{Pearson})} = (\rho_{ij} + 1)/2$, where $\rho_{ij}$ is the Pearson correlation of agents' predictive means.
2. Proximity similarity: $$s_{ij}^{(\text{Proximity})} = \exp(-\lambda_p \|x_i^* - x_j^*\|^2)$$, quantifying optima closeness for global guidance.

The overall similarity score is $$s_{ij} = s_{ij}^{(\text{Pearson})} \times s_{ij}^{(\text{Proximity})}$$. These measures are used to build a consensus matrix $W^{(t)} = \gamma(t) S^{(t)} + (1-\gamma(t)) I$, where $\gamma(t) = \exp(-\alpha t/T)$ is a decay function controlling collaboration intensity. Early iterations prioritize broad collaboration; as agents' surrogates become more accurate, the consensus approaches the identity and agents update more independently.

This mechanism ensures cross-agent information transfer only when surrogates and optima are aligned, mitigating negative transfer and promoting robust collaborative learning.

3. Budget-Aware Asynchronous Sampling Strategy

ARCO-BO enforces resource coordination through asynchronous sampling. Each agent $i$ receives a sampling interval

$$\tau_i = \left\lfloor \frac{B_{\max}}{B_i} \right\rfloor,$$

where $B_{\max}$ is the largest evaluation budget and $B_i$ is agent $i$'s budget. High-budget agents sample more frequently, while low-budget agents conserve their resources and opportunistically exploit shared information.

This strategy removes bottlenecks present in naive synchronous collaboration—where all agents are forced to sample together—and increases sample efficiency, especially for expensive or slow evaluations. It also enables fast feedback propagation from simulations to guide costly physical experiments.

4. Partial Input Space Sharing for Heterogeneous Design Variables

To accommodate agents that work on overlapping but not identical design spaces, ARCO-BO partitions each agent's variables:

• $x_i = [x_{\text{shared},i}; x_{\text{private},i}]$, where $x_{\text{shared},i} \in \mathbb{R}^{d_s}$ and $x_{\text{private},i} \in \mathbb{R}^{d_p}$. During consensus updates, only $x_\text{shared}$ vectors are aggregated using the consensus matrix, while $x_\text{private}$ components remain agent-specific.

This selective sharing preserves confidentiality and allows heterogeneous agents to benefit from collaboration without requiring complete disclosure of proprietary variables or process parameters.

5. Mathematical Formulation

ARCO-BO is mathematically grounded in its consensus and sampling strategies:

• Similarity and consensus update:

$$s_{ij} = \left( \frac{\rho_{ij} + 1}{2} \right) \exp(-\lambda_p \|x_i^* - x_j^*\|^2)$$

$W^{(t)} = \gamma(t) S^{(t)} + (1-\gamma(t)) I$

with decay $\gamma(t) = \exp(-\alpha t / T)$

• Budget-aware sampling interval:

$$\tau_i = \left\lfloor \frac{B_{\max}}{B_i} \right\rfloor$$

• Partial update of design variables:

$$x_i^{(t+1)} = [ W^{(t)} x_{\text{shared},i}^{(t)};\; x_{\text{private},i}^{(t)} ]$$

The consensus matrix $W^{(t)}$ weights agents dynamically according to surrogate and optima similarity, decaying toward independence as local models stabilize.

6. Experimental Validation

ARCO-BO demonstrates strong empirical performance on synthetic and real engineering benchmarks:

• 1D Sasena variants: Agents with conflicting global optima benefit from ARCO-BO's adaptive consensus (agents with similar optima share more, those with disparate optima share little), leading to lower area-under-curve (AUC) and final regrets compared to both independent BO and static collaborative BO.
• 2D Ackley variants: Scenarios with full or partial input sharing and heterogenous budgets show that ARCO-BO achieves faster convergence and lower regrets, particularly benefitting resource-constrained agents.
• High-dimensional problems (Borehole, Wing Weight): ARCO-BO enables low-budget agents to leverage information from high-budget ones, resulting in improved sample efficiency and robustness—even when design spaces differ substantially.

Notably, ARCO-BO consistently outperforms independent BO and standard collaborative consensus approaches in metrics such as normalized final regret and cumulative convergence speed.

7. Practical Implications and Challenges

Applications: ARCO-BO is well-suited for distributed scientific collaborations, multi-fidelity design workflows (simulation + experiment), materials discovery with lab-specific constraints, and scenarios where not all input variables are shareable.

Benefits: Adaptive consensus ensures selective information transfer; asynchronous sampling maximizes resource utilization; partial input sharing preserves privacy and operational autonomy.

Challenges: The selection of consensus decay rates ($\alpha$) and proximity sensitivity ($\lambda_p$) may require manual tuning. Predefined budgets are assumed, but dynamic budget updating and more complex forms of input heterogeneity (such as mixed discrete–continuous spaces) are targets for future research.

Significance: ARCO-BO's mathematical and practical innovations enable heterogeneous agents to jointly accelerate expensive optimization with alignment to available resources, making it highly relevant for modern, complex scientific and engineering design problems (Wang et al., 18 Oct 2025).