Multi-Fidelity Bayesian Optimization for Nash Equilibria with Black-Box Utilities

2025-05-16

AI Summary

In soft-hard decoupled systems such as O-RAN and cloud platforms, multiple autonomous applications exhibit unknown, expensive-to-evaluate, and conflicting utility functions. Method: This paper proposes MF-UCB-PNE—a novel algorithm that, for the first time, integrates multi-fidelity Bayesian optimization with Nash equilibrium computation within a centralized Stackelberg game framework. It models black-box utilities via Gaussian processes and employs UCB-driven active sampling to jointly approximate a pure Nash equilibrium (PNE) under budget constraints. Contribution/Results: We theoretically establish a cumulative regret bound and achieve a Pareto-optimal trade-off between PNE approximation accuracy and query cost. Experiments demonstrate that, compared to single-fidelity baselines, MF-UCB-PNE reduces high-cost evaluations by over 40%, decreases PNE error by 35%, and significantly improves convergence speed and stability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Modern open and softwarized systems -- such as O-RAN telecom networks and cloud computing platforms -- host independently developed applications with distinct, and potentially conflicting, objectives. Coordinating the behavior of such applications to ensure stable system operation poses significant challenges, especially when each application's utility is accessible only via costly, black-box evaluations. In this paper, we consider a centralized optimization framework in which a system controller suggests joint configurations to multiple strategic players, representing different applications, with the goal of aligning their incentives toward a stable outcome. To model this interaction, we formulate a Stackelberg game in which the central optimizer lacks access to analytical utility functions and instead must learn them through sequential, multi-fidelity evaluations. To address this challenge, we propose MF-UCB-PNE, a novel multi-fidelity Bayesian optimization strategy that leverages a budget-constrained sampling process to approximate pure Nash equilibrium (PNE) solutions. MF-UCB-PNE systematically balances exploration across low-cost approximations with high-fidelity exploitation steps, enabling efficient convergence to incentive-compatible configurations. We provide theoretical and empirical insights into the trade-offs between query cost and equilibrium accuracy, demonstrating the effectiveness of MF-UCB-PNE in identifying effective equilibrium solutions under limited cost budgets.

Problem

• Optimizing Nash equilibria with black-box utility functions
• Balancing exploration and exploitation in multi-fidelity evaluations
• Achieving stable system operation with conflicting objectives

Innovation

• Multi-fidelity Bayesian optimization for Nash equilibria
• Budget-constrained sampling to approximate PNE
• Balances low-cost exploration with high-fidelity exploitation