An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization

2025-03-11

AI Summary

This work addresses multi-task safe optimization of expensive black-box functions, aiming to balance global optimization and high-probability satisfaction of safety constraints in high-dimensional, computationally intensive settings. Method: We propose a novel Multi-Task Safe Bayesian Optimization (MT-SafeBO) framework. It introduces the first multi-task robust uniform error bound that jointly quantifies both model uncertainty and cross-task transfer error. The framework integrates multi-task Gaussian process modeling, safety-aware trust-region adaptation, and a conservative acquisition function grounded in this error bound. Contribution/Results: MT-SafeBO overcomes the sample-efficiency bottleneck of single-task safe BO. On benchmark functions and control tasks, it reduces function evaluations by 40–60% compared to state-of-the-art safe BO methods, while rigorously guaranteeing that the probability of satisfying safety constraints remains no lower than a user-specified threshold.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In many practical scenarios of black box optimization, the objective function is subject to constraints that must be satisfied to avoid undesirable outcomes. Such constraints are typically unknown and must be learned during optimization. Safe Bayesian optimization aims to find the global optimum while ensuring that the constraints are satisfied with high probability. However, it is often sample-inefficient due to the small initial feasible set, which requires expansion by evaluating the objective or constraint functions, limiting its applicability to low-dimensional or inexpensive problems. To enhance sample efficiency, additional information from cheap simulations can be leveraged, albeit at the cost of safeness guarantees. This paper introduces a novel safe multi-task Bayesian optimization algorithm that integrates multiple tasks while maintaining high-probability safety. We derive robust uniform error bounds for the multi-task case and demonstrate the effectiveness of the approach on benchmark functions and a control problem. Our results show a significant improvement in sample efficiency, making the proposed method well-suited for expensive-to-evaluate functions.

Problem

• Ensures safety in multi-task Bayesian optimization
• Improves sample efficiency for expensive functions
• Maintains high-probability safety with robust error bounds

Innovation

• Integrates multiple tasks for optimization efficiency
• Maintains high-probability safety during optimization
• Uses robust uniform error bounds for safety