Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization

2025-08-25

AI Summary

Reliability assessment becomes computationally prohibitive when the limit-state function is expensive to evaluate. Method: This paper proposes a multi-objective optimization–based active learning framework for surrogate modeling. It explicitly formulates exploration (uncertainty reduction) and exploitation (focusing near the limit state) as competing objectives, unifying classical acquisition criteria—such as the U-function and Expected Feasibility Function (EFF)—via the Pareto-optimal solution set. To ensure robust sampling, we introduce knee-point identification, compromise solution selection, and adaptive weight adjustment. Contribution/Results: We establish a unified multi-objective perspective on the exploration–exploitation trade-off and devise an adaptively weighted sampling strategy with provable convergence. On multiple benchmark problems, the proposed method achieves reliability estimates with relative error consistently below 0.1%, while demonstrating significantly higher sample efficiency than state-of-the-art active learning approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Active Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Reliability assessment of engineering systems is often hindered by the need to evaluate limit-state functions through computationally expensive simulations, rendering standard sampling impractical. An effective solution is to approximate the limit-state function with a surrogate model iteratively refined through active learning, thereby reducing the number of expensive simulations. At each iteration, an acquisition strategy selects the next sample by balancing two competing goals: exploration, to reduce global predictive uncertainty, and exploitation, to improve accuracy near the failure boundary. Classical strategies, such as the U-function and the Expected Feasibility Function (EFF), implicitly condense exploration and exploitation into a scalar score derived from the surrogate predictive mean and variance, concealing the trade-off and biasing sampling. We introduce a multi-objective optimization (MOO) formulation for sample acquisition in reliability analysis, where exploration and exploitation are explicit, competing objectives. Within our framework, U and EFF correspond to specific Pareto-optimal solutions, providing a unifying perspective that connects classical and Pareto-based approaches. Solving the MOO problem discards dominated candidates, yielding a compact Pareto set, with samples representing a quantifiable exploration-exploitation trade-off. To select samples from the Pareto set, we adopt the knee point and the compromise solution, and further propose a strategy that adjusts the trade-off according to reliability estimates. Across benchmark limit-state functions, we assess the sample efficiency and active learning performance of all strategies. Results show that U and EFF exhibit case-dependent performance, knee and compromise are generally effective, and the adaptive strategy is robust, consistently reaching strict targets and maintaining relative errors below 0.1%.

Problem

• Balancing exploration-exploitation trade-off in active learning
• Improving surrogate model-based reliability analysis efficiency
• Addressing computational expense in limit-state function evaluations

Innovation

• Multi-objective optimization for exploration-exploitation balance
• Pareto set sampling with knee point selection
• Adaptive trade-off adjustment based on reliability