COBRA++: Enhanced COBRA Optimizer with Augmented Surrogate Pool and Reinforced Surrogate Selection

2026-01-30

AI Summary

This work addresses the challenge of solving real-world optimization problems, which are often hindered by expensive function evaluations and complex constraints. Existing approaches typically rely on manually designed surrogate model pools and selection strategies, incurring substantial tuning costs. To overcome these limitations, the authors propose an enhanced adaptive COBRA framework that incorporates a diversified surrogate model pool—extending beyond conventional radial basis functions—and integrates a reinforcement learning–based online model selection mechanism. This enables automatic optimization of both model diversity and selection policy. Experimental results demonstrate that the proposed method significantly outperforms the original COBRA and its adaptive variants across a range of constrained optimization problems. Ablation studies further confirm the effectiveness of each component, highlighting improved adaptability and computational efficiency.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The optimization problems in realistic world present significant challenges onto optimization algorithms, such as the expensive evaluation issue and complex constraint conditions. COBRA optimizer (including its up-to-date variants) is a representative and effective tool for addressing such optimization problems, which introduces 1) RBF surrogate to reduce online evaluation and 2) bi-stage optimization process to alternate search for feasible solution and optimal solution. Though promising, its design space, i.e., surrogate model pool and selection standard, is still manually decided by human expert, resulting in labor-intensive fine-tuning for novel tasks. In this paper, we propose a learning-based adaptive strategy (COBRA++) that enhances COBRA in two aspects: 1) An augmented surrogate pool to break the tie with RBF-like surrogate and hence enhances model diversity and approximation capability; 2) A reinforcement learning-based online model selection policy that empowers efficient and accurate optimization process. The model selection policy is trained to maximize overall performance of COBRA++ across a distribution of constrained optimization problems with diverse properties. We have conducted multi-dimensional validation experiments and demonstrate that COBRA++ achieves substantial performance improvement against vanilla COBRA and its adaptive variant. Ablation studies are provided to support correctness of each design component in COBRA++.

Problem

• expensive evaluation
• complex constraints
• surrogate model selection
• manual tuning
• constrained optimization

Innovation

• surrogate model pool
• reinforcement learning
• adaptive optimization
• constrained optimization
• model selection