Bridging Spherical Black-Box Optimizers

• URL: http://arxiv.org/abs/2606.25761v1
• Date: Wed, 24 Jun 2026 12:35:30 GMT
• Title: Bridging Spherical Black-Box Optimizers
• Abstract summary: Black-box optimization (BBO) methods provide a practical alternative when gradient information is unavailable.<n>We introduce hybrid methods that interpolate between existing methods.<n>We validate our methods on standard BBO benchmarks and higher-dimensional locomotion tasks, demonstrating that the hybrid methods can outperform their constituent algorithms.
• Score: 4.64185880226133
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When gradient information is unavailable, black-box optimization (BBO) methods provide a practical alternative. While Evolution Strategies (ES), Consensus-Based Optimization (CBO), Optimization via Integration (OVI), and related methods have each been studied independently, their connections remain underexplored. We unify these approaches within a common theoretical framework, revealing that they differ primarily in two design choices: fitness aggregation (controlling sharpness preference) and consensus scope (controlling modality). Leveraging these insights, we introduce hybrid optimizers that interpolate between existing methods. Our ES-OVI hybrid allows explicit control over the preference for flat minima, enabling a trade-off between performance and robustness in continuous control tasks. Our CBO-OVI hybrids combine the higher-dimensional efficiency of parametric methods with the multimodal capabilities of particle-based approaches, achieving competitive results on language model merging under limited evaluation budgets. We validate our methods on standard BBO benchmarks and higher-dimensional locomotion tasks, demonstrating that the hybrid methods can outperform their constituent algorithms.

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