We are pleased to present our research at ICML 2026, “Bridging Spherical Black-Box Optimizers”.
When optimizing through simulators, external APIs, or in reinforcement learning, gradients are often unavailable. Black-Box Optimization (BBO) fills this gap, but the field has been historically split into two categories:
Parametric Methods: Algorithms like Evolution Strategies (ES) scale to high dimensions but only find a single solution.
Nonparametric Methods: Algorithms like Consensus-Based Optimization (CBO) find multiple solutions but fail in high dimensions.
Our team asked a simple question: what if they are all doing the same thing?
In our paper, we showed that these distinct families are actually variations of a single update equation. By bridging this theoretical gap, we can now engineer custom hybrid optimizers for specific tasks.
A key application of this is merging foundation models. Building on our previous work in Evolutionary Model Merging, we faced a computational challenge. Evaluating large language models at every step is resource-intensive, but using a smaller evaluation dataset causes standard unimodal optimizers to overfit.
By treating LLM merging as a multimodal problem and deploying our newly developed hybrid optimizers, AdaPol and SchedPol, we successfully navigated this issue. The algorithms identified multiple distinct optima on the smaller dataset, allowing us to find generalized, high-quality merges at a fraction of the compute cost.