Collaborative Bayesian Optimization via Wasserstein Barycenters

Motivated by the growing need for black-box optimization and data privacy, we introduce a collaborative Bayesian optimization (BO) framework that addresses both of these challenges. In this framework agents work collaboratively to optimize a function they only have oracle access to. In order to mitigate against communication and privacy constraints, agents are not allowed to share their data but can share their Gaussian process (GP) surrogate models. To enable collaboration under these constraints, we construct a central model to approximate the objective function by leveraging the concept of Wasserstein barycenters of GPs. This central model integrates the shared models without accessing the underlying data. A key aspect of our approach is a collaborative acquisition function that balances exploration and exploitation, allowing for the optimization of decision variables collaboratively in each iteration. We prove that our proposed algorithm is asymptotically consistent and that its implementation via Monte Carlo methods is numerically accurate. Through numerical experiments, we demonstrate that our approach outperforms other baseline collaborative frameworks and is competitive with centralized approaches that do not consider data privacy.

Language Model Prompt Selection via Simulation Optimization

With the advancement in generative language models, the selection of prompts has gained significant attention in recent years. A prompt is an instruction or description provided by the user, serving as a guide for the generative language model in content generation. Despite existing methods for prompt selection that are based on human labor, we consider facilitating this selection through simulation optimization, aiming to maximize a pre-defined score for the selected prompt. Specifically, we propose a two-stage framework. In the first stage, we determine a feasible set of prompts in sufficient numbers, where each prompt is represented by a moderate-dimensional vector. In the subsequent stage for evaluation and selection, we construct a surrogate model of the score regarding the moderate-dimensional vectors that represent the prompts. We propose sequentially selecting the prompt for evaluation based on this constructed surrogate model. We prove the consistency of the sequential evaluation procedure in our framework. We also conduct numerical experiments to demonstrate the efficacy of our proposed framework, providing practical instructions for implementation.