Bayesian Experimental Design via Contrastive Diffusions

2024-10-15

arXiv.org

AI Summary

Bayesian optimal experimental design (BOED) faces scalability bottlenecks in high-dimensional, nonlinear, and black-box settings due to the intractability of exact expected information gain (EIG) estimation. This paper proposes a differentiable BOED framework grounded in contrastive diffusion: it constructs an easily samplable pooled posterior distribution and jointly models diffusion dynamics with bilevel optimization, yielding—for the first time—a differentiable, low-variance variational EIG gradient estimator. By deeply integrating generative diffusion models into BOED, the method overcomes fundamental limitations of conventional sampling-based and gradient-estimation approaches. Experiments demonstrate substantial improvements in computational efficiency and optimization stability across multiple benchmark tasks, surpassing current state-of-the-art methods. Notably, it enables, for the first time, diffusion-model-driven large-scale adaptive experimental design.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• 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

Abstract

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected contrast between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce a pooled posterior distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.

Problem

• Reduces computational complexity in Bayesian Experimental Design.
• Enables efficient EIG contrast maximization in high dimensions.
• Extends BOED to generative models for broader applications.

Innovation

• Pooled posterior distribution for cost-effective sampling
• EIG gradient expression for tractable contrast maximization
• Diffusion-based samplers with bi-level optimization loop