用扩散模型提升贝叶斯实验设计效率，解决高维复杂场景下的计算难题。
Bayesian Experimental Design via Contrastive Diffusions
- 构造可高效采样的混合后验分布，简化信息增益优化
- 提出新梯度表达式，实现扩散采样与优化的联合迭代
- 首次将生成模型引入贝叶斯实验设计，适用于复杂场景
贝叶斯最优实验设计（BOED）是一种有效降低实验序列成本的工具。基于期望信息增益（EIG）的优化需最大化先验与后验分布间难以处理的期望对比。由于固有的计算复杂性，该方法在高维和复杂设置下难以扩展。本文提出一种具有低成本采样特性的混合后验分布，并通过新的EIG梯度表达式实现对EIG对比的最大化。利用扩散采样器计算混合后验的动态过程，结合双层优化思想，构建高效的联合采样-优化循环。该方法显著提升效率，使BOED能够借助扩散模型的成熟生成能力。通过将生成模型融入BOED框架，拓展了其适用范围，解决了此前不切实际的场景。数值实验及与先进方法的对比验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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