用神经扩散过程求解全局优化，效果在低维任务中出色。
Path Integral Optimiser: Global Optimisation via Neural Schrödinger-Föllmer Diffusion
- 将优化问题转化为量子桥接采样，通过神经网络逼近路径积分。
- 在2到1,247维任务中每步表现优秀，但15.9k参数模型探索能力弱。
- 适合研究随机控制与高维优化的学者，尤其关注扩散模型应用者。
我们首次探索了神经扩散过程在全局优化中的应用，聚焦于Zhang等人的路径积分采样方法。可通过玻尔兹曼分布将优化问题转化为求解薛定谔桥采样问题，利用吉兰索夫定理结合单点先验，将其形式化为随机控制问题，并通过神经网络近似（傅里叶MLP）计算解的积分项。本文提供了该优化器的理论界、在简单优化任务上的结果，以及支撑模型的随机理论概述。最终发现，该优化器在2至1,247维任务中表现出色，但在面对15.9k参数模型时难以有效探索高维空间，表明需进一步研究其在复杂环境中的自适应机制。
原文摘要 · Abstract (English)
We present an early investigation into the use of neural diffusion processes for global optimisation, focusing on Zhang et al.'s Path Integral Sampler. One can use the Boltzmann distribution to formulate optimization as solving a Schrödinger bridge sampling problem, then apply Girsanov's theorem with a simple (single-point) prior to frame it in stochastic control terms, and compute the solution's integral terms via a neural approximation (a Fourier MLP). We provide theoretical bounds for this optimiser, results on toy optimisation tasks, and a summary of the stochastic theory motivating the model. Ultimately, we found the optimiser to display promising per-step performance at optimisation tasks between 2 and 1,247 dimensions, but struggle to explore higher-dimensional spaces when faced with a 15.9k parameter model, indicating a need for work on adaptation in such environments.
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