Sampling Decisions

In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in stochastic optimal control. It extends the continuous-space, continuous-time Path Integral Diffusion sampling technique of [Behjoo, Chertkov 2025] to discrete time and space, while also generalizing the Generative Flow Network (GFN) framework of [Bengio, et al 2021]. In its most basic form an explicit formulation that does not require Neural Networks (NNs), DF leverages the linear solvability of the underlying MDP [Todorov, 2007] to adjust the transition probabilities of the prior sampler. The resulting Markov process is expressed as a convolution of the reverse-time Green's function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model -- compare DF to Metropolis-Hastings to quantify its efficiency, discuss potential NN-based extensions, and outline how DF can enhance guided sampling across various applications.