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A plethora of problems in AI, engineering and the sciences are naturallyformalized as inference in discrete probabilistic models. Exact inference isoften prohibitively expensive, as it may require evaluating the (unnormalized)target density on its entire domain. Here we consider the setting where only alimited budget of calls to the unnormalized density oracle is available,raising the challenge of where in the domain to allocate these function callsin order to construct a good approximate solution. We formulate this problem asan instance of sequential decision-making under uncertainty and leveragemethods from reinforcement learning for probabilistic inference with budgetconstraints. In particular, we propose the TreeSample algorithm, an adaptationof Monte Carlo Tree Search to approximate inference. This algorithm caches allprevious queries to the density oracle in an explicit search tree, anddynamically allocates new queries based on a "best-first" heuristic forexploration, using existing upper confidence bound methods. Our non-parametricinference method can be effectively combined with neural networks that compileapproximate conditionals of the target, which are then used to guide theinference search and enable generalization across multiple targetdistributions. We show empirically that TreeSample outperforms standardapproximate inference methods on synthetic factor graphs.

Approximate Inference in Discrete Distributions with Monte Carlo Tree Search and Value Functions