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

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Lars Buesing, Nicolas Heess, Theophane Weber ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:624-634, 2020.

Abstract

Exact probabilistic inference in discrete models is often prohibitively expensive, as it may require evaluating the (unnormalized) target density on its entire domain. Here we consider the setting where only a limited budget of calls to the unnormalized target density oracle is available, raising the challenge of where in its domain to allocate these function calls in order to construct a good approximate solution. We formulate this problem as an instance of sequential decision-making under uncertainty and leverage methods from reinforcement learning for probabilistic inference with budget constraints. In particular, we propose the TreeSample algorithm, an adaptation of Monte Carlo Tree Search to approximate inference. This algorithm caches all previous queries to the density oracle in an explicit search tree, and dynamically allocates new queries based on a "best-first" heuristic for exploration, using existing upper confidence bound methods. Our non-parametric inference method can be effectively combined with neural networks that compile approximate conditionals of the target, which are then used to guide the inference search and enable generalization of across multiple target distributions. We show empirically that TreeSample outperforms standard approximate inference methods on synthetic factor graphs.

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