Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of random variables. Most recently, a reinforcement learning approach has been proposed to find efficient contraction orders in tensor networks. Due to the duality between graphical models and tensor networks, we adapt this approach to probabilistic inference in graphical models. Furthermore, we incorporate structure exploitation into the process of finding an optimal order. Currently, the agent's cost function is formulated in terms of intermediate result sizes which are exponential in the number of indices (i.e., random variables). We show that leveraging specific structures during inference allows for introducing compact encodings of intermediate results which can be significantly smaller. By considering the compact encoding sizes for the cost function instead, we enable the agent to explore more efficient contraction orders. The structure we consider in this work is the presence of local symmetries (i.e., symmetries within a model's factors).

本研究解决了在图形模型中进行高效概率推理所需的最优消除顺序选择的挑战。通过借鉴强化学习方法并结合结构利用，研究提出了一种新颖的成本函数，能够在推理过程中引入紧凑的中间结果编码，从而显著减少中间结果大小。这种方法在提升推理效率方面具有重要潜力。

结合局部对称性利用与强化学习优化概率推理 -- 进行中的工作