Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about "planning as inference"? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, and that planning corresponds _exactly_ to a _different_ set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

该研究讨论了概率图模型的推理类型，探讨了在规划中使用的不同推理类型以及它们与具体近似或附加约束的关系，并提出了一种变分框架，用于解决在具有大规模状态空间的因式化状态马尔可夫决策过程中进行近似规划的问题。

规划是哪种类型的推理？