Lifted probabilistic inference (Poole, 2003) and symbolic dynamic programming for lifted stochastic planning (Boutilier et al, 2001) were introduced around the same time as algorithmic efforts to use abstraction in stochastic systems. Over the years, these ideas evolved into two distinct lines of research, each supported by a rich literature. Lifted probabilistic inference focused on efficient arithmetic operations on template-based graphical models under a finite domain assumption while symbolic dynamic programming focused on supporting sequential decision-making in rich quantified logical action models and on open domain reasoning. Given their common motivation but different focal points, both lines of research have yielded highly complementary innovations. In this chapter, we aim to help close the gap between these two research areas by providing an overview of lifted stochastic planning from the perspective of probabilistic inference, showing strong connections to other chapters in this book. This also allows us to define Generalized Lifted Inference as a paradigm that unifies these areas and elucidates open problems for future research that can benefit both lifted inference and stochastic planning.
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