Foundations for Generalized Planning in Unbounded Stochastic Domains

Generalized plans, such as plans with loops, are widely used in AI. Among other things, they are straightforward to execute, they allow action repetition, and they solve multiple problem instances. However, the correctness of such plans is non-trivial to define, making it difficult to provide a clear specification of what we should be looking for. Proposals in the literature, such as strong planning, are universally adopted by the community, but were initially formulated for finite state systems. There is yet to emerge a study on the sensitivity of such correctness notions to the structural assumptions of the underlying plan framework. In this paper, we are interested in the applicability and correctness of generalized plans in domains that are possibly unbounded, and/or stochastic, and/or continuous. To that end, we introduce a generic controller framework to capture different types of planning domains. Using this framework, we then study a number of termination and goal satisfaction criteria from first principles, relate them to existing proposals, and show plans that meet these criteria in the different types of domains.