On the properties of belief tracking for online contingent planning using regression

Planning under partial observability typically requires some representation of the agent's belief state-either online to determine which actions are valid, or offline for planning. Due to its potential exponential size, efficient maintenance of a belief state is, thus, a key research challenge in this area. The state-of-the-art factored belief tracking (FBT) method addresses this problem by maintaining multiple smaller projected belief states, each involving only a subset of the variable set. Its complexity is exponential in the size of these subsets, as opposed to the entire variable set, without jeopardizing completeness. In this paper we develop the theory of regression to serve as an alternative tool for belief-state maintenance. Regression is a well known technique enjoying similar, and potentially even better worst-case complexity, as its complexity depends on the actions and observations that actually took place, rather than all actions and potential observations, as in the FBT method. On the other hand, FBT is likely to have better amortized complexity if the number of queries to the belief state is very large. An empirical comparison of regression with FBT-based belief maintenance is carried out, showing that the two perform similarly.