Point-Based Value Iteration for VAR-POMDPs

Partially observable Markov decision processes have been widely adopted in the automatic planning literature since it elegantly captures both execution and observation uncertainties. In our previous paper, we proposed a model called vector autoregressive partially observable Markov decision process (VAR-POMDP) which extends the traditional POMDP by considering the temporal correlation among continuous observations. However, it is a non-trivial problem to develop a tractable planning algorithm for the VAR-POMDP model with performance guarantees as most existing algorithms need to explicitly enumerate all possible observation histories, which is in an unbounded continuous space. In this letter, we extend the famous point-based value iteration algorithm to a double point-based value iteration and show that the VAR-POMDP model can be solved by dynamic programming through approximating the exact value function by a class of piece-wise linear functions. Meanwhile, we prove that the approximation error is bounded. The effectiveness of the proposed planning algorithm is illustrated by an example.