  Decentralized partially observable Markov decision process (DEC-POMDP) models
sequential decision making problems by a team of agents. Since the planning of
DEC-POMDP can be interpreted as the maximum likelihood estimation for the
latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in
EM for DEC-POMDP, the forward--backward algorithm needs to be calculated up to
the infinite horizon, which impairs the computational efficiency. In this
paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM
algorithm (MBEM) by introducing the forward and backward Bellman equations into
EM. BEM can be more efficient than EM because BEM calculates the forward and
backward Bellman equations instead of the forward--backward algorithm up to the
infinite horizon. However, BEM cannot always be more efficient than EM when the
size of problems is large because BEM calculates an inverse matrix. We
circumvent this shortcoming in MBEM by calculating the forward and backward
Bellman equations without the inverse matrix. Our numerical experiments
demonstrate that the convergence of MBEM is faster than that of EM.
