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Decentralized partially observable Markov decision process (DEC-POMDP) modelssequential decision making problems by a team of agents. Since the planning ofDEC-POMDP can be interpreted as the maximum likelihood estimation for thelatent variable model, DEC-POMDP can be solved by the EM algorithm. However, inEM for DEC-POMDP, the forward--backward algorithm needs to be calculated up tothe infinite horizon, which impairs the computational efficiency. In thispaper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EMalgorithm (MBEM) by introducing the forward and backward Bellman equations intoEM. BEM can be more efficient than EM because BEM calculates the forward andbackward Bellman equations instead of the forward--backward algorithm up to theinfinite horizon. However, BEM cannot always be more efficient than EM when thesize of problems is large because BEM calculates an inverse matrix. Wecircumvent this shortcoming in MBEM by calculating the forward and backwardBellman equations without the inverse matrix. Our numerical experimentsdemonstrate that the convergence of MBEM is faster than that of EM.

Forward and Backward Bellman equations improve the efficiency of EM algorithm for DEC-POMDP