Abstract Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from the optimal value. This paper represents the local policy of each agent using variable-sized FSCs that are constructed using a stick-breaking prior, leading to a new framework called decentralized stick-breaking policy representation (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the DecPOMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.