Branching time active inference is a framework proposing to look at planning as a form of Bayesian model expansion. Its root can be found in active inference, a neuroscientific framework widely used for brain modeling, as well as in Monte Carlo tree search, a method broadly applied in the reinforcement learning literature. Up to now, the inference of the latent variables was carried out by taking advantage of the flexibility offered by variational message passing, an iterative process that can be understood as sending messages along the edges of a factor graph. In this letter, we harness the efficiency of an alternative method for inference, Bayesian filtering, which does not require the iteration of the update equations until convergence of the variational free energy. Instead, this scheme alternates between two phases: integration of evidence and prediction of future states. Both phases can be performed efficiently, and this provides a forty times speedup over the state of the art.

Active inference is a state-of-the-art framework in neuroscience that offers a unified theory of brain function. It is also proposed as a framework for planning in AI. Unfortunately, the complex mathematics required to create new models can impede application of active inference in neuroscience and AI research. This letter addresses this problem by providing a complete mathematical treatment of the active inference framework in discrete time and state spaces and the derivation of the update equations for any new model. We leverage the theoretical connection between active inference and variational message passing as described by John Winn and Christopher M. Bishop in 2005. Since variational message passing is a well-defined methodology for deriving Bayesian belief update equations, this letter opens the door to advanced generative models for active inference. We show that using a fully factorized variational distribution simplifies the expected free energy, which furnishes priors over policies so that agents seek unambiguous states. Finally, we consider future extensions that support deep tree searches for sequential policy optimization based on structure learning and belief propagation.