Learning Generative Models for Active Inference using Tensor Networks

Active inference provides a general framework for behavior and learning in autonomous agents. It states that an agent will attempt to minimize its variational free energy, defined in terms of beliefs over observations, internal states and policies. Traditionally, every aspect of a discrete active inference model must be specified by hand, i.e.\ by manually defining the hidden state space structure, as well as the required distributions such as likelihood and transition probabilities. Recently, efforts have been made to learn state space representations automatically from observations using deep neural networks. However, these models are typically overparameterized, with the risk of overfitting the data at hand. In this paper, we present a novel approach of learning state spaces using quantum physics-inspired tensor networks. The ability of tensor networks to represent the probabilistic nature of quantum states as well as to reduce large state spaces makes tensor networks a natural candidate for active inference. We show how tensor networks can be used as a generative model for sequential data. Furthermore, we show how one can obtain beliefs from such a generative model and how an active inference agent can use these to compute the expected free energy. Finally, we demonstrate our method on the classic T-maze environment.