Active inference is a theory of perception, learning, and decision making that can be applied to neuroscience, robotics, psychology, and machine learning. Recently, intensive research has been taking place to scale up this framework using Monte Carlo tree search and deep learning. The goal of this activity is to solve more complicated tasks using deep active inference. First, we review the existing literature and then progressively build a deep active inference agent as follows: we (1) implement a variational autoencoder (VAE), (2) implement a deep hidden Markov model (HMM), and (3) implement a deep critical hidden Markov model (CHMM). For the CHMM, we implemented two versions, one minimizing expected free energy, CHMM[EFE] and one maximizing rewards, CHMM[reward]. Then we experimented with three different action selection strategies: the ε-greedy algorithm as well as softmax and best action selection. According to our experiments, the models able to solve the dSprites environment are the ones that maximize rewards. On further inspection, we found that the CHMM minimizing expected free energy almost always picks the same action, which makes it unable to solve the dSprites environment. In contrast, the CHMM maximizing reward keeps on selecting all the actions, enabling it to successfully solve the task. The only difference between those two CHMMs is the epistemic value, which aims to make the outputs of the transition and encoder networks as close as possible. Thus, the CHMM minimizing expected free energy repeatedly picks a single action and becomes an expert at predicting the future when selecting this action. This effectively makes the KL divergence between the output of the transition and encoder networks small. Additionally, when selecting the action down the average reward is zero, while for all the other actions, the expected reward will be negative. Therefore, if the CHMM has to stick to a single action to keep the KL divergence small, then the action down is the most rewarding. We also show in simulation that the epistemic value used in deep active inference can behave degenerately and in certain circumstances effectively lose, rather than gain, information. As the agent minimizing EFE is not able to explore its environment, the appropriate formulation of the epistemic value in deep active inference remains an open question.

The ability of Variational Autoencoders to learn disentangled representations has made them appealing for practical applications. However, their mean representations, which are generally used for downstream tasks, have recently been shown to be more correlated than their sampled counterpart, on which disentanglement is usually measured. In this paper, we refine this observation through the lens of selective posterior collapse, which states that only a subset of the learned representations, the active variables, is encoding useful information while the rest (the passive variables) is discarded. We first extend the existing definition to multiple data examples and show that active variables are equally disentangled in mean and sampled representations. Based on this extension and the pre-trained models from disentanglement_lib}, we then isolate the passive variables and show that they are responsible for the discrepancies between mean and sampled representations. Specifically, passive variables exhibit high correlation scores with other variables in mean representations while being fully uncorrelated in sampled ones. We thus conclude that despite what their higher correlation might suggest, mean representations are still good candidates for downstream tasks applications. However, it may be beneficial to remove their passive variables, especially when used with models sensitive to correlated features.