Active Inference and Decision Making

In the cognitive neurosciences and machine learning, we have formal ways of understanding and characterising perception and decision-making; however, the approaches appear very different: current formulations of perceptual synthesis call on theories like predictive coding and Bayesian brain hypothesis. Conversely, formulations of decision-making and choice behaviour often appeal to reinforcement learning and the Bellman optimality principle. On the one hand, the brain seems to be in the game of optimising beliefs about how its sensations are caused; while, on the other hand, our choices and decisions appear to be governed by value functions and reward. Are these formulations irreconcilable, or is there some underlying imperative that renders perceptual inference and decision-making two sides of the same coin.