Active inference and agency: optimal control without cost functions

TLDR

In active inference, actions and posterior beliefs about hidden states jointly minimise a free‑energy bound on the negative log‑likelihood of observed states under a generative model. The paper presents a variational free‑energy formulation of partially observable Markov decision problems for decision making under uncertainty. The authors model control as a hidden state to represent agency, formulate optimal trajectories based on future posterior beliefs, and use a variational free‑energy approach to solve the problem. They show that optimal control can be cast as a pure inference problem by absorbing rewards into prior beliefs, enabling Bayesian filtering, and distinguishing agency‑based from agency‑free models.

Abstract

This paper describes a variational free-energy formulation of (partially observable) Markov decision problems in decision making under uncertainty. We show that optimal control can be cast as active inference. In active inference, both action and posterior beliefs about hidden states minimise a free energy bound on the negative log-likelihood of observed states, under a generative model. In this setting, reward or cost functions are absorbed into prior beliefs about state transitions and terminal states. Effectively, this converts optimal control into a pure inference problem, enabling the application of standard Bayesian filtering techniques. We then consider optimal trajectories that rest on posterior beliefs about hidden states in the future. Crucially, this entails modelling control as a hidden state that endows the generative model with a representation of agency. This leads to a distinction between models with and without inference on hidden control states; namely, agency-free and agency-based models, respectively.