Sophisticated Inference

TL;DR

This paper introduces a recursive, belief-about-beliefs extension of active inference, enabling deep planning over future belief sequences, demonstrated through numerical simulations of complex decision tasks.

Contribution

It develops a recursive form of expected free energy in active inference, allowing agents to model beliefs about beliefs and perform deep belief-based planning.

Findings

Recursive free energy enables deep belief tree search.

Agents can model counterfactual beliefs about future states.

Numerical simulations demonstrate improved decision-making.

Abstract

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.