What is the Active Inference ``Goal''? Priors, Hyperpriors, Precision, and the Role of the Epistemic Term

Active inference has one goal, not two — and this note exists to prove it.

The framework called Active Inference (AIF) is often described as balancing two drives: satisfying preferences (exploitation) and gathering information (exploration). This note argues that framing is misleading. There is a single objective — minimize Expected Free Energy (EFE) — and the "epistemic" exploration term falls out of it automatically, as a mathematical consequence of pursuing preferences under uncertainty. If you can't see the world clearly, you should first act to see it better. That's not a second goal; it's what the first goal demands when observations are noisy and hidden states are uncertain.

The mechanics work like this. For each candidate policy, the agent predicts what it would observe if it followed that policy, then scores the policy by how well those predicted observations match its preferred outcomes (the "risk" term) and how informative those observations would be about the underlying hidden state (the "ambiguity" term). The ambiguity term penalizes policies that would leave the agent confused about what's actually going on. In the limit where the agent already knows everything, ambiguity vanishes and the agent just chases preferences. In the limit where preferences are flat, the agent explores purely to reduce uncertainty. The balance is endogenous — it emerges from the math, not from a separate controller.

The note also carefully distinguishes what is fixed versus what can be learned. The model structure is fixed. But parameters like "policy precision" (how sharply the agent commits to the best-scoring policy) can themselves be treated as uncertain quantities with their own priors, and inferred from data. This means the explore-exploit tradeoff can shift over time without any external tuning — the agent learns how confident to be in its own preferences.

The second half of the note maps this onto a separate framework called KT (Kolmogorov Theory / algorithmic agent framing, from Ruffini et al.), which describes agents in terms of an explicit Objective Function tied to telehomeostasis — roughly, staying in viable states. The claim is that AIF is a Bayesian implementation of the same idea: preferences encode viability, the accuracy-complexity tradeoff in variational free energy mirrors the compression emphasis in KT, and the epistemic term in AIF corresponds to what KT treats implicitly — that optimizing telehomeostasis with an uncertain model naturally rewards uncertainty reduction. The two frameworks are converging on the same architecture from different directions.

This is a technical note — relatively short and dense with equations — so the source does not develop extended empirical claims or simulations. Its value is conceptual clarification: dissolving a false dichotomy and showing the structural alignment between two theoretical frameworks.