The algorithmic brain and the autonomous nervous system: trading off exploration and exploitation in a changing world

Two independently developed theories of mind — one from algorithmic information, one from Bayesian physics — turn out to be describing the same agent from different altitudes.

Kolmogorov Theory (KT) asks the most abstract version of the question: what must any bounded, persistent system do to keep existing? The answer is compress the world into models, score outcomes by some objective, and act. This is deliberately substrate-free — it applies to cells, viruses, institutions, and AI alike. The Free Energy Principle / Active Inference (FEP/AIF) asks a more specific question: how does a biological system, separated from its environment by a probabilistic boundary (a Markov blanket), actually implement perception, action, and learning? Its answer — minimize variational free energy, a bound on how surprised your model is by the world — is mathematically precise, neurobiologically grounded, and has driven a large empirical research program. The paper's central claim is that these two are not rivals but levels: KT is the computational-level "what," FEP/AIF is the algorithmic-level "how."

The bridge is built in three steps. First, exact Kolmogorov compression is uncomputable, so any real agent must maintain a portfolio of models weighted by simplicity and past performance — which is just Bayesian inference. Second, once you read the agent's information boundary as a Markov blanket (adding conditional independence structure to what KT calls an "information membrane"), variational free energy falls out as the natural objective. It's not arbitrary; it's what you get when hidden causes are inferred probabilistically and action is policy selection under prior preferences. Third, the specific choices that give standard active inference its shape — a single unified objective, prior-relative simplicity, a fixed balance between curiosity and goal-seeking — are exactly the ones active inference's own extensions are already loosening. KT just names what stays invariant across those extensions.

The most interesting architectural difference is in how the two frameworks handle goals. Active inference folds preferences into the generative model: exploration and exploitation both emerge from minimizing one expected free energy functional, with no separate dial. KT keeps the objective separate from the model — a distinct "telehomeostatic" valuation function that the model serves. Neither is uniformly better. The joined form is elegant and self-consistent; the separable form makes it easier to ask whose persistence an agent is serving, handle non-stationary goals, or diagnose cases where the model is accurate but the objective is pathological. This matters especially for artificial agents and alignment.

The paper works through exploration-exploitation as a concrete illustration. In active inference, the autonomic nervous system tunes precision — the gain on prediction errors — via neuromodulators: acetylcholine for sensory precision, noradrenaline for prior precision. High prior precision locks the agent into exploitation ("better safe than sorry"); low precision opens it to exploration. Persistent stress that keeps prior precision elevated is offered as a mechanistic sketch of anxiety — the brain stuck in a locally adaptive but globally maladaptive exploitative regime. Both frameworks converge on the same therapeutic intuition: restore tolerance for prediction error to re-enable learning.