A fundamental question in AI, control theory, and Bayesian statistics is this: when can you solve estimation and decision-making separately, and when must you solve them together? This paper gives the first information-theoretic answer valid for arbitrary nonlinear, non-Gaussian systems. We introduce KAMIORZUEN, a unified operator framework that decomposes any system with hidden state into five components: observables (KA), latent state (MI), dynamics (OR), actions (ZU), and outcomes (EN). The central result is the KA–OR Independence Theorem: the quantity δ = I (xₜ₊₁; aₜ | sₜ₊₁) — a single conditional mutual information — is both necessary and sufficient for the classical separation principle to hold. When δ = 0, estimation and control decouple exactly. When δ > 0, joint optimization is strictly required, and the performance gap grows monotonically with δ. This strictly generalizes the linear-quadratic separation principle to arbitrary POMDPs. Building on this theorem, we derive ZAPS, an adaptive algorithm that estimates δ during a short logarithmic burn-in phase and selects its planning mode accordingly, achieving a regret bound of O (Rₘax (1−γ) ⁻¹ √ (T ln T) ). Experiments on Tiger, Active Sensing, and RockSample confirm the theory: ZAPS matches the oracle joint agent when δ > 0 and incurs no overhead when δ = 0, while a separation-only baseline fails by over 180% in the dependent case. The package includes the full paper, a complete mathematical course with proofs (temario), and an accessible guide for non-technical readers (guía).
Atienza R. Alvaro (Sat,) studied this question.