Separating Inference from Control in Sequential Bayesian Experimental Design through Homeostatic Policies over Derived Control States
Sequential Bayesian experimental design is often formulated around posterior learning and expected utility, but in real settings the design process is also shaped by costs, risks, and feasibility constraints that evolve over time. We present a framework that separates inference from control in sequential Bayesian design. The inferential layer is represented by posterior updating, while the control layer tracks variables that affect admissible future actions. This yields a derived control state that summarizes the information needed for sequential decisions. We then define homeostatic design policies over filtered quotient states, which provide interpretable decision rules even when history is replaced by compressed, decision-relevant representations. The framework offers a principled way to combine Bayesian learning with operational viability, and it motivates a view of experimental design in which preserving the future capacity to experiment is part of rational decision making.
Keywords: Bayesian optimal experimental design sequential experimental design Bayesian decision-making homeostatic policies derived control states filtered quotient states constrained design