Signed Residuals for Setpoint Bayesian Optimisation: Why an Active-Inference Acquisition Collapses to Greedy

Setpoint problems, such as holding a physiological reading at a clinical target while the response drifts, are usually given to Bayesian optimisation by folding the residual into a distance to be maximised. We show that this encoding, rather than the acquisition function, decides whether a preference-based acquisition can work. Our case study is BOBA (Kelly et al., 2025), an active-inference acquisition function for dynamic BO. We prove that its pragmatic term orders candidates by the posterior mean whenever the preferred outcome lies above every prediction, which holds on 94.6% of recorded states, and that its epistemic term is too small to change the decision, so the method acts greedily. Folding guarantees this condition for every target, because it places the preferred outcome at the supremum of the objective. Keeping the residual signed restores the preference term’s ordering, raising the share of states whose candidates bracket the target from 5.0% to 57.7% on a clinical digital twin and from 5.6% to 84.5% on fourteen synthetic setpoint problems. Once the encoding is fixed, the epistemic term no longer helps: in none of eight synthetic cells is it significantly beneficial, and a two-line proximity rule (GREEDY-H) matches or beats every active-inference variant we test. On a digital twin of closed-loop anaesthesia built from 50 patient-specific models fitted to surgical recordings, the proximity rule beats a fixed clinical protocol at every budget, although a forgetting-kernel baseline overtakes it at longer budgets. Where the target is unreachable, arms with an information term degrade 1.9× in location error against 1.1× for greedy and proximity rules. Redirecting BOBA’s epistemic term at the optimum (BOBA-OPT) improves on BOBA but not on GP-UCB.