Loop Engineering of Agentic, Developer, and External Feedback Cycles for Large-Scale Enterprise Healthcare Applications

Abstract

Large scale enterprise healthcare applications are grown through three feedback loops that run at different speeds: an agentic coding loop that builds and tests software in minutes, a developer feedback loop that steers priorities in hours, and an external feedback loop that learns real user value from clinicians and patients in days. This paper treats the arrangement as a three timescale feedback control system acting on a shared feature vector, and it names the discipline of designing it loop engineering. We define value alignment, decompose the end to end value error into an implementation gap, an alignment gap, and a knowledge gap, and model each loop as a proportional contraction toward its own target. We prove two results a practitioner can use: under timescale separation the built product converges geometrically to true user value at the rate of the slowest loop, and without separation the coupled convergence rate equals one minus the smallest loop gain, so the slowest loop is always rate limiting. We propose an architecture, the Triple Loop Healthcare Delivery Engine, that binds the three loops to an enterprise platform through a clinical safety gate and a federated cross tenant insight aggregator. Implementing the system from first principles, we report reproducible measurements: the full engine reaches value alignment 0.960 and utility 90.9, an ablation shows a single active loop reaches only 0.000 and two loops only 0.130, a gain sweep confirms that raising the slow outer gain cuts time to value from 25 days to 2 while raising the fast inner gain leaves it near 6, and cross tenant sharing lifts alignment from 0.404 at one hospital to 0.837 at sixty four while residual value error falls from 1.902 to 0.521. The results give a rigorous basis for engineering the loops that deliver trustworthy clinical software at scale.