Deficit Loop: Closed-Loop Adaptive Calorie Targeting with Per-User AI Agents over Messaging

Abstract

Digital weight-loss tools prescribe daily calorie targets open-loop: a prediction equation estimates energy expenditure, a deficit is subtracted, and the number is rarely checked against what actually happens to the individual. We describe the deficit loop, a closed-loop calorie-target controller deployed in production inside an AI coaching service delivered entirely over consumer messaging (SMS and WhatsApp). Each user is served by an isolated, stateful AI agent; a deterministic controller re-estimates the user's energy expenditure each week from their own logged meals and weigh-ins, and re-derives the target under layered physiological safety guardrails. The central design problem is that the measurement channel is systematically dirty — self-reported intake carries large, person-specific under-reporting bias — so the controller maintains two expenditure estimates in deliberately different units and uses their relationship to route between opposite interventions: adjust the target, or repair the measurement. We prove a fixed-point property of the control law: with an absolute (not multiplicative) deficit applied in the user's own logging units, the steady-state true deficit equals the intended deficit regardless of stable reporting bias. We report engineering constraints of operating hundreds of long-lived stateful agents over carrier messaging (latency, delivery, safety filtering, structural separation between a deterministic controller and a generative messaging layer), and field observations from seven weeks of closed-loop operation: measured expenditure runs materially below both consumer-calculator and textbook-formula predictions (median ≈300 kcal/day below the plan's textbook formula and ≈500 below the consumer-calculator recommendation), and on 28-day forward weight-change prediction the loop nearly eliminates the formula baseline's systematic bias (−0.02 vs −0.15 kg/week) while improving median absolute error (0.26 vs 0.36 kg/week). We discuss why the dominant harm of expenditure over-estimation in an LLM-mediated coach is behavioral — the model confidently urges the user to eat more — and how the architecture contains it. This is an observational systems report, not a clinical-efficacy claim; limitations and ethics are discussed throughout.

Keywords

closed-loop control · energy balance · conversational agents · LLM agents · mHealth · weight management · self-report bias

Cite this preprint

@misc{li2026deficitloop,
  author = {Li, Xiaomeng},
  title  = {Deficit Loop: Closed-Loop Adaptive Calorie Targeting
            with Per-User AI Agents over Messaging},
  year   = {2026},
  month  = oct,
  note   = {Preprint},
  doi    = {10.2196/preprints.113767},
  url    = {https://nanorhino.com/research/deficit-loop-preprint.pdf}
}