Beyond the Novelty Effect: Mathematical Frameworks for Sustainable Robot-Assisted Habit Formation

Socially Assistive Robots (SARs) show promise for initiating positive behaviour change, yet sustaining habits beyond the intervention period remains a persistent challenge. This paper moves beyond interaction-based analysis to propose mathematical frameworks for modelling habit formation dynamics. We introduce three complementary models: Probabilistic Habit Formation optimised via Reinforcement Learning, Rational Habit Strength with hybrid decay, and Long-Term Retention with booster interventions. Using school-based handwashing as an exemplar, Monte Carlo simulations (𝑁 = 1000) predict that RL-optimised reinforcement could accelerate habit formation by 32%, while strategic boosters may maintain habit strength 1.3× above withdrawal baselines. These frameworks offer a potentially generalisable approach for robotassisted behaviour change across health, education, and other socially assistive contexts, pending empirical validation.