Minimax Optimization of Personalized Training Strategies for Student Physical Fitness under Performance Uncertainty

Abstract

Making decisions on a personalized physical-fitness programme is a decision problem in which the expected benefit has to be weighed against the uncertain physical-fitness performance and the limited resources of the intervention. This study proposes a framework for prioritizing training needs of students in a public Chinese university dataset with the minimax criterion. The 2,489 observations consisted of two merged student-profile files which included exercise habits, body type, exercise stability, willpower tier, active days and behavioral pattern. The student profile data was clustered using k-means to obtain four readable student profiles. Observed features were used to build a performance proxy and a cross-sectional uncertainty score which are not actual physiological results. Four decision options were tested: foundation consistency, performance enhancement, robust behavioural support, and baseline (non-personalised). A worst-case performance criterion with uncertainty and strategy cost penalties was maximized. For three less successful or more uncertain profiles, a foundation of consistency was recommended, and baseline for the highly active consistent profile. The minimax allocation yielded larger average performance modelled across the set of tested uncertainty weights than the baseline allocation, and smaller uncertainty modelled across the set of tested uncertainty weights than the baseline allocation. The results highlight the potential of minimax reasoning to structure personalized fitness decisions in the presence of uncertainty, and indicate that there is a need for fitness measurements over time as well as empirically determined intervention effects before causal and clinical claims can be made.