Background and Objectives: This paper focuses on using AI to assess the cognitive function of older adults with mild cognitive impairment or mild dementia using physiological data provided by a wearable device. Cognitive screening tools are disruptive, time-consuming, and only capture brief snapshots of activity. Wearable sensors offer an attractive alternative by continuously monitoring physiological signals. This study investigated whether physiological data can accurately predict scores on established cognitive tests. Research Design and Methods: We recorded physiological signals from 23 older adults completing three NIH Toolbox Cognitive Battery tests, which assess working memory, processing speed, and attention. The Empatica EmbracePlus, a wearable device, measured blood volume pulse, skin conductance, temperature, and movement. Statistical features were extracted using wavelet-based and segmentation methods. We then applied supervised learning and validated predictions via cross-validation, hold-out testing, and bootstrapping. Results: Our models showed strong performance with Spearman's ρof 0.73-0.82 and mean absolute errors of 0.14-0.16, significantly outperforming a naive mean predictor. Sensor roles varied: heart-related signals combined with movement and temperature best predicted working memory, movement paired with skin conductance was most informative for processing speed, and heart in tandem with skin conductance worked best for attention. Discussion and Implications: These findings suggest that wearable sensors paired with AI tools such as supervised learning and feature engineering can noninvasively track specific cognitive functions in older adults, enabling continuous monitoring. Our study demonstrates how AI can be leveraged when the data sample is small. This approach may support remote assessments and facilitate clinical interventions.