Despite progress in the development of COVID-19 vaccines, reaching herd-immunity is believed unlikely in many countries due to such factors as vaccine availablity, hesitancy, and emergence of new variants. Among COVID-19's early symptoms is a sudden decrease in smell function which is often unrecognized without objective testing. Thus, practical, sensitive, and inexpensive smell tests may aid in the early identification of COVID-19 patients. To compare the efficacy of 8 machine learning methods for identifying odorant test items sensitive to COVID-19. To develop, using such methods, highly specific, sensitive, and brief parallel olfactory tests that can be sequentially administered with minimal test item remembrance. The 40-item University of Pennsylvania Smell Identification Test (UPSIT^®) was administered to 100 COVID-19 patients and 132 healthy controls. Binary UPSIT^® item response data were used to train and test machine learning methods, including logistic regression, artificial neural networks, decision trees, and k-nearest algorithms. A simple linear discriminant analysis (LDA) classifier, based on the total number of correct, was also employed. For each model, a sequential feature selection strategy was used to select an initial optimal subset of odorants. To provide tests useful for practical serial testing of COVID-19, an optimization search for multiple sets was performed. LDA) using 29 odorant items achieved the best overall performance, with an accuracy of 95.7%. Four sets of 8-odorant tests with 91%-93% accuracy were developed that can be used separately or sequentially over multiple days to aid in the early identification of COVID-19. Machine learning algorithms can be employed to optimize the sensitivity and specificity of olfactory tests for identifying patients with COVID-19. We found that a minimum of 8 odorant/response items was needed to achieve high sensitivity and specificity..