Companies and healthcare providers are developing and implementing new applications of medical artificial intelligence (MAI), including the AI sub-type of medical machine learning (MML). MML is based on the application of machine learning (ML) algorithms to automatically identify patterns and act on medical data to guide clinical decisions. MML poses challenges and raises important questions, including 1) How will regulators evaluate MML-based medical devices to ensure their safety and effectiveness?, and 2) What additional MML considerations should be taken into account in the international context? To address these questions, we analyze the current regulatory approaches to MML in the United States and Europe. We then examine international perspectives and broader implications, discussing considerations such as data privacy, exportation, explanation, training set bias, contextual bias, and trade secrecy.