Techniques for packaging and deploying algorithms utilizing containers for flexible machine learning are described. In some embodiments, users can create or utilize simple containers adhering to a specification of a machine learning service in a provider network, where the containers include code for how a machine learning model is to be trained and/or executed. The machine learning service can automatically train a model and/or host a model using the containers. The containers can use a wide variety of algorithms and use a variety of types of languages, libraries, data types, etc. Users can thus implement machine learning training and/or hosting with extremely minimal knowledge of how the overall training and/or hosting is actually performed.