1. A system, comprising: one or more computing devices configured to: receive, via a particular programmatic interface of a set of programmatic interfaces implemented at a network-accessible machine learning service of a provider network, a first request from a client, wherein the machine learning service performs machine learning operations on behalf of clients using one or more entity types supported by the machine learning service, wherein the first request corresponds to a particular operation associated with an instance of an entity type, and wherein the entity type comprises one or more of: (a) a data source to be used for a machine learning model, (b) a set of statistics to be computed from a particular data source, (c) a set of feature processing transformation operations to be performed on a specified data set, (d) a machine learning model employing a selected algorithm, (e) an alias associated with a machine learning model, or (f) a result of a particular machine learning model; insert a job object corresponding to the first request in a job queue of the machine learning service; provide an indication to the client that the first request has been accepted for execution; determine, in accordance with a first workload distribution strategy identified for the first request, a first set of provider network resources to be used to perform the particular operation; receive, prior to a completion of the particular operation indicated in the first request, a second request from the client to perform a second operation dependent on a result of the particular operation; insert a second job object corresponding to the second request in the job queue, wherein the second job object includes an indication of a dependency of the second operation on a result of the particular operation; prior to initiating execution of the second operation, provide a second indication to the client that the second request has been accepted for execution; and in response to a determination that the particular operation has been completed successfully, schedule the second operation on a second set of provider network resources.