Version vector-based rules are used to facilitate asynchronous execution of machine learning algorithms. The method uses version vector based rule to generate aggregated parameters and determine when to return the parameters. The method also includes coordinating the versions of aggregated parameter sets among all the parameter servers. This allows to broadcast to enforce the version consistency; generate parameter sets in an on-demand manner to facilitate version control. Furthermore the method includes enhancing the version consistency at the learner's side and resolving the inconsistent version when mismatching versions are detected.