On the one hand, BigML is an Amazon Technology Partner, and the default cloud environment which BigML uses for Managed VPCs is AWS.
On the other hand, Self-Managed VPCs can be implemented on any of the cloud providers currently supported by BigML which are: Amazon AWS, Google Cloud, and Microsoft Azure. While BigML is working on expanding the list of supported cloud providers, it should be noted that BigML can currently be deployed on any cloud provider by treating it as an On-Premises deployment. Of course this will remove some of the benefit of running in the cloud, but can be a good option when those benefits are not important, for example when running BigML in a single instance, or when otherwise constrained to a cloud provider that BigML does not currently support.