Can I limit the type of instances that data scientists can launch for training jobs in SageMaker?

Yes, you can limit the types of instances that are available for your data scientists to launch in SageMaker by using an IAM policy similar to the following one:

Note: This example IAM policy allows SageMaker users to launch only Compute Optimized (ml.c5)-type training jobs and hyperparameter tuning jobs.

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Sid": "EnforceInstanceType",
            "Effect": "Allow",
            "Action": [
                "sagemaker:CreateTrainingJob",
                "sagemaker:CreateHyperParameterTuningJob"
            ],
            "Resource": "*",
            "Condition": {
                "ForAllValues:StringLike": {
                    "sagemaker:InstanceTypes": ["ml.c5.*"]
                }
            }
        }

     ]
}