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exception thrown.For the cases where is , there is an overhead of execution of subsequent operators. For the cases where exception is thrown, there is no overhead of execution of subsequent operators
Approach1Approach2
Forces to execute operators even if prev operators failed. This can be a problem if subsequent operators after a failed operator throw exceptions other than dmlc::Error

Once there is a failed operator all the operators that depend on the current operator won't be executed.

Minimal api changes.The lambda closure expected by PushAsync has a different signature after adding onstart callback.
For the cases where exception is thrown, there is an overhead of execution of subsequent operators. For the cases where exception is thrown, there is no overhead of execution of subsequent operators.
Performance impact should be minimal in cases where there will be no exception thrown.Performance impact needs to be investigated because of additional overhead of the onstart callback even for cases where no exception thrown.

Recommendation

My recommendation is to take Approach1 since this introduces minimal api changes and also minimal performance impact in the case where no exception is thrown.

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