Today we cannot run TensorBoard on a AI Platform notebook on a native way (it may already exist few tricks to fix the issue).

I was told by the GCP AI Platform notebook team that this scenario is not supported because TensorBoard widget is trying to do port forwarding under the hood and the AI Platform notebook proxy prevents it from connecting to non-HTTPS ports.
It will be great to be use TensorBoard on AI Platform notebook or any kind of other services in a native way and secure way (something that could also work with corporate proxy). I don't have the know to build such solution but I can help in the testing phase both on AI Platform notebook (GCP) and with corporate proxy (TLS interception).