Q:

How to publish a LUIS App

How can I publish LUIS APP as a web service on Azure.
Most of the tutorials and help online shows steps on the old Luis website (luis.ai). 
How to do it on the updated luis.ai website?

A:

The Microsoft docs for publishing your luis ai app as a webservice to Azure is explained in the link:
https://docs.microsoft.com/en-us/azure/cognitive-services/luis/publishapp
Open your app by clicking its name on the My Apps page, and then click Publish App in the left panel. The following screenshot shows the Publish App page if you haven't published your app yet.

If you have previously published this app, this page looks like the following screenshot:

If you want to use a key other than the Starter key, click Change next to the Assigned endpoint key label. This action opens a dialog that allows you to select an existing endpoint key to assign to the app.

