Package management initialization failed: Access Denied Error when opening Visual Studio 2017

It turns out that this is a bug, that hasn't yet been resolved. This error also occurs when starting Visual Studio after an update.

But there is a workaround from this thread that worked for me,

Delete the privateregistry.bin file from the following folder:

C:\users\%username%\Appdata\Local\Microsoft\VisualStudio\15.0_<version id>\

This is however a temporary fix and resets the user's preferences. That's why it worked when I started it as an administrator, since the problem is user specific.

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Update

This bug is supposedly fixed in the latest versions of Visual Studio. But for the bug fix to work, the old privateregistry.bin file still needs to be deleted.

@neil-patrao answer works fine. To open the AppData folder try to type:

%AppData%

directly in the Address bar.

https://support.pointlogic.com/faq/troubleshooting/accessing-the-appdata-folder