ALT-TAB is working for me in DX11 now, however if I ALT-TAB out, I don't see the window in the middle of the desktop that shows running applications and allows you to switch between them. If I go back into AH and ALT-TAB out again, then I will see this popup window in the middle of the desktop. Seems to work correctly in the DX9 version though.
If you are in game and ALT-TAB to the desktop, right clicking on AH3's application button in the taskbar brings up a menu - but if you select "Close Window" in this popup, it takes you right back into the game. If you Quit the game from the clipboard menu, but stay at the arena selection menu on the clipboard, THEN "Close Window" on the taskbar application button menu works correctly. Maybe this is correct operation for an application running in full screen, instead of windowed mode?