Authcache will cache user menu I have used Authcache and memcache to cache pages for authenticated users.

However, I have a user specific menu displayed at top right of every page, and the menu sometimes displayed a wrong users' infomation (avartar, username).

I have checked the Authcache Retrieve menu title using Ajax or ESI option at every menu entry's config page.

I also have tried to generate the menu items in code, but both with no good.
If you serve your menus as blocks then you can use Authcache Block sub module. On the block admin page you will find an Authcache personalization setting.