One of the overloaded methods adds a parameter for htmlAttributes. I am using preview 2, so hopefully this is there for whatever version you are using.
public static string ActionLink<T>( Expression<Action<T>> action, string linkText, object htmlAttributes )
Your code would be something like this:
<li><%= Html.ActionLink<VanillaController.AuthenticationController>( x => x.Logout(), "Logout", new { class = "Logout" } )%></li>
If that isn't available, you can always create the anchor tag by hand and set the href using Url.Action method. Then you have complete control over how your anchor tag is written out.