The problem is that cooking on Yom Tov is only permissible if the food is intended for a Jew. There are ways to invite the non-Jew as an afterthought or "accidentally" make extra.
Some of this is a Fence. My former rabbi (who is more particular than most) held that one could not even revert to Shabbos-mode entertaining lest he forget and do a Yom Tov cooking activity for the non-Jew.
One is allowed, however, to serve only cold food and invite the Non-Jew.
Of course, my ex-rabbi could have been exceedingly stringent on himself (and his congregants) so not only CYLOR, but consult several rabbis to find where the actual issur ends and the fences begin.