One who is reviled by the people, who saves people as the result of villainy, and who clarifies good with evil.
A savior who is both worshipped and cursed in equal measure. That is an anti-hero.
That said, a pure anti-hero does not exist.
The closest thing would be those who do good despite being evil.
Assassin and Archer fall under this category.
Rider and Caster, on the other hand, are not proper heroic spirits, but they can’t really be called anti-heroes, either.

Fate/side material: Fate Encyclopedia