Which of these actors did not win an Academy Award for Best Director?

From the actors listed, Quentin Tarantino is the one who has not won an Academy Award for Best Director. Warren Beatty (b. March 1937) won the Oscar for Best Director for "Reds", a 1981 American epic historical drama. Richard Attenborough (August 1923 – August 2014) won two Academy Awards, Best Picture and Best Director for "Gandhi", a 1982 period biographical film based on the life of Mahatma Gandhi. Robert Redford (Charles Robert Redford Jr., born August 1936), is one of only six men to win an Academy Award for Best Director for a film debut. He won in 1981 for "Ordinary People", a 1980 American psychological drama.

Quentin Tarantino (b. March 1963 in Knoxville, Tennessee) is an American film director, screenwriter, producer, film critic, and actor. He has had 6 major films receive 7 Oscars (Academy Awards) out of a total of 34 Oscar nominations. His films have won the Academy Award once (Best Original Screenplay, "Pulp Fiction"), once (Best Supporting Actor for Christoph Waltz, "Inglourious Basterds"), once (Best Best Original Score, "The Hateful Eight"), twice (Best Supporting Actor for Christoph Waltz and Best Original Screenplay for Tarantino, "Django Unchained"), and twice (Best Supporting Actor for Brad Pitt and Best Production Design for Barbara Ling and Nancy Haigh, "Once Upon a Time in Hollywood".

Notwithstanding all his film work, many awards, and many nominations for major awards, Tarantino is still missing the Oscar for Best Director. He has hope.