He was married to Jennifer Esposito. There were blind items about emotional abuse in the marriage and she wrote about it in her book.
http://www.dailymail.co.uk/tvshowbiz/article-2625632/Jennifer-Esposito-blasts-ex-husband-Bradley-Cooper-new-book.html
http://www.dailymail.co.uk/tvshowbiz/article-2625632/Jennifer-Esposito-blasts-ex-husband-Bradley-Cooper-new-book.html