Katherine Archuleta, the director of the Office of Personnel Management, will resign effective Friday, according to a White House official, one day after it was revealed that sweeping cyberintrusions at the agency resulted in the theft of the personal information of more than 22 million people. Ms. Archuleta went to the White House on Friday morning to personally inform Mr. Obama of her decision, saying that she felt new leadership was needed at the federal personnel agency to enable it to “move beyond the current challenges,” the official said. The president accepted her resignation.