AlphaGo is approximating global optimality by finding local optimality. Local optimality is already computationally very hard, but it is exactly what AlphaGo is doing.

The rollouts they are doing, evaluating every probable move, it is a search process of trying to find local optimality. You have a current state of the board and you're trying to find a decision that minimizes your future regret. It is by definition local optimality.

Global optimality would be finding a sequence of moves that wins you a game.