[kotach]

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.

[robotresearcher]

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

Is it known that Go is winnable? It may be that only a draw could be guaranteed. A globally optimal player would be provably able to do (whichever of these it turns out to be) for any legal position. This is harder than winning a particular game.

[kotach]

7.5-point komi variant played by AlphaGo and Lee has a win or lose outcome. There's no draw. But yes, a more formal definition of global optimality does not include victory as a necessary outcome.

[robotresearcher]

Wikipedia says:

"the stronger player will typically play with the white stones and players often agree on a simple 0.5 point komi to break a tie ("jigo") in favor of white."

Which suggests ties can occur in practice with human players, but are then broken wrt an external parameter.

In terms of optimality, is it known in Go whether an optimal player can force a win against (i) all suboptimal players; and (ii) another optimal player, based on whether they play first or second?

I realize we don't know the optimal policy but sometimes we can decide (non)-existence anyway. Anyone happen to know for Go?

[kotach]

The questions you pose require solving the game, at least (ii).

https://en.wikipedia.org/wiki/Solved_game