Rosa Gini

Luca Pasqualini, Gianluca Amato, Marco Fantozzi et al.

In the last years, the DeepMind algorithm AlphaZero has become the state of the art to efficiently tackle perfect information two-player zero-sum games with a win/lose outcome. However, when the win/lose outcome is decided by a final score difference, AlphaZero may play score-suboptimal moves because all winning final positions are equivalent from the win/lose outcome perspective. This can be an issue, for instance when used for teaching, or when trying to understand whether there is a better move. Moreover, there is the theoretical quest for the perfect game. A naive approach would be training an AlphaZero-like agent to predict score differences instead of win/lose outcomes. Since the game of Go is deterministic, this should as well produce an outcome-optimal play. However, it is a folklore belief that "this does not work". In this paper, we first provide empirical evidence for this belief. We then give a theoretical interpretation of this suboptimality in general perfect information two-player zero-sum game where the complexity of a game like Go is replaced by the randomness of the environment. We show that an outcome-optimal policy has a different preference for uncertainty when it is winning or losing. In particular, when in a losing state, an outcome-optimal agent chooses actions leading to a higher score variance. We then posit that when approximation is involved, a deterministic game behaves like a nondeterministic game, where the score variance is modeled by how uncertain the position is. We validate this hypothesis in AlphaZero-like software with a human expert.

Francesco Morandin, Gianluca Amato, Marco Fantozzi et al.

We develop a new model that can be applied to any perfect information two-player zero-sum game to target a high score, and thus a perfect play. We integrate this model into the Monte Carlo tree search-policy iteration learning pipeline introduced by Google DeepMind with AlphaGo. Training this model on 9x9 Go produces a superhuman Go player, thus proving that it is stable and robust. We show that this model can be used to effectively play with both positional and score handicap, and to minimize suboptimal moves. We develop a family of agents that can target high scores against any opponent, and recover from very severe disadvantage against weak opponents. To the best of our knowledge, these are the first effective achievements in this direction.

Francesco Morandin, Gianluca Amato, Rosa Gini et al.

We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero paradigm. The winrate as a function of the komi is modeled with a two-parameters sigmoid function, so that the neural network must predict just one more variable to assess the winrate for all komi values. A second novel feature is that training is based on self-play games that occasionally branch -- with changed komi -- when the position is uneven. With this setting, reinforcement learning is showed to work on 7x7 Go, obtaining very strong playing agents. As a useful byproduct, the sigmoid parameters given by the network allow to estimate the score difference on the board, and to evaluate how much the game is decided.