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Scalable decision-making for games of imperfect information

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Samuel Sokota, Eugene Vinitsky, Hengyuan Hu, Zhiyuan Fan, J. Zico Kolter, Gabriele Farina

For years, computers could master games where everything was visible, but hidden information stopped them cold. Then one system beat Stratego’s most decorated human player by a margin never seen at the highest level.

Abstract

Real-world decision-making generally involves hidden information, that is, information that is unknown to one agent but possessed by another. Unfortunately, the presence of large amounts of hidden information renders established reinforcement learning and search approaches ineffective. Even with multimillion-dollar industrial research efforts1, top-human-level play at Strategoa board wargame with hidden information on a massive scalehas remained beyond the reach of artificial intelligence (AI). Here we introduce Ataraxos, an AI for Stratego based on general techniques that we developed for both self-play reinforcement learning and test-time search under hidden information. Ataraxos defeated the most decorated human Stratego player of all time by a large marginachieving, to our knowledge, the first superhuman result in the games historywhile consuming orders of magnitude less compute and data than previous efforts. Using the same techniques, we built a superhuman AI for Barrage Stratego and state-of-the-art AIs for Hanabi and dou dizhu, all with low cost and high sample efficiency. The success of this approach across adversarial, cooperative and team games establishes a design pattern for reinforcement learning and search that is effective under large amounts of hidden information, a longstanding desideratum of the field of strategic decision-making.

Transcript

For years, computers could master games where everything was visible, but hidden information stopped them cold. Then one system beat Stratego’s most decorated human player by a margin never seen at the highest level. Real-world decision-making generally involves hidden information: information unknown to one agent but possessed by another.

That is why situations such as negotiations and conflict are difficult for machines. Large amounts of hidden information render established learning and search approaches ineffective. Even multimillion-dollar industrial research efforts had not reached top-human-level play at Stratego, a board wargame with hidden information on a massive scale.

Stratego is difficult for AI because players must move pieces whose identities are hidden, then make sudden decisions when two pieces meet and are revealed. A captured flag ends the game, so one unseen mistake can decide everything.

Ataraxos uses a design that combines learning from games against itself with search at decision time. Think of a person planning a trip: first they learn which routes usually work, then they check the roads before leaving. One part proposes decisions and predicts outcomes.

Another models hidden information. A search then refines the choice at the moment it is needed. At decision time, Ataraxos begins by generating possible versions of the hidden information. It does not pretend that one guess is certain; it considers different ways the unseen situation might be.

It plays out candidate actions under each possible version and estimates their value from the positions reached. It then uses those estimates to update only the current decision and chooses from the updated policy. Because this step mimics the updates used during self-play learning, the search inherits improvement properties from that learning process.

Ataraxos defeated Pim Niemeijer, the most decorated Stratego player of all time, by fifteen wins to one, with four draws in a twenty-game series. The result came while training cost only a few thousand dollars. Across twenty games, the system’s assessment usually moved toward a clear win, often well before the final move, while the drawn games stayed near an even chance or ended with uncertainty.

That makes the fifteen wins, one loss and four draws feel like sustained control rather than a run of narrow escapes. The same techniques produced a superhuman AI for Barrage Stratego and state-of-the-art AIs for Hanabi and dou dizhu, with low cost and high sample efficiency.

The results span adversarial, cooperative and team games, suggesting that the approach is not tied to one particular kind of contest. The techniques were applied across Barrage Stratego, Hanabi and dou dizhu, spanning two-player competitive games, fully cooperative games and two-team competitive games.

In all cases, the systems achieved state-of-the-art results across a diverse collection of settings with hidden information. Combining learning from experience with search has been a powerful recipe for strategic decision-making, but it once had limited use when important information was hidden.

These results show that large amounts of hidden information are no longer prohibitive. Practical AI is within reach for many strategic problems when fast, accurate simulators can be built. The search is not unlimited: its improvement is bounded because it mimics a single update step.

A more sophisticated search could use additional computing to keep improving the policy. The search's improvement is bounded because it mimics only a single update step. A more sophisticated algorithm could use additional computation to keep improving the policy, with knowledge-limited subgame solving as one possible route.

The key is to let an AI imagine what it cannot see, test possible choices, and improve the choice it makes now. That brings practical decision-making systems closer to real situations where crucial facts are hidden.

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