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Intuitively, experience playing against one mixture of opponents in a givendomain should be relevant for a different mixture in the same domain. Wepropose a transfer learning method, Q-Mixing, that starts by learning Q-valuesagainst each pure-strategy opponent. Then a Q-value for any distribution ofopponent strategies is approximated by appropriately averaging the separatelylearned Q-values. From these components, we construct policies against allopponent mixtures without any further training. We empirically validateQ-Mixing in two environments: a simple grid-world soccer environment, and acomplicated cyber-security game. We find that Q-Mixing is able to successfullytransfer knowledge across any mixture of opponents. We next consider the use ofobservations during play to update the believed distribution of opponents. Weintroduce an opponent classifier -- trained in parallel to Q-learning, usingthe same data -- and use the classifier results to refine the mixing ofQ-values. We find that Q-Mixing augmented with the opponent classifier functionperforms comparably, and with lower variance, than training directly against amixed-strategy opponent.

Learning to Play against Any Mixture of Opponents