Learning to play against any mixture of opponents

Intuitively, experience playing against one mixture of opponents in a given domain should be relevant for a different mixture in the same domain. If the mixture changes, ideally we would not have to train from scratch, but rather could transfer what we have learned to construct a policy to play against the new mixture. We propose a transfer learning method, Q-Mixing, that starts by learning Q-values against each pure-strategy opponent. Then a Q-value for any distribution of opponent strategies is approximated by appropriately averaging the separately learned Q-values. From these components, we construct policies against all opponent mixtures without any further training. We empirically validate Q-Mixing in two environments: a simple grid-world soccer environment, and a social dilemma game. Our experiments find that Q-Mixing can successfully transfer knowledge across any mixture of opponents. Next, we consider the use of observations during play to update the believed distribution of opponents. We introduce an opponent policy classifier—trained reusing Q-learning data—and use the classifier results to refine the mixing of Q-values. Q-Mixing augmented with the opponent policy classifier performs better, with higher variance, than training directly against a mixed-strategy opponent.