Designing Learning Algorithms over the Sequence Form of an Extensive-Form Game

We focus on multi-agent learning over extensive-form games. When designing algorithms for extensive-form games, it is common the resort to tabular representations (i.e., normal form, agent form, and sequence form). Each representation provides some advantages and suffers from some drawbacks and it is not known which representation, if any, is the best one in multi-agent learning. In particular, a wide literature studies algorithms for the normal form, but this representation is prohibitive in practice since it is exponentially large in the size of the game tree. In this paper, we show that some learning algorithms defined over the normal form can be redefined over the sequence form so that the dynamics of the two algorithms are realization equivalent (i.e., they induce the same probability distribution over the outcomes). This allows an exponential compression of the representation and therefore makes such algorithms employable in practice.