  Although recent work in AI has made great progress in solving large,
zero-sum, extensive-form games, the underlying assumption in most past work is
that the parameters of the game itself are known to the agents. This paper
deals with the relatively under-explored but equally important "inverse"
setting, where the parameters of the underlying game are not known to all
agents, but must be learned through observations. We propose a differentiable,
end-to-end learning framework for addressing this task. In particular, we
consider a regularized version of the game, equivalent to a particular form of
quantal response equilibrium, and develop 1) a primal-dual Newton method for
finding such equilibrium points in both normal and extensive form games; and 2)
a backpropagation method that lets us analytically compute gradients of all
relevant game parameters through the solution itself. This ultimately lets us
learn the game by training in an end-to-end fashion, effectively by integrating
a "differentiable game solver" into the loop of larger deep network
architectures. We demonstrate the effectiveness of the learning method in
several settings including poker and security game tasks.
