  Many applications in machine learning can be framed as minimization problems
and solved efficiently using gradient-based techniques. However, recent
applications of generative models, particularly GANs, have triggered interest
in solving min-max games for which standard optimization techniques are often
not suitable. Among known problems experienced by practitioners is the lack of
convergence guarantees or convergence to a non-optimum cycle. At the heart of
these problems is the min-max structure of the GAN objective which creates
non-trivial dependencies between the players. We propose to address this
problem by optimizing a different objective that circumvents the min-max
structure using the notion of duality gap from game theory. We provide novel
convergence guarantees on this objective and demonstrate why the obtained limit
point solves the problem better than known techniques.
