In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifi...

The fictitious domain method for the solution of variational inequalities with the Signorini boundary conditions is analyzed.

In the Fictitious Domain Method with Lagrange multiplier (FDM) the physical domain is embedded into a simpler but larger domain called the fictitious domain. The partial differential equation is extended to the fictitious domain using a Lagrange multiplier to enforce the prescribed boundary conditions on the physical domain while all the other data are extended to the fictitious domain. This le...

Decentralised optimisation tasks are important components of multiagent systems. These tasks can be interpreted as n-player potential games: therefore game-theoretic learning algorithms can be used to solve decentralised optimisation tasks. Fictitious play is the canonical example of these algorithms. Nevertheless fictitious play implicitly assumes that players have stationary strategies. We pr...

Generative adversarial networks (GANs) are powerful tools for learning generative models. In practice, the training may suffer from lack of convergence. GANs are commonly viewed as a two-player zerosum game between two neural networks. Here, we leverage this game theoretic view to study the convergence behavior of the training process. Inspired by the fictitious play learning process, a novel t...