However, finding Lyapunov functions for general nonlinear systems is a challenging task.

Consider a team of cooperative players that take actions in a networkedenvironment. At each turn, each player chooses an action and receives a reward that is an unknown function of all the players' actions. The goal of the team of players is to learn to play together the action profile that maximizes the sum of their rewards. However, players cannot observe the actions or rewards of other players, and can only get this information by communicating with their neighbors.

When f is convex with respect tox, many efficient algorithms can be powerful tools for solving Problem(1). One well-known algorithm is mirror descent (MD) [5]which is based on Bregman divergence.

In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.