  Game theory serves as a powerful tool for distributed optimization in
multi-agent systems in different applications. In this paper we consider
multi-agent systems that can be modeled by means of potential games whose
potential function coincides with a global objective function to be maximized.
In this approach, the agents correspond to the strategic decision makers and
the optimization problem is equivalent to the problem of learning a potential
function maximizer in the designed game. The paper deals with two different
information settings in the system. Firstly, we consider systems, where agents
have the access to the gradient of their utility functions. However, they do
not possess the full information about the joint actions. Thus, to be able to
move along the gradient toward a local optimum, they need to exchange the
information with their neighbors by means of communication. The second setting
refers to a payoff-based approach to learning potential function maximizers.
Here, we assume that at each iteration agents can only observe their own played
actions and experienced payoffs. In both cases, the paper studies unconstrained
non-convex optimization with a differentiable objective function. To develop
the corresponding algorithms guaranteeing convergence to a local maximum of the
potential function in the game, we utilize the idea of the well-known
Robbins-Monro procedure based on the theory of stochastic approximation.
