A distributed learning algorithm with bit-valued communications for multi-agent welfare optimization

A multi-agent system comprising N agents, each picking actions from a finite set and receiving a payoff that depends on the action of the whole, is considered. The exact form of the payoffs are unknown and only their values can be measured by the respective agents. A decentralized algorithm was proposed by Marden et al. [1] and in the authors´ earlier work [2] that, in this setting, leads to the agents picking welfare optimizing actions under some restrictive assumptions on the payoff structure. This algorithm is modified in this paper to incorporate exchange of certain bit-valued information between the agents over a directed communication graph. The notion of an interaction graph is then introduced to encode known interaction in the system. Restrictions on the payoff structure are eliminated and conditions that guarantee convergence to welfare minimizing actions w.p. 1 are derived under the assumption that the union of the interaction graph and communication graph is strongly connected.