Robust pricing mechanism for resource sustainability under privacy constraint in competitive online learning multi-agent systems

We consider the problem of resource congestion control for competing online learning agents under privacy and security constraints. Based on the non-cooperative game as the model for agents' interaction and the noisy online mirror ascent as the model for the rationality of the agents, we propose a novel pricing mechanism that gives the agents incentives for sustainable use of the resources. An advantage of our method is that it is privacy-preserving in the sense that mainly the resource congestion serves as an orientation for our pricing mechanism, in place of the agents' preference and state. Moreover, our method is robust against adversary agents' feedback in the form of the noisy gradient. We present the following result of our theoretical investigation: In case that the feedback noise is persistent, and for several choices of the intrinsic parameter (the learning rate) of the agents and of the mechanism parameters (the learning rate of the price-setters, their progressivity, and the extrinsic price sensitivity of the agents), we show that the accumulative violation of the resource constraints of the resulted iterates is sub-linear w.r.t the time horizon. To support our theoretical findings, we provide some numerical simulations.