Ensuring Truthfulness in Distributed Aggregative Optimization (2501.08512v3)

Abstract: Distributed aggregative optimization methods are gaining increased traction due to their ability to address cooperative control and optimization problems, where the objective function of each agent depends not only on its own decision variable but also on the aggregation of other agents' decision variables. Nevertheless, existing distributed aggregative optimization methods implicitly assume all agents to be truthful in information sharing, which can be unrealistic in real-world scenarios, where agents may act selfishly or strategically. In fact, an opportunistic agent may deceptively share false information in its own favor to minimize its own loss, which, however, will compromise the network-level global performance. To solve this issue, we propose a new distributed aggregative optimization algorithm that can ensure truthfulness of agents and convergence performance. To the best of our knowledge, this is the first algorithm that ensures truthfulness in a fully distributed setting, where no "centralized" aggregator exists to collect private information/decision variables from participating agents. We systematically characterize the convergence rate of our algorithm under nonconvex/convex/strongly convex objective functions, which generalizes existing distributed aggregative optimization results that only focus on convex objective functions. We also rigorously quantify the tradeoff between convergence performance and the level of enabled truthfulness under different convexity conditions. Numerical simulations using distributed charging of electric vehicles confirm the efficacy of our algorithm.