Asynchronous Networked Aggregative Games

Differentially private distributed algorithms for stochastic aggregative games

“…In the derivation, it can be seen that the aggregateestimation error m i=1 v k i − vk does not decrease geometrically with k, which makes it impossible to use existing proof techniques for distributed Nash-equilibrium computation algorithms. In fact, in existing distributed Nash-equilibrium computation algorithms (e.g., [5], [23], [24], [25], [26], [27]) and their stochastic variants (e.g., [28] and [20]), because the inter-player interaction is persistent, the aggregativeestimation error m i=1 v k i − vk always decreases geometrically, which makes it possible to separate the evolution analysis of the aggregate-estimation error and the decision distance from the Nash equilibrium. However, in the proposed algorithm, the diminishing γ k leads to a non-geometric decreasing of the aggregative estimation error, which makes it impossible to analyze the evolution of the aggregate estimate v k i and the decision x k i separately, and hence makes the proposed proof technique fundamentally different from existing analysis.…”

“…The convergence analysis for the proposed algorithms has fundamental differences from existing proof techniques. More specifically, existing convergence analysis of distributed (generalized) Nash-equilibrium computation algorithms for aggregative games (e.g., [5], [23], [24], [25], [26], [27]) and their stochastic variants (e.g., [20] and [28]) rely on the geometric (exponential) decreasing of the aggregateestimation error (consensus error) among the players, which is possible only when all nonzero coupling weights are lower bounded by a positive constant. Such geometric (exponential) decreasing of aggregate-estimation error is key to proving exact convergence of all players' iterates to the Nash equilibrium.…”

An Optimal Distributed Algorithm with Operator Extrapolation for Stochastic Aggregative Games

“…The proposed algorithm can achieve the optimal convergence rate with only one communication round per iteration in comparison with multiple communication rounds required by [6] and [29]. Though [27] can achieve convergence rate 1/k with fixed step-sizes for a deterministic game, our work can achieve the optimal convergence result with diminishing step for a stochastic game, which can model various information uncertainties.…”

“…Furthermore, [26] proposed a distributed gradient algorithm based on iterative Tikhonov regularization method to resolve the class of monotone aggregative games. [27] proposed a fully asynchronous distributed algorithm and rigorously show the convergence to a Nash equilibrium. Besides, [28,9] proposed a continuous-time distributed algorithm for aggregative games.…”

Ensure Differential Privacy and Convergence Accuracy in Consensus Tracking and Aggregative Games with Coupling Constraints

“…5) Even without considering privacy protection, our proof techniques are fundamentally different from existing counterparts and are of independent interest. More specifically, existing proof techniques (in, e.g., [13], [31], [3], [34], [35], [36], [37], [38]) for partial-decision information games rely on the geometric decreasing of consensus errors among the players. In the proposed approach, the diminishing interplayer interaction makes it impossible to have such geometric decreasing of consensus errors, which entails new proof techniques.…”