Differentially private distributed algorithms for stochastic aggregative games

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

“…Noting that the summand in the left hand side of the preceding inequality is actually γ k m i=1 x k i − xk 2 , and the right hand side of the preceding inequality is less than infinity almost surely under the proven result in (32) and the assumption in (18), we have that…”

“…However, these approaches are restricted in that they either require the communication graph to satisfy certain properties, or can only protect the cost function value from being uniquely identifiable. As differential privacy (DP) has become the de facto standard for privacy protection due to its strong resilience against arbitrary post-processing and auxiliary information [29], recently [30] and [31] achieve DP in aggregative games at the cost of losing accurate convergence to the exact Nash equilibrium. By co-designing the Nash-equilibrium seeking mechanism and the DP-noise injection mechanism, our prior results [32], [33] successfully achieve both ǫ-DP and accurate convergence in coupling-constraint free Nashequilibrium seeking.…”

“…As differential privacy (DP) has become the de facto standard for privacy protection due to its strong resilience against arbitrary post-processing and auxiliary information [29], recently [30] and [31] achieve DP in aggregative games at the cost of losing accurate convergence to the exact Nash equilibrium. By co-designing the Nash-equilibrium seeking mechanism and the DP-noise injection mechanism, our prior results [32], [33] successfully achieve both ǫ-DP and accurate convergence in coupling-constraint free Nashequilibrium seeking. However, these results are inapplicable to GNE seeking problems, where the shared coupling constraints increase attack surfaces, and hence, pose additional challenges to privacy protection.…”

“…3) Besides achieving rigorous ǫ-DP, the approach can simultaneously ensure accurate convergence to the GNE, which is in sharp contrast to existing DP solutions for coupling-constraint free aggregative games (e.g., [30], [31]) that have to trade accurate convergence for DP.…”

“…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.…”