Edge-cloud computing networks integrate dispersed computing resources of edges and clouds through networks, which improves resource utilization by flexibly scheduling tasks to suitable computing nodes. The performance of edge-cloud computing networks depends significantly on the amount of computing resources and the task scheduling scheme. In this work, we propose a novel computing resource trading and task scheduling framework for edge-cloud computing networks with arbitrary network topology. Specifically, we consider a third-party platform which incentivizes computing nodes to share computing resources by designing proper resource pricing mechanisms, and charges customers execution fees by scheduling tasks optimally in the edge-cloud computing network. The platform’s resource pricing and task scheduling optimization problem captures the unique features of edge-cloud computing networks including the heterogeneities of computing resources and tasks, as well as the multi-hop offloading in arbitrary topology, which is challenging to solve. We solve the problem for the homogeneous workload scenario and the heterogeneous workload scenario, respectively. For the homogeneous workload scenario, we propose a multi-round proposer-voter algorithm (MPV) that achieves the global optimum in polynomial time for the non-competitive case. For the heterogeneous workload scenario, we first propose a Gibbs sampling based iterative algorithm (GSI), which updates task scheduling strategies iteratively using Gibbs sampling and converges to the global optimum with high probability. We further propose a distributed alternating update algorithm (DAU), which converges to the local optimum in a distributed manner with linear complexity. Numerical results demonstrate the effectiveness of our proposed resource trading and task scheduling schemes.

In cross-silo federated learning (FL), clients of common interest cooperatively train a global model without sharing local sensitive data, but they still face potential privacy leakage due to privacy threats from malicious attackers. Although some articles have proposed effective privacy-preserving mechanisms for FL (such as differential privacy (DP)), clients in cross-silo FL are usually different companies or organizations who may behave selfishly to optimize their own benefits. In this article, we study DP-based cross-silo FL where clients selfishly decide their participation levels (i.e., data sizes for model trainings) and privacy leakage tolerance levels to trade off between model accuracy loss and privacy loss, and we model clients’ interactions as a participation-dependent privacy preservation game. It is challenging to analyze the game since the comprehensive impact of participation levels and privacy leakage tolerance levels on model accuracy is unclear and the behaviors of heterogeneous clients are coupled in a highly complex manner. To capture the impact of participation and privacy preservation behaviors, we first characterize the optimality gap of DP-based cross-silo FL for both convex and non-convex models, where the privacy leakage tolerance levels and the participation levels are coupled nonlinearly. We model clients’ costs based on the optimality gap, and prove that clients’ selfish participation-dependent privacy preservation game is a potential game. To analyze the optimal strategies of heterogeneous clients in a stable state, we derive the closed-form expression for the unique Nash equilibrium (NE), where clients may choose full participation or partial participation, and the equilibrium privacy preservation strategy depends on clients’ accuracy-privacy preference ratios. We analyze the social efficiency of the NE by calculating the price of anarchy (PoA) and show that the PoA increases with the number of clients and the heterogeneity of clients’ model accuracy preferences. To improve the social efficiency achieved at equilibrium, we design a socially efficient incentive mechanism that allows clients with large model accuracy preferences to compensate clients with small model accuracy preferences. Extensive experiments verify our theoretical results for both the convex and non-convex models as well as both the i.i.d. data distribution case and the non-i.i.d. data distribution case.