An Incentive Mechanism for Federated Learning:A Continuous Zero-Determinant Strategy Approach

As a representative emerging machine learning technique, federated learning(FL) has gained considerable popularity for its special feature of “making data available but not visible”. However, potential problems remain, including privacy breaches, imbalances in payment, and inequitable distribution.These shortcomings let devices reluctantly contribute relevant data to, or even refuse to participate in FL. Therefore, in the application of FL, an important but also challenging issue is to motivate as many participants as possible to provide high-quality data to FL. In this paper, we propose an incentive mechanism for FL based on the continuous zero-determinant(CZD) strategies from the perspective of game theory. We first model the interaction between the server and the devices during the FL process as a continuous iterative game. We then apply the CZD strategies for two players and then multiple players to optimize the social welfare of FL, for which we prove that the server can keep social welfare at a high and stable level. Subsequently, we design an incentive mechanism based on the CZD strategies to attract devices to contribute all of their high-accuracy data to FL.Finally, we perform simulations to demonstrate that our proposed CZD-based incentive mechanism can indeed generate high and stable social welfare in FL.

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

A Game Theoretic Approach for a Minimal Secure Dominating Set

The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.

Modeling of Mesoscale Creep Behaviors and Macroscale Creep Responses of Composite Fuels Under Irradiation Conditions

A finite-strain homogenization creep model for composite fuels under irradiation conditions is developed and verified,with the irradiation creep strains of the fuel particles and matrix correlated to the macroscale creep responses,excluding the contributions of volumetric strain induced by the irradiation swelling deformations of fuel particles.A finite element(FE)modeling method for uniaxial tensile creep tests is established with the irradiation effects of nuclear materials taken into account.The proposed models and simulation strategy are numerically implemented to a kind of composite nuclear fuel,and the predicted mesoscale creep behaviors and the macroscale creep responses are investigated.The research results indicate that:(1)the macroscale creep responses and the mesoscale stress and strain fields are all greatly affected by the irradiation swelling of fuel particles,owing to the strengthened mechanical interactions between the fuel particles and the matrix.(2)The effective creep rates for a certain case are approximately two constants before and after the critical fission density,which results from the accelerated fission gas swelling after fuel grain recrystallization,and the effects of macroscale tensile stress will be more enhanced at higher temperatures.(3)The macroscale creep contributions from the fuel particles and matrix depend mainly on the current volume fractions varying with fission density.(4)As a function of the macroscale stress,temperature,initial particle volume fraction and particle fission rate,a multi-variable mathematical model for effective creep rates is fitted out for the considered composite fuels,which matches well with the FE predictions.This study supplies important theoretical models and research methods for the multi-scale creep behaviors of various composite fuels and provides a basis for simulation of the thermal–mechanical behavior in related composite fuel elements and assemblies.