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Price-Discrimination Game for Distributed Resource Management in Federated Learning

Han Zhang, Halvin Yang, Guopeng Zhang

TL;DR

The paper tackles resource management in federated learning by introducing a price-discrimination game (PDG) where a single PS sets differentiated payments to heterogeneous clients based on their contribution to FL performance and resource endowments. It formulates the interaction as a Nash equilibrium of a mixed-integer nonlinear program, and develops a distributed semi-heuristic solver to compute near-optimal strategies for both sides while respecting client-selection constraints. The proposed approach yields a favorable trade-off between model accuracy, training latency, and incentive costs, achieving performance close to the best-practice accuracy strategies while improving fairness among clients and reducing PS utility relative to uniform pricing. The work demonstrates the practical viability of price-discriminatory, energy-aware pricing in FL and outlines extensions to non-IID data, oligopoly markets, and more sophisticated pricing models to curb price gaming.

Abstract

In vanilla federated learning (FL) such as FedAvg, the parameter server (PS) and multiple distributed clients can form a typical buyer's market, where the number of PS/buyers of FL services is far less than the number of clients/sellers. In order to improve the performance of FL and reduce the cost of motivating clients to participate in FL, this paper proposes to differentiate the pricing for services provided by different clients rather than simply providing the same service pricing for different clients. The price is differentiated based on the performance improvements brought to FL and their heterogeneity in computing and communication capabilities. To this end, a price-discrimination game (PDG) is formulated to comprehensively address the distributed resource management problems in FL, including multi-objective trade-off, client selection, and incentive mechanism. As the PDG is a mixed-integer nonlinear programming (MINLP) problem, a distributed semi-heuristic algorithm with low computational complexity and low communication overhead is designed to solve it. The simulation result verifies the effectiveness of the proposed approach.

Price-Discrimination Game for Distributed Resource Management in Federated Learning

TL;DR

The paper tackles resource management in federated learning by introducing a price-discrimination game (PDG) where a single PS sets differentiated payments to heterogeneous clients based on their contribution to FL performance and resource endowments. It formulates the interaction as a Nash equilibrium of a mixed-integer nonlinear program, and develops a distributed semi-heuristic solver to compute near-optimal strategies for both sides while respecting client-selection constraints. The proposed approach yields a favorable trade-off between model accuracy, training latency, and incentive costs, achieving performance close to the best-practice accuracy strategies while improving fairness among clients and reducing PS utility relative to uniform pricing. The work demonstrates the practical viability of price-discriminatory, energy-aware pricing in FL and outlines extensions to non-IID data, oligopoly markets, and more sophisticated pricing models to curb price gaming.

Abstract

In vanilla federated learning (FL) such as FedAvg, the parameter server (PS) and multiple distributed clients can form a typical buyer's market, where the number of PS/buyers of FL services is far less than the number of clients/sellers. In order to improve the performance of FL and reduce the cost of motivating clients to participate in FL, this paper proposes to differentiate the pricing for services provided by different clients rather than simply providing the same service pricing for different clients. The price is differentiated based on the performance improvements brought to FL and their heterogeneity in computing and communication capabilities. To this end, a price-discrimination game (PDG) is formulated to comprehensively address the distributed resource management problems in FL, including multi-objective trade-off, client selection, and incentive mechanism. As the PDG is a mixed-integer nonlinear programming (MINLP) problem, a distributed semi-heuristic algorithm with low computational complexity and low communication overhead is designed to solve it. The simulation result verifies the effectiveness of the proposed approach.
Paper Structure (12 sections, 2 theorems, 26 equations, 5 figures, 2 algorithms)

This paper contains 12 sections, 2 theorems, 26 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Energy consumption for training $\omega_m$
  4. Energy consumption for uploading $\omega_m$
  5. Problem Formulation
  6. The objective of clients
  7. The objective of the PS
  8. Solving The Game
  9. Optimal strategies for the clients
  10. Optimal strategy for the PS
  11. Simulation Results
  12. Conclusions and Future Directions

Key Result

Lemma 1

Regardless of the maximum limit of $f_m$ in constraint maximum frequency of client, the optimal time for client $m$ ($\forall m \in \mathcal{N}$), to complete a session of local training satisfies

Figures (5)

  • Figure 1: The convergence of accuracy.
  • Figure 2: Performance of client selection algorithm.
  • Figure 3: The utility achieved by clients using different algorithms.
  • Figure 4: The utility of the PS with different pricing strategy.
  • Figure 5: The utility of clients with different pricing strategy.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof