Energy Minimization for Participatory Federated Learning in IoT Analyzed via Game Theory

TL;DR

This work tackles energy minimization in participatory federated learning for IoT by formulating a distributed game where each node chooses its participation probability $p_i$. The model accounts for local sensing/training energy, wireless transmission, and idle energy, with the round duration following a Poisson-Binomial distribution and convergence measured by a target accuracy. A utility incorporating expected convergence time, AoI-based incentives, and participation cost yields a symmetric Nash equilibrium, whose efficiency is captured by the Price of Anarchy. Experiments with CIFAR-10 and ResNet-18 demonstrate that AoI-based incentives can substantially improve participation and bring decentralized performance close to the centralized optimum, highlighting practical implications for energy-aware IoT deployments.

Abstract

The Internet of Things requires intelligent decision making in many scenarios. To this end, resources available at the individual nodes for sensing or computing, or both, can be leveraged. This results in approaches known as participatory sensing and federated learning, respectively. We investigate the simultaneous implementation of both, through a distributed approach based on empowering local nodes with game theoretic decision making. A global objective of energy minimization is combined with the individual node's optimization of local expenditure for sensing and transmitting data over multiple learning rounds. We present extensive evaluations of this technique, based on both a theoretical framework and experiments in a simulated network scenario with real data. Such a distributed approach can reach a desired level of accuracy for federated learning without a centralized supervision of the data collector. However, depending on the weight attributed to the local costs of the single node, it may also result in a significantly high Price of Anarchy (from 1.28 onwards). Thus, we argue for the need of incentive mechanisms, possibly based on Age of Information of the single nodes.

Figures (6)

• Figure 1: Total energy spent $(\mathcal{E})$ vs. number of rounds to converge $(d)$.
• Figure 2: Utility from a fit of the FL simulation, applying \ref{['eq:utility']} with $c=0$.
• Figure 3: NE solution of the participation probability for various cost factors $c$ and incentive weights $\gamma$.
• Figure 4: Nodes' participation probability in the optimal centralized solution and at the NE with and without incentive.
• Figure 5: Utility obtained by the optimal centralized nodes' participation probability and at the NE for various values of the $c$ parameter.