CHANNEL-DRIVEN DECENTRALIZED BAYESIAN FEDERATED LEARNING FOR TRUSTWORTHY DECISION MAKING IN D2D NETWORKS Luca Barbieri Osvaldo Simeoney and Monica Nicoli

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CHANNEL-DRIVEN DECENTRALIZED BAYESIAN FEDERATED LEARNING FOR

TRUSTWORTHY DECISION MAKING IN D2D NETWORKS

Luca Barbieri?, Osvaldo Simeone†, and Monica Nicoli?

?Politecnico di Milano, Milan, Italy

†KCLIP lab, Department of Engineering, King’s College London

ABSTRACT

Bayesian Federated Learning (FL) offers a principled frame-

work to account for the uncertainty caused by limitations

in the data available at the nodes implementing collabora-

tive training. In Bayesian FL, nodes exchange information

about local posterior distributions over the model parameters

space. This paper focuses on Bayesian FL implemented in a

device-to-device (D2D) network via Decentralized Stochas-

tic Gradient Langevin Dynamics (DSGLD), a recently intro-

duced gradient-based Markov Chain Monte Carlo (MCMC)

method. Based on the observation that DSGLD applies

random Gaussian perturbations of model parameters, we

propose to leverage channel noise on the D2D links as a

mechanism for MCMC sampling. The proposed approach

is compared against a conventional implementation of fre-

quentist FL based on compression and digital transmission,

highlighting advantages and limitations.

Index Terms—Federated Learning, Markov Chain

Monte Carlo, Bayesian inference, Decentralized networks

1. INTRODUCTION

Federated Learning (FL) enables the collaborative training of

Machine Learning (ML) models without the direct exchange

of data in both star and fully decentralized architectures [1,

2, 3]. FL is particularly useful when the participating nodes

have limited data. This is the case, for instance, in vehicular

applications in which individual vehicles can only sense part

of a scene (see Fig. 1) [4]. When data sets are size limited,

the classical, frequentist, implementation of FL is known to

produce models that fail to properly account for the uncer-

tainty of their decisions [5]. This is an important issue for

safety-critical applications, such as in automated driving ser-

vices that require trustworthy decisions even in situations with

limited data. A well-established solution to this problem is to

implement Bayesian learning, which encodes uncertainty in

the posterior distribution of the model parameters (see, e.g.,

The work of O. Simeone was supported by the European Research Coun-

cil (ERC) under the European Union’s Horizon 2020 Research and Innova-

tion Programme (grant agreement No. 725732) and by an Open Fellowship

of the EPSRC.

𝑵

𝟐

𝟑

Fig. 1. In the decentralized FL set-up under study, nodes

(here N= 4) implement Bayesian learning via Decentral-

ized Stochastic Gradient Langevin Dynamics (DSGLD) by

levearging noise on inter-agent communications for sampling.

[5]). However, a federated implementation of Bayesian learn-

ing poses challenges related to the overhead of communicat-

ing information about model distributions [6, 7].

In a centralized setting, Bayesian learning is practically

implemented via approximate methods relying on variational

inference (VI) [8] or Markov Chain Monte Carlo (MCMC),

with the latter representing the target posterior distribution

via random samples [9, 5]. Distributed implementations

of Bayesian learning have been emerging for both star and

device-to-device (D2D) topologies adopting VI [10, 6] or

MCMC [11, 12], while assuming ideal communication links.

In this paper, we propose a new MCMC-based Bayesian FL

system tailored for wireless D2D networks with noisy links

subject to mutual interference.

To this end, we focus on Stochastic Gradient Langevin

Dynamics (SGLD) [13], an MCMC scheme that has the prac-

tical advantage of requiring minor modiﬁcations as compared

to standard frequentist methods. In fact, SGLD is based on

the application of Gaussian perturbations to model parame-

ters updated via gradient descent. Reference [14] introduced

a federated implementation of SGLD over a wireless star,

i.e., base station-centric, topology. The work [14] argued that

channel noise between devices and base station can be repur-

posed to serve as sampling noise for the SGLD updates, an

approach referred to as channel-driven sampling. In this pa-

arXiv:2210.10502v1 [eess.SP] 19 Oct 2022

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CHANNEL-DRIVENDECENTRALIZEDBAYESIANFEDERATEDLEARNINGFORTRUSTWORTHYDECISIONMAKINGIND2DNETWORKSLucaBarbieri?,OsvaldoSimeoney,andMonicaNicoli??PolitecnicodiMilano,Milan,ItalyyKCLIPlab,DepartmentofEngineering,King'sCollegeLondonABSTRACTBayesianFederatedLearning(FL)offersaprincipledframe-worktoaccountfor...

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CHANNEL-DRIVEN DECENTRALIZED BAYESIAN FEDERATED LEARNING FOR TRUSTWORTHY DECISION MAKING IN D2D NETWORKS Luca Barbieri Osvaldo Simeoney and Monica Nicoli

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