# Distributed Swarm Learning for Edge Internet of Things

Yue Wang, , Zhi Tian, , Xin Fan, ,
Zhipeng Cai, , Cameron Nowzari, , and Kai Zeng

## Abstract

The rapid growth of Internet of Things (IoT) has led to the widespread
deployment of smart IoT devices at wireless edge for collaborative machine
learning tasks, ushering in a new era of edge learning. With a huge number of
hardware-constrained IoT devices operating in resource-limited wireless
networks, edge learning encounters substantial challenges, including
communication and computation bottlenecks, device and data heterogeneity,
security risks, privacy leakages, non-convex optimization, and complex
wireless environments. To address these issues, this article explores a novel
framework known as distributed swarm learning (DSL), which combines artificial
intelligence and biological swarm intelligence in a holistic manner. By
harnessing advanced signal processing and communications, DSL provides
efficient solutions and robust tools for large-scale IoT at the edge of
wireless networks.

## Introduction

Smart Internet of Things (IoT) become the workhorse at wireless edge, where
IoT devices gather valuable data directly from edge environments and fuel the
recent trend of artificial intelligence (AI) applied at the edge, a.k.a. edge
learning. However, traditional machine learning (ML) methods are not suitable
for edge learning, since they hinge on collecting raw data from local devices
and raising concerns of privacy leakages and security risks. Alternatively,
federated learning (FL) has emerged to allow distributed learning while
keeping data locally [1], which has led to fruitful attempts in implementing
AI among distributed terminal users, e.g., cell phones.

The success of vanilla FL typically relies on ideal learning conditions and
perfect wireless environments, where cell phones possess powerful computing
capability and communicate over secure networks with stable connectivity[1].
But, these assumptions become invalid in many real-world edge IoT
applications, where low-cost IoT devices typically have constrained
computation and communication capability. Further, when neural networks are
employed, the large size of model parameters poses a major challenge in
transmitting all the updates from distributed workers during the training
stage of FL. In addition, stochastic gradient descent (SGD) is widely used for
model training, assuming independent and identically distributed (i.i.d.) data
samples at local workers. This assumption however does not hold in edge IoT,
as IoT devices only access small-volume data. All these factors give rise to
the following challenges to IoT-driven edge learning.

Challenge-1: Communication bottleneck. The large size of learning models and
huge number of distributed workers incur high communication costs for edge
learning in IoT systems, while low-cost IoT devices are prone to power
constraints, bandwidth limits, and communication resource scarcity.

Challenge-2: Non-convex optimization. Gradient-based algorithms get trapped in
local optima when tackling non-convex problems, e.g., training neural networks
with nonlinear activation. This problem worsens in distributed learning,
particularly in IoT scenarios where edge devices access limited data.

Challenge-3: Data and device heterogeneity. Edge learning faces statistical
heterogeneity in local training data across workers, also known as the
non-i.i.d. data issue, as well as device heterogeneity in IoT hardware
capability and link quality, which degrades edge learning performance
significantly.

Challenge-4: Privacy and security concerns. Although standard FL excels in
idealized networks and attack-free learning scenarios, it proves susceptible
to outliers, eavesdroppers, privacy breach, and Byzantine attacks, all of
which inevitably exist in IoT applications, wireless systems, and edge
networks.

Challenge-5: Complex network environments. Edge IoT systems usually experience
communication errors, node failures and link interruptions. Further, for
large-scale networks, workers have to deal with time-varying topology and
environments where traditional designs for the static case fail to work.

While some of the aforementioned challenges have been partially addressed in
recent literature on FL for IoT [2], the primary focus and main efforts are
found on revising, adapting, and customizing standard FL methods. Most
existing results stem from the AI perspective alone, but neglect unique
characteristics of edge IoT, including the large population of IoT devices,
limited capability of each IoT device, and local data of small volume.
Intriguingly, biological organisms in nature having swarm intelligence, even
if individually weak, have successfully demonstrated superior strength in
collectively searching the optimal solutions, recovering from errors, and
adapting to environment changes. Since these attributes are sought out by IoT-
driven edge learning, biological intelligence (BI) is expected to boost
efficiency and robustness of edge learning among massive low-cost IoT.

This article investigates a holistic integration of AI and BI, by leveraging
swarm intelligence and cooperative gains among massive IoT workers to develop
efficient and robust distributed learning techniques at wireless edge. A new
edge learning paradigm, called distributed swarm learning (DSL) [3], is
proposed by connecting the AI-enabled FL with the BI-inspired particle swarm
optimization (PSO) [4], as shown in Fig. 1. While the discussions in this
article mainly refer to the vanilla FL for clarity, the DSL framework allows
the PSO-related techniques to be combined with the general FL family, to
address the key challenges and unique characteristics of edge IoT systems with
a large number of resource-constrained devices.

Figure 1: Distributed swarm learning framework for edge IoT.

First, to overcome Challenge-1, DSL judiciously selects only a small number of
workers to share their local model updates for collaboration in the swarm.
Thus, the communication costs and transmit power consumed in DSL can be saved
dramatically. Further, communication efficiency of DSL can be strengthened in
combination with parsimonious transmission methods and strategies.

Second, DSL combines the velocity in PSO with the gradient in SGD, which
amounts to embedding a bio-inspired mechanism to FL. Thanks to the
exploration-exploitation mechanism of PSO in velocity updating, particle
solutions in swarm have an increased chance to escape from the local optimum
traps in Challenge-2, given heterogeneous data and devices in Challenge-3.
Thus, iterative DSL algorithms converge faster to better accuracy at reduced
overall communication/computation rounds than PSO or FL alone.

Third, by using over-the-air aggregation, multiple workers are allowed to
simultaneously transmit their local model variables over the same time-
frequency resources. Hence, device restrictions in communication bandwidth and
resource constraints in Challenge-1 would minimally affect the DSL operations.
Further, over-the-air aggregation enhances privacy preserving capability due
to the inherent inaccessibility to individual local updates, which mitigates
the risk of potential model inversion attacks in Challenge-4.

Fourth, introducing a very small-volume global dataset plays a key role in
providing high accuracy, efficiency and robustness of DSL in the presence of
non-i.i.d. data in Challenge-3 and adversarial attacks in Challenge-4. A part
of this globally shared dataset is used for training, whose effectiveness in
alleviating the non-i.i.d. problem is proved through model divergence
analysis. The other part is used to calculate the fair-value loss for scoring
the models, which not only helps in worker selection but also enables to
screen potential attacks.

Last, in response to Challenge-5, per the efficient and robust updating rule
of DSL established in swarm, even if some workers do not respond to the
request for sharing local updates, the rest workers are still able to work as
long as the network connectivity is not broken. This enhances the robustness
of DSL against node and link failures happened in edge IoT scenarios. DSL has
potentials to be implemented in massively parallel and adaptive manners, and
so scale better than traditional distributed approaches.

## Framework of Distributed Swarm Learning

This article refers to IoT-driven edge learning paradigms, where massive low-
cost IoT workers collaboratively learn common model parameters form
distributed local data, given limited communication, computation, and storage
capabilities at each worker. Further, the learning performance is impacted by
bandwidth limits, malicious attacks, node malfunctions, link failures,
heterogeneity in devices and data, and complex network environments.

### Federated Learning

Standard FL is originally designed in ideal learning and network settings [1],
without the additional constraints on IoT devices and edge environments.
Therein the minimization of the loss function is typically carried out by the
SGD algorithm, whose performance highly relies on i.i.d. data samples and
error-free transmissions. At workers, they individually update their local
models, and then the global model or averaged gradient is calculated from all
local updates, which works as the initial point for local updating at the next
iteration. Computation and communication take place at all local workers in
every iteration, until FL convergence. In the case of non-convex problems,
existing gradient-based FL solutions may converge to undesired local optima,
but without effective mechanisms to escape from such traps.

### Particle Swarm Optimization

Inspired by the BI behavior of swarming animals, PSO is capable of solving
complex optimization problems without requiring convexity assumptions [4]. In
PSO, mimicking swarm behavior in animal flocks, particles run the movements of
a swarm to collectively search for an optimal solution. Each particle’s
position represents a potential solution to the problem, while its velocity
dictates the direction for updating in the following step. To discover the
globally optimal solution within the swarm, particles collaboratively update
their velocities and positions over iterations. Notably, the velocity update
is achieved through a weighted combination of three components: inertia from
the previous direction, individual guidance toward each particle’s historical
best variable, and social guidance toward the globally best variable
discovered by the entire swarm. Such a weighted combination introduces an
effective mechanism for balancing self-exploration and group-exploitation in
swarm optimization.

### Distributed Swarm Learning

For model updating, the gradient in FL and the velocity in PSO play a similar
role as the updating direction, but their updating principles are different.
In PSO, the velocity is a weighted combination of three sub-directions, where
the collaboration is reflected in the socially updated sub-direction towards
the up-to-date globally best variable. As a gradient-free stochastic
optimization method, PSO excels in its ability to collaboratively search for
the globally optimal solutions to complex problems, thanks to its built-in
exploration-exploitation mechanism and the swarm nature. But, PSO assumes a
globally common loss function for all workers to facilitate collaboration,
which no longer holds in distributed learning problems characterized by data-
dependent local loss functions. In contrast, FL is a gradient-based learning
algorithm with fast convergence. However, it is subject to local optimum traps
and suffers from high communication costs in massive IoT systems.

The advantages and disadvantages mentioned for FL and PSO motivate to
establish a connection between distributed learning and swarm optimization
techniques. This integration aims to harness the strengths of both artificial
and biological intelligence for enhanced problem-solving capability. There
exist few recent efforts to directly employ PSO concepts to enhance the
performance of FL. In [5], FL is applied in the learning process, whereas PSO
is used separately for the purpose of searching the optimal hyperparameters.
In [6], PSO and FL are combined in a straightforward manner for an idealized
distributed setting with i.i.d. data among workers and in the absence of any
security attacks. The work [6] builds on an implicit assumption that a common
loss function is accessible to all local workers, simplifying the process of
evaluating the globally best model through a simplistic single-worker
selection scheme. However, the loss function is only partially observable at
local workers, which is data-dependent and therefore varies across workers in
distributed learning cases. Thus, the method of [6] may not perform
effectively in edge IoT scenarios where non-i.i.d. data is encountered at
distributed local workers.

To fill the identified technical gaps above, DSL is recently proposed as a
novel distributed learning framework tailored to edge IoT [3], which is
schematically illustrated through the following model updating step per
iteration:

$\displaystyle\mathbf{w}_{i,t+1}\\!=\\!\mathbf{w}_{i,t}+$
$\displaystyle\;\underbrace{\lambda_{t}(c_{0}\mathbf{v}_{i,t}\\!+\\!c_{1}(\mathbf{w}_{i,t}^{p}\\!-\\!\mathbf{w}_{i,t}\\!)\\!+\\!c_{2}(\mathbf{w}_{t}^{g}\\!-\\!\mathbf{w}_{i,t}\\!))}_{\mathbf{BI}}\underbrace{-{(}1{-}\lambda_{t}\\!{)}\alpha\nabla
F_{i}(\mathbf{w}_{i,t};\mathcal{D}_{i}\\!)}_{\mathbf{AI}}\,,$ (1)

where $\lambda_{t}\in[0,1]$ plays an adaptive tradeoff between the BI
contributions to escape from local optimum traps via swarm intelligence and
the AI contributions to learn the underlying mapping function from local
training data $\mathcal{D}_{i}$. Intuitively, a larger $\lambda_{t}$
encourages workers to update their models by utilizing the exploration-
exploitation gains from the swarm, whereas a smaller $\lambda_{t}$ suggests to
update models by mainly following the guidelines from the gradients with
learning rate $\alpha$. Further, among the three PSO coefficients, $c_{0}$ is
a positive number while $c_{1}$ and $c_{2}$ are positive and random (say,
uniformly distributed for stochastic optimization). Such three coefficients
jointly determine a combination of three sub-directions of the PSO terms,
where $c_{0}$ can be set linearly decreasing over iterations to tune the
solution search process from exploration to exploitation, $c_{1}$ and $c_{2}$
indicate the random exploration level at individual workers and the
exploitation level in swarm, respectively. Thus, $c_{0}$, $c_{1}$, and $c_{2}$
balance exploration of individuals and exploitation in the swarm.

In this sense, for each worker $i$, its local model parameter vector
$\mathbf{w}_{i,t}$ is updated through local velocity $\mathbf{v}_{i,t}$ and
gradient $\nabla F_{i}$ terms jointly in (Distributed Swarm Learning), where
$\mathbf{w}_{i,t}^{p}$ records its own historical best variable,
$\mathbf{w}_{t}^{g}$ is the globally best variable of the swarm,
$F_{i}(\cdot)$ is the local loss evaluated on the local dataset
$\mathcal{D}_{i}$. Upon updating $\mathbf{w}_{i,t}$, at each worker, the
locally best variable $\mathbf{w}_{i,t}^{p}$ and the fair-value loss
$F_{i,t}^{p}$ are calculated by using a small global dataset $\mathcal{D}_{g}$
that is introduced and made available to all workers:

$\left\\{\mathbf{w}^{p}_{i,t}\,,F_{i,t}^{p}\right\\}=\min\left\\{F_{i,t-1}^{p}\,,F_{i}(\mathbf{w}_{i,t};\mathcal{D}_{g})\right\\}.$
(2)

To do this, each edge device only needs to locally store the previous best
model $\mathbf{w}_{i,t-1}^{p}$ and its associated loss function value
$F_{i,t-1}^{p}$. These two quantities about the historical information are
locally maintained by either overwriting the memory as
$\mathbf{w}^{p}_{i,t}=\mathbf{w}_{i,t}$ and
$F_{i,t}^{p}=F_{i}(\mathbf{w}_{i,t};\mathcal{D}_{g})$ when a better local
solution is reached with a lower loss i.e.,
$F_{i}(\mathbf{w}_{i,t};\mathcal{D}_{g})<F_{i,t-1}^{p}$, or simply keeping the
previous ones i.e., $\mathbf{w}^{p}_{i,t}=\mathbf{w}^{p}_{i,t-1}$ and
$F_{i,t}^{p}=F_{i,t-1}^{p}$ otherwise. As a result, such memory overhead is
quite small for maintaining the historical models and function values at each
local device.

When a central server is present, it collects these scalar loss values
$F_{i,t}^{p}\,,i=1,\dots,U$ from all $U$ workers to perform adaptive worker
selection, so that only a few (say $S_{t}$) workers with the lowest losses are
selected to transmit their locally best variables $\mathbf{w}_{i,t}^{p}$ to
the server for updating the global $\mathbf{w}_{t}^{g}$ via over-the-air
aggregation:

$\mathbf{w}_{t}^{g}=\frac{1}{S_{t}}\sum_{i\in\mathcal{S}_{t}}\underbrace{\mathbf{p}_{i,t}\odot\mathbf{h}_{i,t}\odot}_{\textbf{Over-
the-air}}\mathbf{w}^{p}_{i,t}+\mathbf{n}_{t}\,,$ (3)

where $\odot$ is the Hadamard product, $\mathbf{n}_{t}$ is additive noise,
$\mathcal{S}_{t}$ of size $S_{t}=|\mathcal{S}_{t}|\,(1\leq S\leq U)$ is a
subset of selected workers, $\mathbf{p}_{i,t}$ and $\mathbf{h}_{i,t}$
represent the transmit power and channel state at the $i$-th worker,
respectively. When channel states are known, power control and worker
selection offer the freedom for design tradeoffs, which can be carried out via
joint optimization for worker selection and resource allocation [8].
Meanwhile, over-the-air analog aggregation not only improves communication
efficiency, but also enhances the data privacy preserving capability thanks to
the inherent inaccessibility to individual local updates.

## Efficient Distributed Swarm Learning

A body of literature has been devoted to address the communication efficiency
of FL, via gradient sparsification, message quantization, and infrequent
transmissions of local model updates. They either compress the information to
be transmitted or drop less-informative transmissions prior to aggregation of
local updates. On the other hand, all of these methods still entail all
participating workers to exchange their local model updates, which is however
not well-suited for edge IoT systems and leads to tremendous communication
costs, especially when dealing with a large number of IoT devices. To save
device energy consumption and reduce total communication cost in edge
networks, DSL incorporates parsimonious transmission and aggregation schemes
with the built-in exploration-exploitation mechanism in a swarm.

### Efficient Communication and Computation

Recall the different collaboration mechanisms between FL and PSO: In FL, all
workers report their local updates for global averaging; while in PSO, only
one worker is selected as the up-to-date global best to share its local update
with others. For the purpose of the best worker selection in PSO, each worker
is also requested to share the minimum value of its historical local loss
functions to compare with that of others. FL and PSO work as the two extreme
cases under the DSL framework. To collect the benefits from both sides, the
communication and aggregation protocols in DSL need to be carefully designed
with theoretical backing.

#### Communication Censoring

In DSL, all the workers report their individual historical best local function
values, based on which a few best workers with the lowest losses are selected
for the calculation of the global model variables in each iteration as (3).
Even though the loss function values are scalar, such a reporting process
still consumes large communication overhead as the total number of workers
goes large in edge IoT. Note that the reported values are sorted for worker
selection, while the sorting operation accommodates some level of value
approximations. It prompts to introduce a communication-censoring strategy at
each worker to save individual communication cost. That is, each worker
assesses how much its current local best function value differs from its
previously recorded one, and reports only when the difference is large enough
to exceed a censoring threshold. Otherwise, the worker does not report to save
transmission, and worker selection is made based on its previously reported
value as an approximation of its current value. The censoring process is
autonomous based on the judiciously designed local censoring threshold to
guarantee convergence [7].

#### Adaptive Multi-Worker Selection

After collecting or approximating workers’ historical best local function
values through the communication censoring scheme, it is essential to deploy a
multi-worker selection strategy by deciding $S_{t}$, the number of selected
workers who will contribute their local historical best variables to the
global variable updating in (3). Note that DSL encourages local workers to
move along the social direction towards the global best variable as a means of
exploitation of swarm collaboration in (Distributed Swarm Learning). To
effectively fulfill the exploration-exploitation mechanism with communication
efficiency, an adaptive strategy can be employed to increase the value of
$S_{t}$ along the iterations. Intuitively, a smaller $S_{t}$ at the early
stage of iterations allows individual workers to focus on exploring the
solutions locally at little communication overhead, and then a larger $S_{t}$
during later iterations brings more workers to contribute to the collective
swarm intelligence for high model training accuracy at convergence.

On one hand, when worker selection is involved, DSL does require double
iterations of communication for each round (one to communicate the loss values
for worker selection and the other to communicate the local variables of
selected workers for global model updating). Interestingly, such a strategy is
designed to reduce the overall communication overhead and time complexity,
which turns out to a reduction of the total energy consumption. Note that the
loss value is scalar, which consumes little cost to communicate compared with
communicating the model variables. This extra worker selection step allows to
pick a small number of most effective devices to communicate, which
drastically reduces the total cost of communicating the models of all devices
in the absence of this extra step. Alternatively, if worker selection is made
randomly or naively as in vanilla FL, these selected devices would not
optimally contribute to model updating; in turn, it may take longer time to
converge and hence incur higher communication cost until convergence. Overall,
DSL employs a low-cost worker selection step to alleviate the heavy cost of
the model communication step, thus achieving overall communication and energy
efficiency.

#### Over-The-Air Analog Aggregation

Recently, a promising technique emerges as FL over-the-air [8]. This approach
leverages the fact that the model-aggregation operation in FL aligns with the
waveform-superposition property of wireless analog multi-access channels
(MAC). In DSL, the global variable updating in (3) only requires the averaged
updates of $S_{t}$ selected workers rather than their individual local
variables. DSL over-the-air works in a direct and efficient way of
implementing global variable updating. It employs analog aggregation based
transmission and enables the $S_{t}$ selected workers to simultaneously
transmit their local variables over the same time-frequency resources. This is
achieved when the aggregated waveform effectively represents the averaged
updates, through proper transmit power control[8]. Thus, the total consumed
bandwidth is minimized and independent of $S_{t}$. Since $S_{t}$ reflects the
degrees of freedom in DSL to control the exploration-exploitation mechanism in
swarm intelligence, adaptive multi-worker selection strategy can be co-
designed and assessed based on the impact of the over-the-air transmission on
the learning performance. In addition, DSL can further incorporate other
efficiency-enhancing strategies such as 1-bit compressed sensing, which
amounts to combining compression, quantization and concurrent transmission to
attain impressive efficiency [9].

### Convergence Behavior

DSL offers superiority in solving non-convex problems, which mainly benefits
from the inherent capability in escaping from local optimum traps owing to the
random weights and exploration-exploitation mechanisms embedded in PSO. Such a
benefit of swarm intelligence are intuitive and widely appreciated. From the
theoretical side, the global convergence properties of PSO have been of
interest to the computational science community [10]. While the superiority of
PSO lies in its high probability of achieving global convergence, PSO itself
does not necessarily improve the order of convergence speed, unless joint
optimization for parameter selection and resource allocation is carried out at
the system level. In convergence analysis of DSL, the metric of interest is
the expected convergence rate of local workers, which is used to evaluate the
convergence of stochastic algorithms. A closed-form expression for the
expected convergence rate achieved by DSL is derived as a function of the
number of communication rounds $T$ and the PSO-related exploration-
exploitation parameters in [3], which is bounded on the order of
$\mathcal{O}({1}/{T})$.

### Joint Optimization of Communication and Computation

The convergence behavior of DSL unveils a fundamental connection between edge
communications and distributed learning. It offers a fresh perspective to
measure how the parameter choice of wireless systems and the hyperparameter
design of computational algorithms affect the performance of edge learning.
Guided by the theoretical results from convergence analysis, joint
optimization of learning parameter determination, worker selection, and
transmit power control is formulated as minimizing the loss function subject
to the limited transmit power and bandwidth. It amounts to a network resource
optimization problem that minimizes the learning error subject to the maximum
power constraints of low-cost IoT devices [8, 9], which yields the jointly
optimized worker selection and power control variables for DSL operations.

### Computational Complexity

At the first glance, DSL does incur extra computation than vanilla FL, when
DSL integrates the velocity in PSO with the gradient in SGD in (Distributed
Swarm Learning). But, the added computation and storage overheads are indeed
quite low. This is because FL is a first-order algorithm involving relatively
expensive gradient computation, while PSO is a zeroth-order algorithm that
computes functional values only. Further, the update of the locally best
variable and the corresponding fair-value loss can be implemented by simply
comparing the function value of the current model variable with that of the
previous best loss function value in (2) whose computational cost is near
negligible. In addition, the global model update of DSL in (3) is implemented
in a way similar as FL via analog aggregation but only over selected workers,
which does not incur extra computation at the minimum requirement on
communication bandwidth. Thus, the computational cost of DSL is dominated by
gradient-related term, with little overhead from PSO-related terms. Finally,
the theoretical results on convergence analysis indicate that DSL can expedite
the convergence time than vanilla FL [3]. As a result, the overall number of
computation rounds is reduced, which leads to a reduction in the computational
complexity of DSL, compared to vanilla FL.

## Robust Distributed Swarm Learning

In edge IoT networks, the local data samples of small volume typically turn
out to be non-i.i.d. across workers. Further, there exist malfunctioning
workers and even malicious attackers. In addition, link failure contributes to
unreliable transmissions. All these issues call for robust measures for DSL.

### Global Dataset Generation

As a vital component of the DSL framework, a globally shared dataset is
introduced in (2) to play dual roles: to compute fair-value scores of local
models for multi-worker selection and to alleviate the non-i.i.d. issue.
Centralized data sharing methods would collect raw data samples from
individual workers to form global datasets [11], but raise privacy concerns.
To keep raw data private at local workers, robust data augmentation methods
are developed to form a global dataset, based on federated generative
adversarial network (FedGAN) by training a neural generator in a distributed
manner [12]. This generator can be used to generate synthetic data samples as
the globally shared dataset for DSL. Experiments show that even a very small
amount of global data (say $1\%$ of the entire datasets) is adequate to
deliver the expected high learning performance for robust DSL [3]. This
observation is consistent with other works in the literature employing a
global dataset to improve robustness in FL. The global data can be shared
prior to DSL operations, and the resources needed for sharing and storage are
low due to the small volume of such data.

### Robust Measures against Non-i.i.d. Issues

Having generated a global dataset via the FedGAN-based data augmentation, the
global dataset is further divided into two parts: one for model training to
mitigate the non-i.i.d. challenge, and the other for scoring worker quality
against Byzantine attacks, respectively. To alleviate the non-i.i.d. issue, a
globally shared training dataset is distributed among all local workers. This
simple idea turns out to be effective, as evaluated by a statistical analysis
approach that is developed to evaluate the impact of model weight divergence
on the learning performance of DSL [3]. The model weight divergence is
measured in terms of the distance from the non-i.i.d. data distributions of
local workers to that of the overall data population. The non-i.i.d. data
problem can be further tackled by employing a regularized total variation in
the local loss function. Such a regularized penalty term enforces local
variables to be close to each other by reducing the distance from current
local updates to the previous global variables, which alleviates the impact
from non-i.i.d. datasets.

### Robust Measures against Byzantine Attacks

The second part of global dataset is used to score the local loss values in
(2). Meanwhile, such scoring dataset can also serves to screen out potential
Byzantine attacks where attackers cheat in local scoring and report mismatched
local model updates. DSL will throw away the contaminated model, when the
deviation of its loss value based on the scoring dataset from the averaged
score of the selected workers in their reporting stage larger than a
predefined tolerance threshold. Then, DSL keeps inviting other workers from
the swarm by following certain reselection strategy until the deviation is
acceptable. Analog aggregation transmission is known to enhance the privacy
preserving due to the inherent inaccessibility to the individual local model
updates. While DSL over-the-air closes the doors to model inversion attacks,
it still exposes vulnerabilities to adversaries who can perform Byzantine
attacks. The work [13] indicates that even a single instance of Byzantine
fault has the potential to disrupt distributed learning via analog
aggregation. The impacts of Byzantine attacks to DSL are studied under the
swarm setting at the edge, taking into account of the integrated nature of AI
and BI in DSL [3]. Based on the theoretical analysis [13], a best effort
voting (BEV) based transmission power control policy can be applied to against
Byzantine attacks for DSL over-the-air.

### Robust Measures against Node/Link Failures

Thanks to the analog aggregation transmission as (3), the worker selection is
not subject to constrained communication bandwidth, which allows the selection
of more workers to collectively update the global model variables at no extra
bandwidth. Leveraging such multi-worker diversity, DSL can enhance the
resiliency to unreliable transmission links and malfunctioning workers.
Further, to cope with wireless fading, truncated channel inversion method is
developed for FL over-the-air [14]. When some workers experience deep fading
channels, the truncated channel inversion method is employed to weed out those
workers with low channel gains. For DSL over-the-air, the truncated channel
inversion policy needs to be designed with attention to the incorporation of
the BI terms. By jointly determining the truncation thresholds with the multi-
worker selection scheme in DSL over-the-air, the truncation rules can
effectively balance both the communication and computation aspects of
distributed learning over wireless fading channels.

## Performance Evaluation

For performance evaluation, DSL has been tested with $50$ distributed workers
on a handwritten-digit classification task using the widely-used MNIST dataset
[3], compared with vanilla FL and PSO as the benchmark methods. The common
learning model is a five-layer Convolutional Neural Network with $44426$
trainable parameters, using a cross-entropy loss function. As shown in Figure
2, DSL outperforms FL and PSO in achieving the highest accuracy. At the same
performance level, the communication round of DSL is less than that of FL or
PSO. Such advantage of DSL becomes more obvious in the non-i.i.d. case in
Figure 3, where PSO fails to work properly because its underlying assumption
of a common loss function for all workers can only be approximately true in
the i.i.d. case. Further, DSL can not only effectively defend Byzantine
attacks by proactively screening and removing potential attackers, but also
work robustly in the presence of node/link failures by taking advantage of the
diversity gain via multi-worker selection, as shown in Figure 4. These
simulation results verify that the integration of AI and BI leads to evident
improvement on learning accuracy, communication efficiency, and system
robustness. This brings significant benefits to distributed learning for edge
IoT, particularly when dealing with swarm devices having limited
communication/computation capability and given their small-volume and
heterogeneous local data at the edge of wireless networks.

Figure 2: Performance in i.i.d. cases. Figure 3: Performance in non-i.i.d.
cases. Figure 4: Performance under Byzantine attacks and node/link failures.

## Conclusion and Future Work

This article studies a new DSL paradigm for edge IoT systems, by bridging
federated learning with particle swarm optimization. With theoretical backing,
efficient information extraction and exchanging schemes are designed for high
efficiency in communication and computation of model updates. Robust DSL
solutions are developed to cope with data heterogeneity, node/link failure and
Byzantine attack. While DSL provides promising improvement over existing
methods, some open issues and future directions are summarized below.

#### Decentralized Topology

For DSL adopting a star topology, the central server plays a pivotal role in
coordinating the iterative model updating algorithms at distributed workers.
But, it is more challenging for fully decentralized networks, because every
worker needs to make autonomous decisions regarding the global learning task,
via communication with adjacent workers only [15]. There is a growing interest
in decentralized DSL to capitalize on its inherent resilience to node/link
failures and its ability to handle asynchronous computing in heterogeneous
environments.

#### Security Provisioning

Research on DSL has just started to seek understanding of system-level design
and algorithm-level development, with little effort on security provisioning
yet. DSL over-the-air leaves edge learning systems still vulnerable to
malicious attacks, because there is no mechanism to retrieve individual
messages that help to identify attackers. For proactive security provisioning,
it is urgent to utilize cybersecurity techniques in DSL, such as
authentication and cryptographic mechanisms, while keeping the overhead and
complexity low.

#### Efficiency-Robustness Tradeoff

Due to the natural tradeoff between efficiency and robustness, the adopted
robust aggregation measures may affect the convergence behavior of iterative
DSL algorithms. For DSL over-the-air, multiple selected workers do not consume
extra bandwidth, but do increase the total transmit energy in the DSL systems.
Understanding of such tradeoff is vital, which sheds light on the impacts of
AI learning and BI optimization parameters on DSL convergence behavior.

#### Prototype Development

DSL prototype aims at implementation on the swarming lighter-than-air (LTA)
robots designed for the national Defend The Republic (DTR) robotic blimps
competitions. As shown in Figure 5, in an aerial soccer game, two teams play
against each other in a head-to-head match, where fleets of autonomous robots
must detect and then capture neutrally buoyant balls and finally move them
through goals suspended from the ceiling. Given the onboard hardware
limitation for massive LTA robots, DSL is a good candidate solution to
collaboratively train learning models for detecting and classifying objects,
e.g., different-color balls, and square/circle/triangle-shaped goals in the
game field.

Figure 5: LTA robots for national DTR robotic blimps competitions.

## Acknowledgement

This work was supported by the National Science Foundation under Grants
2003211, 2128596, 2231209, 2146497, 2244219, 2315596, and 2413622.

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## Biographies

Yue Wang [SM] is an Assistant Professor in the Department of Computer Science
at Georgia State University. His interests include the areas of machine
learning, signal processing, and wireless communications, with research
focuses on distributed optimization and learning, compressed sensing, Internet
of Things, cognitive radios, and 5G/6G wireless techniques, and high-
dimensional data analysis.

Zhi Tian [F] is a Professor in the Department of Electrical and Computer
Engineering at George Mason University. Her interests include signal
processing, communications, detection and estimation with focuses on
decentralized optimization and learning over networks, statistical inference
from distributed data, and compressed sensing for random processes, cognitive
radios, and millimeter-wave MIMO communications. She is Editor-in-Chief for
IEEE Transactions on Signal Processing.

Xin Fan [M] is an Assistant Professor with School of Information Science and
Technology, Beijing Forestry University. His interests include wireless
communications, machine learning, security & privacy, optimization,
statistical signal processing, and blockchain.

Zhipeng Cai [F] is a Professor in the Department of Computer Science at
Georgia State University. His expertise lies in resource management and
scheduling, high performance computing, cybersecurity, privacy, networking,
and big data. He is Editor-in-Chief for Wireless Communications and Mobile
Computing, and Associate Editor-in-Chief for Elsevier High-Confidence
Computing Journal.

Cameron Nowzari [SM] is an Associate Professor with the Department of
Electrical and Computer Engineering at George Mason University. His interests
include dynamical systems and control, distributed coordination algorithms,
robotics, event- and self-triggered control, Markov processes, network
science, spreading processes on networks, and Internet of Things.

Kai Zeng [M] is a Professor with the Department of Electrical and Computer
Engineering at George Mason University. His interests include cyber-physical
system security and privacy, physical layer security, network forensics, and
cognitive radio networks.