# Goal-Oriented Communications in Federated Learning via Feedback on Risk-
Averse Participation

Shashi Raj Pandey, Van Phuc Bui, Petar Popovski
Department of Electronic Systems, Aalborg University, Denmark
Emails: {srp, vpb<EMAIL_ADDRESS>This work was supported by the Villum
Investigator Grant “WATER” from the Velux Foundation, Denmark.

###### Abstract

We treat the problem of client selection in a Federated Learning (FL) setup,
where the learning objective and the local incentives of the participants are
used to formulate a goal-oriented communication problem. Specifically, we
incorporate the risk-averse nature of participants and obtain a communication-
efficient on-device performance, while relying on feedback from the Parameter
Server (PS). A client has to decide its transmission plan on when not to
participate in FL. This is based on its intrinsic incentive, which is the
value of the trained global model upon participation by this client. Poor
updates not only plunge the performance of the global model with added
communication cost but also propagate the loss in performance on other
participating devices. We cast the relevance of local updates as _semantic
information_ for developing local transmission strategies, i.e., making a
decision on when to “not transmit”. The devices use feedback about the state
of the PS and evaluate their contributions in training the learning model in
each aggregation period, which eventually lowers the number of occupied
connections. Simulation results validate the efficacy of our proposed
approach, with up to $1.4\times$ gain in communication links utilization as
compared with the baselines.

###### Index Terms:

goal-oriented communication, federated learning, risk analysis, semantic
feedback, multi-arm bandit (MAB), personalization

##  I Introduction

Semantic communication (SemCom) is pursued to go beyond Shannon’s
interpretation of reliable transmission as an engineering problem, where all
bits are treated equally, and focus on the rationale behind data transmission
and its utility at the receiver’s end through interpretation of content,
context and timing aspects [1, 2, 3, 4]. Consequently, this perspective offers
methodologies to limit unnecessary transmissions and prioritize data to
improve goal-oriented performance; hence, SemCom is unanimously attributed to
being goal-oriented communications.

Edge intelligence at scale is envisioned to be one of the prominent
realizations of the next generation of communication systems, where goal-
oriented communications can play a significant role and offer fundamental
gains in several network KPIs (for example, in terms of latency, throughput,
compute costs, communication costs, energy-efficiency, and so on). Edge
intelligence attributes executing machine learning (ML) algorithms at the
network edge to offer low-cost, high accuracy, and fast inference for
downstream tasks. Satisfying such an objective necessitates methods to train
high-quality learning models in a communication-efficient, decentralized
manner without tampering with data privacy for heterogeneous services.
Federated Learning (FL) [5] is one of such popularized paradigms we are
interested in this work, where we show a way to enable goal-oriented
communications and absorb the corresponding gain in the performance metrics.
FL allows training a learning model in a privacy-preserving distributed
manner, with a central parameter server (PS) soliciting devices to share the
local learning parameters instead of their private raw data. The iterative
model training process is refuelled with an updated global model after the
model aggregation at each interaction round – i.e., the global communication –
between the devices and the PS. Two regimes of model aggregation exist in the
FL operation: (i) Synchronous (SYNC) and (ii) Asynchronous (ASYNC). SYNC
imposes tightly coupled iterative training procedures, with issues due to
stragglers, leading to poor _training efficiency_. ASYNC relaxes the
aggregation period, with issues related to poor model updates, i.e.,
staleness; hence, poor _communication efficiency_. Therefore, in both regimes,
the selection of local models to incorporate in the aggregation process is at
the crux of the model training procedure, which, in actuality, contributes to
the number of incurred transmissions.

Figure 1: Risk-averse FL setting: (Left figure) Plain FL, and in (Right
figure) device $k$ is a risk-averse client, which drops itself from the FL
process following _feedback_ from PSat the base station.

Device selection problem [6, 7, 8], i.e., activating a subset of devices to
participate in the model training, and the design of an efficient model
aggregation scheme [9], i.e., choosing a subset of obtained local model
parameters, has been of key interest in the recent FL research works. However,
we argue device selection problem has always been thought of as the PS’s
problem but not considered as an opportunity to stimulate strategic
participation of the selected devices; hence, ignoring distributed
coordination amongst participating devices for goal-oriented communications.
Most of the existing research focuses on tuning the aggregation procedure by
choosing devices that are valuable for the average model performance of the
trained model. However, taking the perspective of a device, the improvements
in their learning tasks through arbitrary participation strategy in the FL
training can be nominal with an average model performance. This suggests the
limited influence of participation of such devices; due to statistical and
system-level heterogeneity, not all selected devices in each communication
round contribute greatly to the trained model. Then, it is intuitive for
devices to decide when not to transmit as well to minimize unnecessary
computing and communication costs. We call such devices “risk-averse”, where
risk is the nominal value of the trained model upon participation. In related
works, device selection at the PS overlooks the individual risks and the
impact on the further participation of each specific device. In actuality, we
observe incorporating risk-averse attributes of devices in participation,
i.e., risk-averse participation, can address goal-oriented communication
problems in FL. We show that it is imperative and of great value to keep track
of the performance of the trained model at both PS and the devices,
particularly to ensure generalization with improved personalization
performance. Therein, feedback from the PS to evaluate risks on participation
enables devices to align their transmission strategies while satisfying the
overall goal-oriented performances after model aggregation at the PS.

###  I-A Contributions

We pose the following problem of goal-oriented communications in FL: Given the
global model and feedback on its instantaneous valuation from the PS, how does
the risk-averse participation of devices impact the number of transmissions?
Precisely, we want to understand the perspective of devices in training the FL
model with their contributions and the value of the global model for their
local learning tasks, i.e., personalization performance. This is done
following the proposed _strategic_ device selection and participation. The
devices derive and evaluate the estimate of the local risk imposed by the
trained model and make a participation decision in the FL process,
anticipating the value of the investment in training the global model. Our
approach is applicable to any closed-loop system and is shown to be effective
in limiting unnecessary transmissions and improving goal-oriented performance.

##  II System Model and Problem Definition

Consider a sensory network with a resourceful PSand several privately owned
resource-constrained IoT devices. Let $\mathcal{K}=[k]$ denote a set of $K$
IoT devices each holding data samples $\mathcal{D}_{k}$ of size
$|\mathcal{D}_{k}|=D_{k}$, with each instance of data
$x^{(i)},\ldots,x^{D_{k}}\in[0,1]^{p}$ explained by $p$-features in a typical
supervised setting, and the set of $D$ total training data samples is
$\mathcal{D}$. As the devices are privately owned, we make a fair assumption
that the devices are privacy-sensitive, i.e., the data are not shared with the
PS unless for some incentives, e.g., monetary compensation for the incurred
cost to transmit private data and/or cost of lowering individual privacy
concerns. This limits PSto infer a summary statistics model
$\mathbf{w}\in\mathbb{R}^{d}$ of the sensory network with high confidence and
efficiency.

We formalize the learning problem as

$\underset{\mathbf{w}\in\mathbb{R}^{d}}{\min}\mathcal{L}(\mathbf{w})\;\;\text{with}\;\;\mathcal{L}(\mathbf{w}):=\frac{1}{D}\sum\nolimits_{i=1}^{D}L(x^{(i)};\mathbf{w}),$
(1)

where $\mathbf{w}\in\mathbb{R}^{d}$ is the unknown model parameter explaining
the summary statistics of the distributed data samples;
$\mathcal{L}:\mathbb{R}^{d}\rightarrow\mathbb{R}$ is the empirical risk (i.e.,
the objective), and
$L(x^{(i)};\mathbf{w}):[0,1]^{p}\times\mathbb{R}^{d}\rightarrow\mathbb{R},\forall
i\in\mathcal{D}$ is the loss function associate with data samples at the
device. Problem (1) can be solved in a distributed setting as of FL with
iterative algorithms leveraging the variants of gradient descent methods, such
as stochastic gradient descent (SGD). Then, the data-parallel reformulation of
(1) is

$\underset{\mathbf{w}\in\mathbb{R}^{d}}{\min}\mathcal{L}(\mathbf{w}):=\frac{1}{D}\sum\nolimits_{k=1}^{K}\sum\nolimits_{i=1}^{D_{k}}L_{k}(x^{(i)};\mathbf{w}),$
(2)

where $L_{k}$ is the local loss function. A basic operation sketch Federated
SGD (FedSGD) [5] to solve this is discussed below. At each communication round
$t$, the PSbroadcast a copy of global model $\mathbf{w}^{t}$ to the devices of
her interest pool (say $K$ devices), either randomly or following a specific
strategy; the chosen devices act as a worker on the received global model;
compute $\nabla L_{k}(\mathbf{w}^{t})$, and strategically111We look at
distributed coordination of devices in transmitting the local model
parameters. We use risk as a semantic measure to capture the relevance of the
device’s data in FL training. upload it to the PS. The round ends once the
PSreceives gradients from the devices and executes the model parameters update
as

$\mathbf{w}^{t+1}=\mathbf{w}^{t}-\eta\sum\nolimits_{k\in\mathcal{K}}\frac{D_{k}}{D}\nabla
L_{k}(\mathbf{w}^{t}),$ (3)

where $\eta$ is a step size. Note that the aggregation of gradients in (3) can
be modified, and the update strategy varies following design requirements, for
instance, with multiple steps of GD during local training, as Federated
Averaging (FedAvg) in [5].

For this, the overall learning objective, set as a goal-oriented
communications problem in FL, at the PS, is to train a high-quality learning
model with better generalization performance in a communication-efficient
manner. This boils down to an iterative procedure of (i) efficient device
selection for PS-, with added feedback that allows (ii) strategic response of
the selected devices to tune their transmission strategies that lower the
participation risk, hence, exploiting the relevance of data contribution in FL
training. In the following, we systematically present the proposed solution
approach.

##  III Risk-averse device selection with feedback

Let $\mathcal{A}^{t}_{k}\in\\{0,1\\}$ be the control algorithm for device $k$
denoting participation strategy in the model training process at time instance
$t>0$. Then, each device is endowed with an instantaneous valuation function
$v^{t}_{k}:\mathbb{R}^{d}\rightarrow\mathbb{R}$, where
$v^{t}_{k}(\mathbf{w}^{t}|\mathcal{A}^{t}_{k}=1)$ denotes the value of device
$k$ for model $\mathbf{w}$. In an iterative model training procedure given the
time horizon $t\in\\{1,2,\ldots,\tau\\}$, such as in FL, the PSsupplies copies
of the updated global model in every communication round $t$222A communication
round in FL is defined as the interaction call between PSand the involved
devices for the exchange of learned model parameters, such as gradients and
weights.. Then, without loss of generality, we define the average valuation of
device $k$ in the training procedure as
$\frac{1}{\tau}\sum\nolimits_{t=1}^{\tau}v^{t}_{k}(\mathbf{w}^{t}|\mathcal{A}^{t}_{k}=1)$.

Local Regret function:  We use regret function
$\mathcal{R}_{k}(\mathbf{w}^{t}):\mathbb{R}^{d}\rightarrow[0,1]$ to define
drop in the valuation of the device’s model parameters for building the global
model $\mathbf{w}$ in every successive communication round. Formally,
$\mathcal{R}_{k}(\mathbf{w}^{t})=v^{t}_{k}(\mathbf{w}^{t})-v^{t-1}_{k}(\mathbf{w}^{t-1})$,
with $v^{0}_{k}(\mathbf{w}^{0})$ as initial valuation of device $k$ of model
$\mathbf{w}^{0}$ broadcast by the PS. We will assume the devices drop off the
training process at any $t$ such that
$\mathcal{R}_{k}(\mathbf{w}^{t})\leq\delta_{k}$333This parameter captures the
system-level constraints on each device., i.e., the communication round, after
which the global model negatively influences the local performance. Note that
this stopping time is private information, and the device contribution might
be valuable for the PS to improve generalization.

Multi-arm Bandits (MAB)-based Selection: In each communication round, the
PSselects $\mathcal{M}\subseteq\mathcal{K}$ devices, where choosing each
device is considered as an arm pulled for an obtained valuation, i.e., the
instantaneous reward, plus a penalty factor to capture the number of times
that arm has been pulled. Upper Confidence Bound (UCB) algorithm assigns the
following value to each arm:

$f_{k,t}=\underbrace{\mu_{k,t}}_{\text{average marginal
contribution}}+\underbrace{\sqrt{\frac{\ln t}{N_{k,t}}}}_{\text{penalty
term}},$ (4)

where $N_{k,t}$ is the number of times device $k$ has been selected before.
Then, selecting an arm is equivalently solving the following:

$\mathcal{M}_{t}=\underset{k\in\\{1,2,\ldots,K(t)\\}}{\arg\max}f_{k,t},$ (5)

where $K(t)$ is the number of possible devices available at time instance $t$,
and $\mathcal{M}_{t}$ is the set of $M_{t}$ devices selected amongst $K(t)$
choices, i.e., $\mathcal{M}_{t}\in\\{1,2,\ldots,K(t)\\}$. Since the PSselect a
set of devices $\mathcal{M}_{t}$ per communication round, it naively applies
the UCB score (4), orders possible candidate devices based on their
contribution, and selects a subset of them per the available candidate
selection budget to define $M_{t}$.

In (4), it is straightforward for the PS to evaluate past device selection
choices; however, the value of instantaneous marginal contribution $\mu_{k,t}$
is _unknown_ to the devices; hence, they naively transmit the local model
parameters when asked for. At the PS side, we resort to Shapley Value (SV)
[10] for evaluating the contribution of the received model parameters. In
principle, SV calculates the average marginal contribution of each device $k$
on all possible combinations of coalition subsets as

$\mu_{k,t}(K,U)=\frac{1}{K!}\sum_{\mathcal{S}\subseteq\mathcal{K}\setminus\\{k\\}}\frac{U(\mathcal{S}\cup\\{k\\})-U(\mathcal{S})}{\binom{K-1}{|\mathcal{S}|}},$
(6)

where the function $U(\cdot)$ gives the value for any subset of the devices,
e.g., let $\mathcal{S}$ be a subset of $K$, then $U(\mathcal{S})$ gives the
value of that subset [11]. For devices, in literature, ways such as the
statistical methods and game-theoretic models [12, 13] exist to use for an
estimation of $\mu_{k,t}$ in each aggregation round $t$, though not
considering the overall objective of the PS.

We argue PS can incorporate one of these techniques to maximize its expected
long-term reward with the virtue of an efficient client selection by the time
horizon while signalling the devices with feedback to infer the relevance of
their transmission in prior. This is done as follows. Along with the
aggregated global model, the PS feedback the model regret (defined later in
(11)) due to risk-averse participation in the successive communication round.
The feedback is provided to specific devices; these devices are strategically
selected by executing the UCB-based algorithm while considering the risk-
averse participation of the devices. To formulate such device selection, the
PS first sniffs the average risk across devices participating in the FL
process. This allows it to maximize the benefits of its selection strategy in
the subsequent communication round, i.e., derive $M_{t}$ for the global model
broadcast and provide the feedback. After local training, the selected devices
evaluate the utility of participation as the value of the trained model with
the feedback and derive the relevance of their transmitted model parameters at
the PS in the next round. This suggests an effective approach for goal-
oriented communications in FL. Therein, we have the following definition.

Algorithm 1 Risk-averse Participation with Feedback in FL

1: Initialize: Number of devices $K(t)$, $\delta_{k},\forall k\in[k]$.

2: repeat

3: Execute UCB algorithm that solves (5);

4: Broadcast feedback $\\{\mathbf{w}^{t},\mathcal{R}_{t,\theta}\\}$;

5: for all devices $m\in M_{t}$ do

6: Set $v_{m}^{(t+1)}\leftarrow\mathcal{R}_{t,\theta}$;

7: Solve the local learning problem using SGD;

8: Evaluate $\mathcal{R}_{m}(\mathbf{w}^{t})$

9: Update transmission variable $\mathcal{A}^{t}_{m}$;

10: end for

11: until the model converges.

######  Definition 1.

Consider a dynamic population of devices in the FL system. Then, if
$\theta\in[0,1]$ is the average risk across participating devices,
$K_{\theta}(\epsilon,t)$ is the number of devices having data that can
contribute at least $\epsilon\in[0,1]$ improvement in the learning model.

Following Definition 1, the available devices with average $\theta$ risk on
the global learning model can be obtained as

$K_{\theta}(t)=\underset{\epsilon\rightarrow
1}{\lim}\;K_{\theta}(\epsilon,t).$ (7)

Then, the total available devices at the communication round $t$ are

$K(t)=\sum\nolimits_{\theta}K_{\theta}(t),$ (8)

with the average risk of collaborative training defined as

$R(t)=\frac{\sum\nolimits_{\theta}\theta\cdot K_{\theta}(t)}{K(t)}.$ (9)

Note that, in this work, we are not interested in modelling the arrival
process of the local parameters. Instead, our aim is to develop a device
selection strategy at the PS and the participation strategy at the risk-averse
device’s side with the feedback. Definition 1 considers average
$\theta\in[0,1]$ risk across the participating devices that brings a value of
averaged reward $[0,1]$, and plans also to empower the performance of risk-
averse devices for better generalization. To be _semantically relevant_ ,
devices should also be strategic in updating the local parameters while the
aggregator implementation of UCB for candidate selection in every global
iteration. With this motivation, we adopt value-at-risk (VaR) in reformulating
the stochastic bandit selection criterion to perform device selection at the
PS, which introduces extra signalling for the devices to align their
transmission plan. We begin defining conditional VaR (CVaR) in the following.

For any bounded random variable $X$ with cumulative distribution function
(CDF) $F(x)=\mathbb{P}[X\leq x]$, the Conditional VaR (CVaR) of $X$ is defined
as [14]

$\textrm{CVaR}_{\alpha}(X):=\underset{\nu}{\textrm{sup}}\bigg{\\{}\nu-\frac{1}{\alpha}\mathbb{E}[(\nu-X)^{+}]\bigg{\\}},$
(10)

at level $\alpha\in(0,1)$ signifying worst $\alpha-$ fraction of realizations,
where $(x)^{+}=\max(0,x)$. CVaR analysis allows the PS to consider the full
distribution of the contribution of devices while making strategic device
selection in the FL training process, given devices are risk-sensitive. It
also captures the average drop in the learning performance following this
naive device selection approach. We recast the device-selection problem using
CVaR-based UCB as follows. Let $F_{\mu_{k}}$ be the CDF of the contribution
selecting device $k$ on estimated $[0,\theta]$ capturing population risk. The
true distribution of device contribution is obtained following the available
samples in each round and evaluating marginal contributions of devices in
training the global model. With the action profile on device participation
upon random selection $\mathcal{A}_{t}$ with probability $\varepsilon$ at time
$t$, i.e., selecting a subset of devices from a pool of $K(t)$ devices, we
then use the definition of CVaR-regret at global aggregation round $\tau$ as

$\mathcal{R}_{\tau,\theta}=\tau\max_{k}\bigg{[}\textrm{CVaR}_{\theta}(F_{\mu_{k}})\bigg{]}-\mathbb{E}\bigg{\\{}\sum\nolimits_{t=1}^{\tau}\textrm{CVaR}_{\theta}(F_{\mathcal{A}_{t}})\bigg{\\}},$
(11)

to capture the contribution profile of selected devices. The right-hand term,
considering the most optimistic estimates, can be approximated to be bounded
as,

$\mathcal{R}_{\tau,\theta}\leq\frac{4\max\\{\epsilon_{k},\forall
k\in\mathcal{A}_{t}\\}}{\theta}\sqrt{\tau K\ln(\sqrt{2}\tau)},$ (12)

where $\theta$ is updated in each global communication round with the
resulting CVaR-based risk-averse device selection problem as

$\mathcal{M}_{t\in\\{1,2,\ldots,\tau\\}}=\underset{k\in\\{1,2,\ldots,K(t)\\}}{\arg\max}f_{k,t}-\mathbb{E}[\mathcal{R}_{t,\theta}].$
(13)

The derivation follows [[15], Theorem 1. [16]]. Algorithm 1. summarizes the
proposed approach of strategic selection and risk-averse participation to meet
the learning objectives, i.e., improving training and learning efficiency
through feedback; hence, goal-oriented communications in FL. Therein, we have
the following lemma that quantifies the analytical bounds on stability and
convergence of the average risk, as reflected by the average per-device model
performance.

######  Lemma 1.

Let $\theta_{1},\theta_{2},\ldots,\theta_{k}$ be independent random variables
denoting the quality of local risk at device $k\in\mathcal{K}$ in any instance
such that $|\theta_{k}|\leq\theta_{\textrm{th}}$ almost surely, and
$\mathbb{E}[\theta_{k}^{2}]\leq\alpha_{k}$ for every $k$. Then, for every
$\alpha\geq 0$ we have

$\mathsf{Pr}(|\theta-\mathbb{E}[\theta]|\geq\epsilon)\leq\mathsf{exp}\bigg{(}-\frac{\epsilon^{2}}{2(A+\frac{\epsilon\theta_{\textrm{th}}}{3})}\bigg{)},$
(14)

where $\theta=\sum\nolimits_{k=1}^{K}\theta_{k}$ and
$A=\sum\nolimits_{k=1}^{K}\epsilon_{k}$.

###### Proof.

The proof is easy to establish following Bernstein’s inequality [17]. ∎

##  IV Performance Evaluation

###  IV-A Settings

####  IV-A1 Dataset and Model

To validate the efficacy of our proposed approach, we conducted experiments
with the well-known MNIST dataset [18], covering $70000$ data samples of
$28X28$ grey images in 10 classes equally. The PS is training a convolutional
neural network (CNN) model in a distributed manner. The CNN model has two
hidden layers for feature extraction (10 filters for the first layer and 20
filters for the second layer with kernel size as $5\times 5$) and 2 fully
connected layers for classification.

$0.6$$0.7$$0.8$$0.9$$1$$5$$6$$7$$8$$\displaystyle\delta$No. of global
communication roundsFedSGD (partial participation)FedSGD (full
participation)UCBAlg. 1 (a) Total communication rounds.

$0.6$$0.7$$0.8$$0.9$$1$$2$$3$$4$$5$$\displaystyle\delta$Average no. of
participation per roundFedSGD (partial participation)FedSGD (full
participation)UCBAlg. 1 (b) Communication links per communication round.

Figure 2: Comparative performance evaluation to reach $80\%$ model accuracy
for varying $\delta$.

$0$$20$$40$$60$$80$$100$$0.2$$0.4$$0.6$$0.8$$1$Global communication
roundAccuracyFedSGD (partial participation)FedSGD (full participation)UCBAlg.
1Centralized (a) i.i.d. setting.

$0$$50$$100$$150$$0.2$$0.4$$0.6$$0.8$$1$Global communication
roundAccuracyFedSGD (partial participation)FedSGD (full participation)UCBAlg.
1Centralized (b) non-i.i.d. setting.

Figure 3: Performance analysis in terms of testing accuracy versus the number
of communication rounds.

####  IV-A2 Implementation details

The assessment of goal-oriented performance in communication and training
efficiency at the central server PS involves analyzing the independent and
identically distributed (i.i.d.) and non-i.i.d. characteristics of the used
MNIST dataset. We consider the availability of $K=50$ devices, with
replication of the data distribution and non-i.i.d. setting for performance
evaluation using the methodology outlined in [11]. For training, each device
model is trained for one local epoch by the optimizer, with a batch size of 30
and a learning rate of 0.001. We utilized the SGD optimizer for the i.i.d.
MNIST dataset and the Adam optimizer for the non-i.i.d. setting to enhance the
overall performance. For device selection, we set the selection probability
$\varepsilon=0.1$.

###  IV-B Results and Analysis

We evaluate and compare the performance of our proposed algorithm with four
other intuitive baselines: (i) Centralized, where all the training samples are
available at the PS; (ii) FedSGD [5] (with _full_ participation); (iii) FedSGD
(with _partial_ participation), where $60\%$ of the devices are selected, and
(iv) UCB [8], where devices are selected purely on UCB metric without
considering risk-averse characteristics of the devices.

In Fig. 2, we show the performance of our proposed approach in relation to the
number of global communication rounds needed to achieve an 80% model accuracy
and the average number of communication links utilized per communication round
within the first ten rounds. As observed in Fig. 2(a) and 2(b), UCB offers a
gain in the average communication links in comparison with the traditional
FedSGD scheme while requiring the same number of communication rounds to
achieve $80\%$ of accuracy. This is expected, as UCB allows strategic
selection of devices following their marginal contributions in improving the
model performance. Meanwhile, the proposed Alg. 1 incorporates risk-averse
participation and further improves the performance in terms of incurred number
of communication links per communication round as compared to the UCB approach
while ensuring the model accuracy, especially with $\delta\leq 0.9$. With
$\delta=0.9$, Alg. 1 exhibited an average link consumption of 2.2, which is
1.4$\times$ lower than UCB and FedSGD techniques, while requiring the same
five rounds to achieve $80\%$ model accuracy. This suggests a significant
reduction in the number of transmissions to satisfy the KPIs with goal-
oriented communications in FL training.

Figure 4: Snapshot of risk-averse device selection following their
contributions and participation with $|\mathcal{A}_{t}|=9$ at $t=10$.

Fig. 3 demonstrates the learning performance in terms of convergence of
testing accuracy under both i.i.d and non-i.i.d data settings. We observe Alg.
1 outperforms the other baselines while keeping a competitive performance with
UCB (both in partial and full participation schemes) with fewer connections
per communication round. This analysis is consistent with our observations in
Fig. 2. Obviously, for the non-i.i.d. setting, we see a drop in the
performance; however, our approach outperforms the baseline with lower
utilization of the communication links. In Fig. 4, we take a snapshot of the
risk-averse device selection and device participation strategies at $t=10$ to
describe the operation of the proposed algorithm. In this scenario, we
consider the availability of $9$ devices working in tandem with heatmaps
reflecting contributions evaluated incorporating risk-averse participation and
devices are selected accordingly for $M_{t}=5$ (represented by the ones
enclosed in red boxes). Following the feedback, we observe the strategic
participation of devices (Alg. 1), where only a subset of devices (represented
by red blocks) transmit their local model parameters to PS. hence, we achieve
greater flexibility compared to the naive UCB algorithm, which involves a
fixed set of devices selected based on their marginal contribution only and
their subsequent participation. Our approach considers the risk-averse
participation of devices, considering the influence of instantaneous
transmission of local model parameters in improving the global model
performance. This suggests a potential reduction in the number of irrelevant
transmissions that would otherwise contribute to higher cumulative regrets.

$0$$10$$20$$30$$0$$200$$400$$600$$800$$1{,}000$Global communication roundCVaR-
RegretCVaR-regret with UCBCVaR-regret with Alg. 1 Figure 5: CVaR-regret with
UCB following strategic selection and risk-averse participation for an average
risk of $0.9$ per device.

Finally, in Fig. 5, we show the CVaR-regret of our algorithm as compared to
optimistic estimates, as shown in (12). We observe the risk-averse
participation approach offers lower CVaR-regret as compared to the worst-case
scenario, offered for $90\%$ accuracy on a non-i.i.d. setting. This suggests a
competitive sub-linear performance of our approach, offering better
convergence benefits.

##  V Conclusion and Future Work

We evaluated the relevance of local model parameters for goal-oriented
communications in FL through risk-averse profiling of participating devices.
The proposed approach incorporates feedback to stir the transmission
strategies of distributed devices towards a common goal of training a
communication-efficient, better-generalized, high-quality FL model, hence,
improving the overall goal-oriented performance.

In this work, we offer a goal-oriented perspective on semantic communication
with data valuation for edge intelligence. Our early results suggest how
fundamental it is to develop theoretical and algorithmic methodologies that
capture the relevance of data prior to its transmission, to realize goal-
oriented communications. While it is yet a challenge to ensure fully
distributed coordination of transmission strategies, our future works will
focus on timeliness in exploiting efficient data valuation techniques to
anchor such attributes of semantic communications. Another potential direction
of our interest is to devise techniques to manage the scale and utility of
participation of devices in the networked real-time systems for goal-oriented
tasks.

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