LBI-FL: Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
Authors: Li Ding
Hao Zhang
Wenrui Dai
Chenglin Li
Weijia Lu
ZHIFEI YANG
xiaodong Zhang
Xiaofeng Ma
Junni Zou
Hongkai Xiong
Venue: ICML 2025 poster (2025)
Keywords: Federated learning
low-bit integerized training
network quantization
Primary area: general_machine_learning->everything_else

Abstract: Federated learning (FL) is greatly challenged by the communication bottleneck and computation limitation on clients. Existing methods based on quantization for FL cannot simultaneously reduce the uplink and downlink communication cost and mitigate the computation burden on clients. To address this problem, in this paper, we propose the first low-bit integerized federated learning (LBI-FL) framework that quantizes the weights, activations, and gradients to lower than INT8 precision to evidently reduce the communication and computational costs. Specifically, we achieve dynamical temporal bit-width allocation for weights, activations, and gradients along the training trajectory via reinforcement learning. An agent is trained to determine bit-width allocation by comprehensively considering the states like current bit-width, training stage, and quantization loss as the state. The agent efficiently trained on small-scale datasets can be well generalized to train varying network architectures on non-independent and identically distributed datasets. Furthermore, we demonstrated in theory that federated learning with gradient quantization achieves an equivalent convergence rate to FedAvg. The proposed LBI-FL can  reduce the communication costs by 8 times compared to full-precision FL. Extensive experiments show that the proposed LBI-FL achieves a reduction of more than 50\% BitOPs per client on average for FL with less than 2\% accuracy loss compared to low-bit training with INT8 precision.

LBI-FL: Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
Li Ding"
Hao Zhang !
Wenrui Dai 2 Chenglin Li
Weijia Lu Hongkai Xiong'
Zhifei Yang*
Xiaodong Zhang?
Xiaofeng Ma
Junni Zou
Communication cost
Abstract
FP32
FP32
Ours
FP32
Ours
84.4
75
Federated learning (FL) is greatly challenged by the communication bottleneck and computation limitation on clients. Existing methods based on quantization for FL cannot simultaneously reduce the uplink and downlink communication cost and mitigate the computation burden on clients. To ad- dress this problem, in this paper, we propose the first low-bit integerized federated learning (LBI- FL) framework that quantizes the weights, acti- vations, and gradients to lower than INT8 preci- sion to evidently reduce the communication and computational costs. Specifically, we achieve dy- namical temporal bit-width allocation for weights, activations, and gradients along the training tra- jectory via reinforcement learning. An agent is trained to determine bit-width allocation by com- prehensively considering the states like current bit-width, training stage, and quantization loss as the state. The agent efficiently trained on small- scale datasets can be well generalized to train varying network architectures non-independent and identically distributed datasets. Furthermore, we demonstrated in theory that federated learning with gradient quantization achieves an equivalent convergence rate to FedAvg. The proposed LBI- FL can reduce the communication costs by times compared to full-precision FL. Extensive experi- ments show that the proposed LBI-FL achieves a reduction of more than 50% BitOPs per client average for FL with less than 2% accuracy loss compared to low-bit training with INT8 precision.
Top-1 Accurucy
-8.5%
-87.5%
-87.5%
81
71
Computation cost
U18
Ours
UI8
Ours
UI8
Ours
Top-1 Accuracy
-51.4% 1%%
-51.5%
-54.1%
81
84
71
LeNet
ResNet-18
VIT-S
Figure I: Image classification results on CIFAR-IO with the low-bit integerized federated learning framework (LBI-FL). The proposed method can simultaneously reduce both the communication cost and computational cost. The areas of bubbles are positively correlated with the communication cost the BitOPs for training the model.
1. Introduction
Federated learning (FL) a distributed machine learning framework designed to enable model training without the local data exchange. In FL., multiple clients independently train model on their local data and periodically send the updated model parameters (or model updates) to a central server for aggregation. This paradigm can address the data privacy and security concerns while effectively leveraging the computational resources distributed over local clients.
"Equal contribution 'Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China. 'Department of Computer Science and Engineering, Shanghai Jiao Tong Uni- versity, Shanghai, China. "United Automotive Electronic Sys- tems, Shanghai, China. Correspondence Wenrui Dai <daiwen- rui @ wwtessj.uuuuuuu edu.en>, Chenglin Li @ew.19955sjuu.cu..c.....
However, significant challenge in FL is the communi- cation overhead, it necessitates frequent transmission of models or updates between local clients and the central server. To address this, a substantial body of literature has fo- cused on compressing the model updates through techniques such as quantization and sparsification. Compression- federated algorithms such as QSGD (Alistarh et al., 2017)
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
and SignSGD (Bernstein et al., 2018) reduce the amount of model updltee be uploaded to the server by quantizing the gradient values into lower-precision integers. Though these methods can mitigate the uplink communication cost, they still require downloading a full-precision model. Exploring lower bit-width training in both the uplink and downlink communication becomes promising to further reduce the communication overhead for FL systems.
computation costs at tolerable level of performance loss as shown in Figure 1. We leverage reinforcement learning (RL) to dynamically determine the bit-widths for weights, activations, and gradients by comprehensively considering the quantization loss along the training trajectory. An agent is efficiently trained on a small local dataset and generalized to large-scale models and complicated datasets. Our main contributions are summarized as follows.
Network quantization (Hubara et al., 2017; Jacob et al., 2018), as mainstream strategy to achieve network com- pression, has been extensively studied for network inference and training, since it enjoys the merit of reducing compu- tation burden without modifying the model architecture. Different from inference quantization (Jacob et al., 2018: Banner et al., 2019; Choi et al., 2018; Jung et al., 2019) that quantizes the weights and activations of networks to accelerate the inference process for deployment, low-bit training (training quantization) simultaneously projects gra- dients, weights, and activations into low bit-width during training. Thus, low-bit training can reduce the uplink and downlink communication overhead for federated learning using low-bit representation of weights for training. More- over, it can decrease the computation load for each client by reducing the computational cost of backward computation (backpropagation) that is nearly twice the cost for forward computation (Zhao et al., 2021).
To our best knowledge, this is the first successful at- tempt to achieve low-bit training FL that evidently reduces the communication overhead and computation cost compared to full -ull-peecison and INT8 training.
We propose novel reinforcement learning method for temporally dynamic bit-width allocation for weights, activations and gradients along the training trajectory to achieve an average bit-width below INT8.
We demonstrate in theory that federated learning with gradient quantization achieves equivalent convergence rate to the standard FedAvg algorithm (McMahan et al., 2017) with sufficiently large number of communication rounds and further empirically verify the convergence rate.
Comprehensive experiments on low-bit integerized fed- erated learning with a wide range of network models including ResNets and VIT's validate the effectiveness of the proposed method.
Recent attempts on low-bit training, including directive sen- sitive gradient clipping (Zhu et al., 2020) and vectorized gradient quantization (Zhao al., 2021), can alleviate or even eliminate the accuracy loss of networks trained under the INT8 precision. However, these methods could collapse when the precision is further decreased to INT4. Consider- ing that neural networks vary in sensitivity to quantization at different training stages, it is reasonable to assign differ- ent bit-widths for quantization at different stage of network training to minimize the impact of quantization error. In mixed precision of INT4, INT6,
2. Related Work
Inference quantization. According to the stage of quan- tization, model quantization can be divided into two cat- egories: inference quantization and training quantization. Inference quantization quantizes the weights or activations of the trained neural networks from full precision to low-bit data format representations before deploying the models. Typical works (Hubara et al., 2016; Rastegari et al., 2016; Liu et al., 2023) utilize the binary or ternary bit-widths for weights and activations to speed up the inference. Dong et al. (2019; 2020) achieve good compression performance through the mixed-precision quantization.
this paper, we focus and INT8 for dynamic temporal bit-width assignment to reduce both communication and computation costs for FI.. Zhang et al. (2020) use a predetermined threshold to decide layer-wise switching of bit-widths for gradients with fixed bit-widths for weights and activations. Nevertheless, as shown in Figure 2, the quantization loss varies for different networks during the training process and predetermined threshold cannot achieve consistent compression ratio for varying networks or datasets. There is a lack of mixed- precision bit-width allocation that can dynamically fit the varying training processes for different networks on non- independent and identically distributed training data.
Training quantization. Training quantization stands for quantizing simultaneously the gradients, weights, and activa- tions to accelerate the training process. There are two main types of methods in existing studies of low-bit training. The first is to use low-bit floating point for training (Wang et al., 2018; 8; Mellempudi et al., 2019; Cambier et al., 2020). This method can achieve almost lossless accuracy with the full- precision model, but harms the acceleration performance compared to integer quantization. The second involves quantizing the model with integers. Some methods quantize the entire network (Zhou et al., 2016; Yang et al., 2020a)
In this paper, we propose the first low-bit integerized federal learning (LBI-FL) framework that allows an average preci- sion below INT8 to further reduce the communication and
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LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit- Bit-Width Allocation
which yields a higher compression but harms the model performance. Some other methods only quantize the con- volutional layers in the model (Zhu et al., 2020; Zhao et al., 2021) which can achieve a better model performance. The low-bit training framework in this paper is closest to these methods, but the goal is to further reduce the bit-width on the existing full INT8 basis for a more efficient FL scheme.
multiplies the data by the scaling factor s. Here, M and m are the maximal and minimal clipping values for z respec- tively. The scaled data is fed into the rounding function,
Big = (a'y (
= round (= ( ( (I)
where the scaling factor s (M m) m2 1) given the bit-width N for quantization. De-quantization is realized by yy (xy =) Different from asymmetric quantization, symmetric quantization obtains zeros for the zero point.
Federated learning. Federated learning, as a rapidly evolv- ing application of distributed learning in large-scale client networks, has garnered significant research interest. This surge of attention has led to substantial body of work exploring the intersection of FL with various domains, in- cluding robustness (Ghosh et al., 2019), fairess (Wei & Huang, 2024), federated reinforcement learning (Yue et al., 2024), and federated optimization (Reddi et al., 2021). For more detailed comparison, we defer to the comprehensive survey papers (Li et al., 2020; Kairouz et al., 2021).
Fig = rouuddd (1 33 = Figg 8, 8 2
max ((r))
(2)
Nearest rounding is usually used for the weight and activation quantization, while stochastic rounding is adopted (Gupta et al., 2015) for the gradient quantization, since its loss has much more impact on model accuracy,
round (x) = { [+],
w.p. 1- (x - [x])
Efficient FL. Given the communication bottlenecks and computational resource constraints on the client side in FL, introducing pruning (Prakash et al., 2022; Mcinhardt et al., 2024) or quantization techniques is a natural progression, and we mainly introduce the quantization methods here. To enhance communication efficiency, various methods have adopted quantized SGD (Alistarh et al., 2017; Bernstein et al., 2018; Mishchenko et al., 2022), where model updates (i.e., the sum of gradients) are directly quantized and com- pressed. Some methods (Li & Li, 2023; Bernstein et al., 2018) also incorporate error feedback to mitigate quanti- zation errors. However, these quantized model updates primarily reduce the uploaded traffic without accelerating training or alleviating downloaded traffic. To further expe- dite the local training and inference, certain strategies (Chen et al., 2024) explore the use of quantized neural networks within FL. Nevertheless, these methods often treat the prob- lem as an optimization task, focusing on determining the optimal quantization bit-width. While theoretically perfor- mant, their empirical results exhibit slight decrease in the model effectiveness. Moreover, some methods improve the FL efficiency by optimizing energy consumption. Yang et al. (2020b) derive the time energy consumption models and Marnissi et al. (2024) propose an optimization frame- work to minimize the total energy consumption.
[ +1 w.p.
I x
where [x]] returns the largest integer not greater than x.
Deep Q-Network. Reinforcement learning optimizes the accumulative rewards interacting with the environment. The interaction between the agent and environment can be mod- eled as a Markov decision process (MDP) represented by a five-tuple (s, a, r, 7) of state s, action a, transition func- tion f, reward function r, and discounting factor y.
The Q-function q" (s, a) is defined the expectation re- ward of taking specific action on the current state. Deep Q-network (DQN) is a classic based algorithm using neural network (s. a) to approximate this Q-function q" (s, a). DQN consists two important components, i.e., tar- get network and experience replay (Mnih et al., 2015). The target network stabilizes the training results and experience replay diversifies the batch data. In this paper, we employ DQN considering that it is lightweight and sample-efficient. DoubelDQN and DuelDQN are two typical improved ver- sions of DQN ( (Van Hasselt et al., 2016; Wang et al., 2016).
Federated Learning, In general, the optimization problem of federated learning (FL) can be formulated as:
1 m
min f(w) weRd
m Σ F((w).
(4)
3. Preliminaries
where Fe(w) ER function of the i-th client with the data sample & drawn from distribution D, Data is typically heterogeneous for FL such that D, and D, can be extremely different for two distinct clients i and j. Additionally, the FL. systems often operate under a limited bandwidth and constrained client-side com- puting resources, making both the communication overhead from exchanging model parameters and the computational burden on the client a significant bottleneck.
( (R,,, (w) represents the local loss
Quantization. Integer quantization maps floating-poin value to a fixed-point number. Uniform quantization is pop- ular in network quantization. It is classified into two kinds, i.e., symmetric quantization and asymmetric quantization, based on whether the mapping is identical for the zero point.
Asymmetric quantization first substracts the zero-point z from the clipped data z'y- clamp(æ, y, m. M) and then
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LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
Table I: Classification accuracy (%) by altering bitwidths from INT4 to INT8 or from INT8 to INT4 on CIFAR-10.
LeNet
ResNet-18
MobileNetV2
100
INT4-INT8
82.67
83.76
85.19
NYT8-INNT
82.30
82.81
NaN
(a) Gradient
(h) Weight
(c) Activation
Figure 2: Average quantization loss of full INTS quanti-
4. Proposed Method
zation on (a) gradients, (b) weights, and (c) activations, respectively, over all the layers through the training process.
In this section, we first introduce motivations, and then propose the low-bit integerized training framework for fed- eral learning (LBI-FL), and finally elaborate on the training process of the temporal bit-width selection agent.
Server
Server
Agent
Quant Quant
Quant
Quant
4.1. Motivation
Datasct 10% CIRARED
Shared
Communication and computational costs are the two main costs in FL. Low-bit training can reduce the computational load during training, while the calculation with low bit- width weights helps mitigate both of these costs. However, low-bit integerized federated learning needs to address two challenges as summarized below.
Ageat
Agent
Agent Truining
Model Training
Figure 3: Overview of the proposed low-bit integerized fed- erated learning. The agent is firstly pre-trained small lo- cal dataset, such as 10% of the CIFAR- 10 dataset. It is then applied to another model or dataset for federated learning with low-bit training, which can reduce both the communi- cation overhead and computational cost. The purple arrows, representing the uplinks and downlinks for communication, transmit low-bit weights with bit-width whet leading to a significantly reduction in the communication cost.
i) Varying impacts of quantization at different stages of training. We conduct experiments on the CIFAR-10 dataset by switching from INT4 to INT8 at 40% of the training process and from INT8 to INT4 at 60% of the training process, respectively. Table shows that using lower bit-wssths in the later stage of training suffers from evident performance loss, and might cause model collapse. Therefore, it is meaningful to use different bit- bit-widths at different training stages.
efits for the acceleration of federated learning. (i) Since the model weights are quantized with low bit-widths, only the low-bit weights are transmitted when the model is uploaded from the clients to the server. Similarly, when the model is downloaded from the server, the weight is quantized be- fore transmission. As result, the communication overhead during both the uploading and downloading process is sig- nificantly reduced compared to the coll-precision commu- nication. (ii) Moreover, we implement a low-bit training on each client, replacing the full-precision matrix opera- tions with low-bit integer ones. which can further reduce the computation cost and accelerate the training process.
ii) Varying training curves for different datasets and models. Figure shows that the quantization loss calculated by Equation (5) in (Zhang al., 2020) varies across different models. We are thus motivated to train an RL agent to dynamically determine the temporal bit-width allocation for different models at different stages of training.
4.2. Low-Bit Integerized Federal Learning
As depicted in Figure 3, the proposed framework for low- bit integerized federal learning consists of two parts. First, the temporal bit-width selection agent is trained with re- inforcement learning. The pretraining is conducted on a relatively small local dataset (10% of CIFAR-10 used in our approach). Second, the pre-trained agent is distributed to the clients to perform federated learning new mod- els or datasets. For every Itv epochs, the agent on each client decides whether to adjust the bit-widths of weights, activations, and gradients.
4.3. Agent Training for Temporal Bit-Width Allocation
As illustrated in Figure 4, our framework, temporally dy- namic bit-width allocation is achieved with reinforcement learning. The agent is trained to determine whether to alter the bit-widths for the weights, activations, and gradients, considering the training state of the networks including train- ing time and quantization loss of data. After each action, a reward is obtained based on the current model training accuracy and the compression ratio. The reward function,
The low-bit integerized federal training framework is de- tailed in Algorithm 1. This framework offers two main ben-
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LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit- Bit-Width Allocation
Algorithm Low-bit Integerized Federated Learning.
Time
bit
dir
Pretrained agent, number of clients M, number of epochs N, and update interval Itv. Output:
Input:
State
W
Trained model with low-bit weights and activa-
Action
tions.
1:
Initialize the weight, activation, and gradient bit-widths Whit, Obit; and gbst for each client as INT4.
2: for 1 N do
3: Train and update the local model with low bit-width whit. fir. and th on each client.
Reward
Quant
Agent
4: Quantize the model on each client with bit-width wha (k E [1, MD before uploading to the server.
Figure Overview of the reinforcement learning method of selecting bit-widths for the network during training.
5: Server averages models to obtain a new global model.
6: Quantize the model with bit-width whe before down- loading the model from the server to each client.
Balanced reward function. As the agent aims preserve accuracy and reduce the bit-width simultaneously, the re- ward function needs to balance the model accuracy and com- pression ratio. The balanced reward formulation is carefully designed, which consists of three parts: the quantization index, accuracy index, and time step.
7: if iTttv = then
8: Utilize the pre-trained agent to determine whether each client should adjust its bit-widths.
9: end if
10: end for
reward = q_idæ aidd L_step
(6)
therefore, needs to balance the maintenance of model ac- curacy and the reduction of computation cost. Since the early stage of training can tolerate more noise as shown in Section 1, the bit-widths are initialized as INT4 and can only switch from lower bit-widths to higher low-widths. Details of the reinforcement learning method are elaborated below.
Quantization index. In this paper, the computation cost of convolution is approximately calculated with BitOPs (Yang & Jin, 2021). Supposing the multiplication of a kw bit weight value and a ha bit activation value, the BitOPs of this multiplication ka BitOPs an easy-to-calculate metric and independent of the actual hardware.
State space. To well transfer the agent to different models and datasets, we exclude factors that are strongly related to the models and datasets. Consequently, the designed state space composed of four types of factors.
The compression ratio À is obtained by comparing the cur- rent training with full INT8 quantization. The quantization index is formulated in Equation (7), where @ is the hyperpa- rameter to adjust the quantization importance in the reward,
(i) Time step that denotes the ratio of the current training epoch to the total number of epochs. (ii) Current bit-width of weights, activations, and gradients. (iii) Quantization loss of weights, activations, and gradi- ents. The quantization loss is calculated using Equation (5) in (Zhang et al., 2020) to capture the data distribution differ- ence for revealing the training process.
g gid = 0/(1 X)
Accuracy index. To evaluate the model accuracy of low bit training, the model accuracy of full INT8 training at each epoch is stored as reference a,. The accuracy index is obtained by comparing the current training accuracy with full INT8 model. 8 in Equation (8) is also a hyperparameter to adjust the accuracy importance,
(iv) Last changing time step of the bit-width for weights, ac- tivations, and gradients. If the bit- width has never changed,
the value is set to 1. From this value, the agent can esti- mate the compression ratio,
{
1 1/(1+ [111+(a,,))) (a, -a) 88)
if a > a, if a S a,
a Lida
(8)
Σ
b
Egg
Loss
(5)
Time step. The ultimate objective of the agent is to increase the final compression ratio while maintaining the model accuracy. Therefore, the reward at the late stage of training is more important for which the reward is multiplied by the time step.
Action space. We adopt the mixed INT4, INT6 and INT8 format during the training stage. We set the agent only able to increase bidths. The agent has four actions: (i) Do not change the bit-widths. (ii-iv) Increase the bit-width of weights, activations, or gradients by A
Value network. To keep the extra computation cost of the agent low during training, the agent network should be
5

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kept small. Our Q-network has only one hidden layer of 128 neurons and the number of neurons in the first and final layer is equal to the number of states and the actions, respectively, LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
4.5. Convergence Analysis
In this section, we focus on the convergence analysis of the gradient quantization, considering that the impact of weight and activation quantization the loss function could be ac- cumulated by layers and is difficult to analyze quantitatively. Similar to Yang et al. (2021), we introduce Assumption 4.1 on the loss functions ff and F,, i = 1...., m.
Since we do not have access to all the data in many situa- tions, we train the agent on a relatively small local dataset (10% of the CIFAR-I0) with ResNet-20 model and transfer it to other models and datasets.
Assumption 4.1. Given any client i E M in the client set M, for W,, w/ E IRd, we have the following assumptions.
4.4. Teacher Samples for Behaviour Cloning
As pure policy-based method (Schulman et al., 2017) usually needs the whole episode and the episode number in this scenario is limited, pure poliey-based method is not suitable. Therefore, we adopt the typical off- off-policy method: deep Q- network (Mnih et al., 2015) to utilize its sample efficiency.
i) If F-function is L-smooth, then [VF((w)) V (w(()) S L [w-w[l]
ii) Let & be a random local data sample in the I-th step at the i-th worker, the local gradient estimator is unbiased B F. (w,,,,,) C:)] = (w:))
Behaviour cloning as regularization (Goecks et al., 2020: Nair et al., 2018) is an effective tool to accelerate reinforce- ment learning from samples. Based on the observation in (Ding et al., 2024) that gradient and activation quanti- zation have more impact on the model performance, we accumulate some state- pacion--rwaad pairs from this prior knowledge as the teacher samples Dr. Specifically, the possible teacher samples have gradient bit-width switched to INT8 with a time step ranging from 0. 0.10 to 0.45 and the activation bit-width switched to INT8 with a time step from 0.50 to 0.90 and the changing time step of weight bit-width ranges from 0.50 to 0.95 or keeps at INT4, These samples can achieve better balance between model performance and compression ratio than the random bit-width allocation.
iii) The variance os of each local gradient estimator is bounded by ([]lF[(w,,))) - (F.(w))] I o. and the global variance og is bounded by ([VF((,)) V.,(w,) S oz.
We further assume in Assumption 4.2 the equivalent additive noise for gradient quantization at each client.
Assumption 4.2. The gradient quantization noise on each client has well-defined expectation and variance (denoted as f'y and (o )2 for the i-th client), and the quantization noise expectation p'y can be viewed as zero
In Theorem 4.3, we develop the convergence rate for LBI- FL (with gradient quantization) associated with the total number of communication rounds T, and demonstrate that the theoretical convergence rate is equivalent to the rate of existing FL algorithms like FedAvg.
The Q-network is trained on the teacher samples by super- vised learning. To push the agent favored with the teacher sample's 's action, only calculating the value differences is not enough. We use the softmax function on the action di- mension and utilize KL divergence measure the distance between the agent policy and the accumulated teacher sam- ples. Thus, the training loss is calculated as sum of value differences and the KL divergence between the agent policy and the teacher samples. Equation (9) is the training loss that makes the initial agent close to the teacher samples, where Ni (s) is the teacher policy from the accumulated sample,
Theorem 4.3. Under Assumptions 4.1 and 4.2 and full worker participation, when the learning rate 1) S (8LK)-1 for each client, the output we generated with gradient quan- lization satisfies:
So fo-18 S. KnT
min E [IV (w))) AE(T]
<
+ 2
(10)
where T is the number of communication rounds I
and &b = c.2m (oz m I. ((ux)2 + (d))))) +
M Σ
2 L2 (0z + +6Ko2)], with e as a constant, K as the number of local updates, and m as the number of clients.
I.
E E(g.))ED
r() (6==0,a=0--0(55000
+ E (L
Proof. Please refer to Appendix A.
where To(a)s) = exp (1(8, 0)) EneA exp (1(8, 0)) denotes the softmax of Q-values for different actions, M is the episode length. By utilizing the teacher samples in the behavior cloning, the agent can be trained quickly in our scenario.
Theorem 4.3 implies that, given 7) (VTLK)-L, the con- vergence rate of gradient quantization is 0(1/ when T is sufficiently large, and is equivalent to the convergence rate of the standard FedAvg algorithm. In Section 5.4, we verify the convergence rate of LBI-FL. with empirical evaluations.
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LBI-FL: Low-Bit Integerized Federated Learning with Temporally Dynamic Bit- Width Allocation
5. Experiments
Table 2: Top-1 classification accuracy (%) on CIFAR-10.
In this section, we first introduce the agent training result and then earry out extensive experiments on different models and datasets. Finally, ablation studies are conducted to evaluate the proposed method.
Model
Method
Top-1 Acc (%)
BitOPs
RR (%)
FP32
83.36
45.5G
U14
81.97
0.71G
75
LeNet
UI8
82.91
2.84G
0
LBI-FL
81.79
1.38G
51.49
5.1. Agent Training
FP32
84.21
114.2G
U14
82.71
1.78G
75
ResNet-18
Experiment setting. We collect the teacher samples by
U18
84.23
7.14G
training ResNet-20 (He et al., 2016) for 100 epochs on subset of the CIFAR-10 dataset randomly sampled with 10% of the original data. In the reward function, 0 is set as 0.25 and 5 as 0.5. 200 episodes of samples are collected. The scaling parameters for quantization are updated every 100 iterations. The experiments in this paper are conducted on a single NVIDIA 3090 GPU.
LBI-FL
84.16
3.28G
54.06
FP32
85.19
258.4G
U14
77.90
4.04G
75
ResNet-50
UI8
84.93
16.15G
0
LBI-FL
83.52
8.45G
47.68
FP32
73.85
1910.5G
U14
69.33
29.9G
75
VIT-S
UI8
71.85
119.4G
0
LBI-FL
72.55
60.3G
49.51
Training result. The training agent converges where the gradient bit-width switches to high bit-widths in the very early stage and the activation bit-width switches based on the quantization difference during training while the weight bit-width fixes at INT4. Therefore, the communication overhead is reduced to 1/8 of the full-precision training method. The learned agent can achieve good balance between compression ratio and model performance. In new training scenario, we can directly use this agent or train new agent with small subset of the local data. Moreover, the agent consists of two linear layers with only 1.92K parameters, and requires 1.97G BitOPs for making one decision. The RL agent makes decision for every epochs. Therefore, the computation cost is much smaller than the network training.
FP32
92.04
290.6G
U14
85.83
4.54G
75
MobileNet-V2
UI8
89.65
18.2G
LBI-FL
89.02
8.83G
51.39
Table 3: Top-1 classification accuracy (%) on CIFAR- 100.
Model
Method
Top- 1 Acc (%)
BitOPs
RR (%)
FP32
48.55
45.5G
U14
44.83
0.71G
75
Lenet
UI8
46.91
2.85G
LBI-FL
47.41
1.39G
50.98
FP32
54.35
114.4G
U14
49.35
1.79G
75
ResNet-18
UI8
53.57
7.15G
0
LBI-FL
53.48
3.30G
53.81
FP32
$1.71
1910.5G
5.2. Evaluation Metrics
U14
46.39
29.9G
75
VIT-S
UI8
49.32
119.4G
0
In our experiment, the communication cost reduced ratio and BitOPs reduced ratio (RR) compared to INT8 training, and the accuracy (Acc) are used evaluation metries. As the agent keeps weights at INT4 during the training process, the reduction ratio of communication cost is 87.5% % compared to full precision and 50% compared to INT8 training. Below, we only report the results for Ace and BitOPs RR. For simplicity, the BitOPs of weight- the forward propagation approximately treated the same as the gradient-weight convolution and gradient-activation convolution. For example, as the forward propagation of LeNet on CIFAR- 10 is 4. Mac, the BitOPs under full precision are 14.81M 32x 45.5G.
LBI-FL
48.32
57.2G
52.08
FP32
74.52
291.0G
U14
60.31
4.55G
75
MobileNet- V2
UI8
72.37
18.2G
LBI-FL
71.61
8.84G
51.40
mines the bit-widths of weights, activations, and gradients from INT4, INT6, and INT8 for every 5 epochs from the 10th epoch. For LeNet, the number of training epochs is set at 2000 and the client number 100. 10% of the clients are selected to update at every epoch. For other larger networks, the number of training epochs is set 200 and the client number is 10. All the clients are updated at every epoch. The local update epoch is 2 and the learning rate decay is 1.
convolution in
5.3. Image Classification
Results. Tables 2 and 3 show that, compared to UI8 (Zhu et al., 2020), the proposed LBI-FL achieves less than 1.5% accuracy loss with 50% reduced BitOPs in most cases (ex- cept for LeNet on CIFAR- 10) for various network architec- tures like LeNet, ResNet-18 18, VIT-S, and MobileNet-V on
Experiment setting. We evaluate with LeNet (LeCun et al., 1998), ResNet-18/50/101 (He et al., 2016), Mo- bileNetV2 (Sandler et al., 2018), and VIT-S (Dosovitskiy al., 2021) on the CIFAR- 10/100 dataset. The agent deter-

---

LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
Table 4: Convergence rate of LBI-FL compared with full- precision, full INT4, and INT8 training. It lists the number of epochs needed to obtain target accuracy.
Table 7: Effect of local update epochs.
Dataset
Lep
Dirichlet
Top-1 Acc (%)
RR (%)
81.79
51.49
Model
Acc (%)
FP32
U18
U14
LBI-FL
0.25
78.56
52.03
CIFAR-10
LeNet
81
472
612
624
569
5
iid
81.62
52.03
ResNet-18
70
76
0.25
77.93
53.20
ViT-S
68
38
52
66
56
iid
47.41
50.98
MobileNet-V2 V2
84
36
39
61
50
CIFAR-100
2
0.25
46.09
51.07
5
iid
45.49
51.46
0.25
43.38
51.70
Table Comparison of our method with random selection.
Table Effects of the learning rate decay.
Model
Method
Acc (%)
BOPS
RR (%)
LeNet
Random
81.76 (-0.03)
1.41G
50.25
Dataset
LD
Dirichlet
Top-1 Ace (%)
RR (%)
LBI-FL
81.79
1.38G
51.49
Random 83.02 (-1.14)
3.39G
52.5
1.0
iid
81.79
51.49
ResNet-18
LBI-FL.
84,16
3.28G
54.06
CIFAR-10
0.25
78.56
52.03
Random 86.91 (-2.11)
8.65G
52.5
0.998
iid
81.53
51.59
MobileNet-V2
LBI-FL
89.02
8.83G
51.39
0.998
0.25
77.49
52.15
1.0
iid
47.41
50.98
1.0
0.25
46.09
51.07
Table 6: The effectiveness of our proposed method under
CIFAR-10
0.998
iid
42.69
51.00
non-iid conditions (Dirichlet = 0.25 0.5).
0.998
0.25
42.06
51.01
Dataset
Dirichlet
Method
Top-1 Acc (%)
RR (%)
Table 9: Effect of initialization seeds.
FP32
80.39
U14
75.79
75
CIFAR-10
0.25
Datasct
Model
Seed
Top-1 Acc (%)
RR (%)
UI8
78.71
0
LBI-FL
78.56
52.03
23
81.79
51.49
FP32
81.27
CIFAR-10
LeNet
60
82.01
51.43
U14
77.42
75
90
81.71
51.45
CIFAR-10
U18
78.97
0
200
81.92
51.60
LBI-FL
78.90
51.68
23
84.16
54.06
FP32
46.22
CIFAR-10
ResNet- 18
60
84.59
54.05
UI4
43.78
75
90
84.33
53.80
CIFAR-100
0.25
UI8
45.81
0
200
84,49
53.98
LBI-FL
46.09
51.07
23
72.55
49.41
FP32
46.73
CIFAR-10
VIT-S
60
72.52
49.66
U14
44.43
75
90
72.21
49.75
CIFAR-100 100
0.5
U18
46.33
0
200
72.17
49.74
LBI-FL
46.25
51.06
23
89.02
51.39
60
89.11
51.40
CIFAR-10
MobileNet-Va
90
89.38
51.43
200
89.44
51.41
CIFAR-10/100.
Morever, the storage overhead of trained network weights and BitOPs for inference are reduced by 50%.
most cases, and is even slightly faster than INTS on the LeNet. Considering that the communication overload is half of that in INT8 training, and the computational load is also reduced by more than half, the slight increase in the number of convergence epochs is acceptable.
5.4. Convergency analysis
In addition the model performance, the convergence rate (the number of epochs required reach target accuracy) is also critical metric in federal learning. Table 4 compares the convergence rate of LBI-FL with full-precision, INT4, and INT8 training to obtain target accuracy. The dataset is
5.5. Ablation Studies
In this section, we first validate the effectiveness of the agent for the temporal bit-width selection, and then conduct ablation studies on some parameters in our method.
selected as CIF
From Table 4, it is evident that the convergence rate of our method lies between full INT4 and INT8 training in
Effect of temporal bit-width selection. We compare the
8

---

LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
proposed method with direct approach where the clients at INT4 are randomly selected with similar reduced ratio. The dataset is selected as CIFAR-10. For LeNet, 33 clients (100 clients overall) are set at INT4, and for ResNet-18 18 and MobileNet-V2 V2, clients (10 clients overall) are set at INT4.
Grant 62431017, Grant 62125109, Grant
Grant 62301299, Grant 621 62120106007, in part by the Program of
Shanghai Science and Technology Innovation Project under Grant 24BC3200800, and in part by the Al Laboratory of United Automotive Electronic Systems (UAES) Co. under Grant 2025-3270.
Table 5 demonstrates that on small networks like LeNet, the performance of random selection may be acceptable. but the loss of performance on larger networks like ResNet-18 and MobileNet-V V2 is not ignorable.
Impact Statement
This paper presents work centered advancing the ma- chine learning field, specifically within the realm of feder- ated learning. There are very few potential societal conse- quences of our work, and none of them must be specifically highlighted here.
Effect of data distribution. We consider both iid (inde- pendent and identically distributed) and non-iid data distri- butions. The parameters of non-iid Dirichlet distribution are 0.25 and 0.5 our experiments. Table 6 shows that, compared to INT8 training, the proposed method yields less than 0.5% performance loss on non-iid ddata distributions.
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12

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LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
A. Proof of Theorem 4.3
Our derivation is basically similar to that Appendix (Yang et al., 2021). For better understanding, please refer to Appendix A in (Yang et al., 2021).
The average update the clients is Å. m > (4) + mt). Take expectation of (*++1) communication round t, we can have:
I. E, || -wel] E, If (W++1)) (wa) (Vf (W) [W+1-- wil) 2-1
= = (w:) (V. (w:) EE 4VA+ (w.) nKVs (w:)]) + -.c ||
L コ/ EE [|
= (w:) n
P kKV (wi)))
(1I)
A2
As the noise nł from the gradient quantization has well-defined expectation which can be viewed as zero (Assumption 4), we have Eg [n]]] = O. The term A₁ is calculated similar to (Yang et al., 2021):
A
V W:) E. A + 1) S (wr)))
m
ngg,, + n²) + nKVF (wv)
f (We), Bt
m
K-1
v (w:), Er
7B8i + /KV (wx)
m
S nk (1 + +15
|VS (1=))] + 5K218122
(oz + +KK2))
7
E,
Σ
K-1
Σ
(wi,))
(12)
2
2Km
i=1
k=0
Moreover, the term A2 can be bounded as:
m
A₂ E.
||
Σ
m
m
172
n
m
E,
n!)
m
E.
Bi.k
K
Ex
Σ
m
(13)
k=0
Considering the quantization noise each client can be supposed independent, the expectation in the second term is calculated as:
E2
m2
E2
nin!
Σ ((xk)² + (ah))) +2 Z p
(14)
According to the assumption that the quantization noise expectation pyy and m can be viewed as zero, we can have:
E,
(15)
i=
13

---

LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit- Width Allocation
Table 10: Ablation studies on training LeNet on CIFAR-10.
CIFAR-10
CIFAR-100
Dirichlet
Lep
LD
Top-1 Acc (%)
RR (%)
Top-1 Acc (%)
RR (%)
81.79(-1.12)
51.49
47.41(+0.50)
50.98
2
0.998
81.53(-0.57)
51.59
42.69(-1.15)
51.00
iid
81.62(-1.10)
52.03
45.49(+1.23)
51.46
5
0.998
81.73(-0.28)
52.83
39.74(+0.62)
51.31
78.56(+0.25)
52.03
46.09(+1.28)
51.07
2
0.998
77.49(-0.83)
52.15
42.06(-1.08)
51.01
0.25
77.93(-1.41)
53.20
43.38(-0.62)
51.70
5
0.998
78.62(+0.10)
53.74
40.00(-0.08)
51.59
1
78.90(+0.13)
51.68
46.25(-0.08)
51.06
2
0.998
79.81(+0.09)
51.91
44.53(-0.58)
51.00
0.5
80.05(-0.73)
52.56
45.14(+0.51)
51.56
5
0.998
79.83(-0.38)
53.35
40.09(-0.51)
51.44
8.0
8.0
7.5
7.5-
node 30
7.0
node 40
7.0
node 10
6.5
node 50
Bit-Wich
6.5
node 20
BitWiid
node 30
6.0
70
6.0
40
5.5
node 80
5.5
node 50
nade 90
node 60
5.0
node 70
80
4.0
90
500
1000 Epoch
1500
2000
500
1000
1500
2000
Epoch
(a) Activations
(b) Gradients
Figure 5: The bitwidth change process (INT4 > INT6, INT6 + INT8) of (a) activations, and (b) gradients through training
LeNet on CIFAR-IO.
From A₁ and A2, we can have:
I. |
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V (w:). E, A + +nK (w:)
A2
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01,
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(16)
Similarly (Yang et al., 2021). rearranging and summing from t T 1. we have:
fo fx
min
|
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+
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KnTT
where +- =
Lag Zm
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14

---

LBI-FL; Low-Bit Integerized Federated Learning with Temporally Dynamic Bit-Width Allocation
B. Ablation Studies Results
Table 10 presents more comprehensive results of ablation studies under different data distributions and hyperparameters. The numbers parentheses indicate the model performance loss compared full INT8 training. It can be seen that our method performs well in iid and non-iid scenarios. most cases, models with local update epochs (Lep) of and learning rate decay (LD) of I perform better, which is consistent with what is mentioned in the main text.
C. Bit-Width Change Process
Figure illustrates the bit-width change process of activations and gradients during the training of LeNet on the CIFAR-10 dataset. The weights are maintained INT4 precision during training. It can observed that gradient bit-widths increase an earlier stage, while activations increase in the later process. There are some differences among different clients, but these differences not significant.
15


Reviews:
[{"review_id": "EBrUL593nT", "reviewer": "Reviewer_EVpv", "summary": "This paper introduces LBI-FL, a novel framework for low-bit integerized federated learning with a focus on temporally dynamic bit-width allocation.  \nThe authors provide both theoretical convergence analysis and empirical validation on multiple FL benchmarks showing reductions in communication and computational cosr while maintaining model accuracy.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable comments and below are our detailed responses to the raised weaknesses and questions.  \n\n>  **W1: Experiments on diverse tasks and datasets.**\n\n**Response:** We have performed extensive experiments on diverse tasks and datasets to demonstrate the effectiveness of our LBI-FL. We use the RL agent trained for image classification on CIFAR-10 without retraining, which proves the generality of our RL agent.\n\ni) Image segmentation with U-Net on DSB2018. We adopt the image size of 96 $\\times$ 96. The table below shows that, compared with UI8 training, we achieve acceptable performance of about 0.6\\% loss in Dice similarity coefficient (DSC) with over 50\\% reduction of BitOPs.\n\n| Dataset | Method | Dice (\\%) | BOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| DSB2018 | FP32 | 89.55 | 19848G | - |\n|  | UI4 | 87.01 | 310.1G | 75 |\n|  | UI8 | 89.48 | 1240.5G | 0 |\n|  | LBI-FL | 88.84 | 604.9G | 51.27 |\n\nii) Image classification with ResNet-18 on Tiny-ImageNet. The image size is 64$\\times$64. Training on Tiny-ImageNet is much more difficult. The table below shows that our LBI-FL achieves over 50\\% reduction of BitOPs with less than 0.1\\% accuracy loss. \n\n| Dataset | Method | Acc (\\%) | BOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| Tiny-ImageNet | FP32 | 35.84 | 457.14G | - |\n|  | UI4 | 34.64 | 7.14G | 75 |\n|  | UI8 | 35.21 | 28.57G | 0 |\n|  | LBI-FL | 35.13 | 14.05G | 50.81 |\n\n> **W2: Baselines using layer-wise quantization.**\n\n**Response:** Most layer-wise quantization based methods (**e.g.**, HAWQ v1-v3) are designed for inference only, and cannot be employed for FL. We compare our LBI-FL with AMPA [A1] that achieves layer-wise quantization based on the sensitivity measurement for centralized low-bit training. We train ResNet-18, MobileNet-V2, and ViT-S on CIFAR-10 using the two methods. The results below show that our LBI-FL achieves higher compression ratios and better performance.\n\n[A1] Li Ding et al. AMPA: Adaptive mixed precision allocation for low-bit integer training. ICML 2024.\n\n| Model | Method | Acc (\\%) | BOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| ResNet-18 | AMPA | 84.10 | 3.49G | 51.11 |\n| | LBI-FL | 84.16 | 3.28G | 54.06 |\n| ViT-S | AMPA | 72.54 | 73.08G | 38.79 |\n|  | LBI-FL | 72.55 | 60.3G | 49.51 |\n| MobileNet-V2 | AMPA | 87.89 | 9.78G | 46.19 |\n|  | LBI-FL | 89.02 | 8.83G | 51.39 |\n\n> **W3: Discussion about works on energy-latency tradeoffs with quantization in FL.**\n\n**Response:** Thanks for the suggestion. We will include relevant works [A2][A3] in the Related Work section. Optimizing energy consumption is indeed essential for practical deployment of FL systems. For instance, [A2] derives the time and energy consumption models for FL and proposes a iterative algorithm to allocate resources. [A3] proposes an optimization framework that minimizes the total energy consumption of local computation and wireless transmission by adaptively selecting the quantization level. These methods are complementary to our LBI-FL that simultaneously reduces computational and communication overheads, and thereby improves energy efficiency with reduced latency in federated learning.\n\n[A2] Yang, Zhaohui, et al. \"Energy efficient federated learning over wireless communication networks.\" IEEE TWC 2020.\n\n[A3] Ouiame Marnissi, Hajar El Hammouti, and El Houcine Bergou. Adaptive sparsification and quantization for enhanced energy efficiency in federated learning.IEEE OJCOMS 2024.\n\n> **Q1: Overhead of RL agent's decision-making.**\n\n**Response:** The overhead of RL agent is very small compared to the computational savings from low-bit training. \n\ni) The RL agent consists of two linear layers with only 1.92K parameters, and requires 1.97G BitOPs for making one decision (i.e., 1.92K Mac$\\times$32$\\times$32).\n\nii) The RL agent makes decision for every 5 epochs rather than each epoch. \n\nWe provide results on CIFAR-10 as examples. When training LeNet using 100 clients, each client has 500 training images and the RL agent makes a decision after training on 250 images on average (participation rate is 0.1). Its inference cost is only 1.1\\% that for UI4 training and 0.275\\% for UI8 training. When training ResNet-18 using 10 clients, each client has 5000 training images. The inference cost of the RL agent is 0.0044\\% and 0.0011\\% those for UI4 and UI8 training.", "claims_and_evidence": "Most of the claims are well supported.\n\nThe selection of the dataset is limited to CIFAR-10 and CIFAR-100, which are both small and lacks evaluation on fundamentally different tasks.", "methods_and_evaluation_criteria": "The methods and evaluation are appropriate and make sense. The models selected are diversified, and the metrics support the claims.", "theoretical_claims": "Theoretical contribution of Theorem 4.3, which analyzes convergence of LBI-FL under gradient quantization with Gaussian noise approximation, looks correct.\nThe convergence rate of $O(1/\\sqrt(T))$ makes sense.", "experimental_designs_or_analyses": "The experiment design are valid.\n\nThe generalization of RL policy to unseen FL tasks is not fully evaluated which limits the claim of broader usage.", "relation_to_broader_scientific_literature": "This work is closely related to FL Basic, theory, quantization and RL for optimization.\n\nThis work extends prior works on low-bit FL by proposing a sub-INT8 training framework that dynamically adjusts bit-width over time using RL seems novel to me.", "essential_references_not_discussed": "Layer-wise quantization based methods are mentioned but not used as baselines.\n\nSome recent works focus on energy-latency tradeoffs in FL with quantization can also be discussed here.", "other_strengths_and_weaknesses": "Strengths:\nThe idea of this paper seems novel, well-written with strong theoretical contribution\nWeakness:\nRL part is not fully discussed.", "other_comments_or_suggestions": "More diversified datasets are recommended in this paper", "questions_for_authors": "How does the RL agent's decision-making overhead compare to the computational savings from low-bit training?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6NZGuBZeNz", "reviewer": "Reviewer_Nft9", "summary": "This paper proposes a low-bit integerized federated learning (LBI-FL) framework, which reduces the uplink and downlink communication overhead and mitigates the computation burden on clients, all with a tolerable level of performance loss. Specifically, a reinforcement learning based agent, which is trained on a small local dataset, is applied to dynamically determine the bit-widths for weights, activations, and gradients. The authors demonstrate, in theory, that federated learning with gradient quantization can achieve an equivalent convergence rate to the standard FedAvg algorithm with a sufficiently large number of communication rounds. Experimental results show the proposed framework 1) reduces the communication overhead to 1/8 of the full-precision training method; 2) reduces over 50% BitOPs per client on average with less than 2% accuracy loss, compared to INT8 training.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable suggestions and below are our responses to the weaknesses and questions. \n\n> **W1: Proof of the theorem.**\n\n**Response:** According to your comment, we have improved the theoretical analysis by relaxing Assumption 4.2 without affecting the final convergence rate. Specifically, instead of assuming the quantization noise to follow a Gaussian distribution with identical variance across all the clients, we now assume only that (a) The gradient quantization noise on each client has a well-defined expectation and variance (denoted as $\\mu_N^i$ and $(\\sigma_N^i)^2$ for the $i$-th client), and (b) The quantization noise expectation $\\mu_N^i$ can be viewed as zero.\n\nBased on this assumption, we provide an updated derivation of the theorem. The noise term does not influence the $A_1$ term in Equation (12). Neglecting the differences across epochs, we reformulate Equation (13) in the appendix as:\n\n$$\n\\begin{aligned}\nA_2 \n& \\le \\frac{\\eta^2}{m^2} \\mathbb{E}\\_t\\left[\\left\\|\\sum\\_{i=1}^m \\sum\\_{k=0}^{K-1} \\mathbf{g}\\_{t, k}^i\\right\\|^2\\right] + \n\\frac{\\eta^2}{m^2}  \\mathbb{E}\\_t \\left[ \\left\\| \\sum_{i=1}^m \\sum\\_{k=0}^{K-1} n_{t, k}^i \\right\\|^2\\right] \\\\\\\\\n& = \\frac{\\eta^2}{m^2} \\mathbb{E}\\_t\\left[\\left\\|\\sum\\_{i=1}^m \\sum_{k=0}^{K-1} \\mathbf{g}\\_{t, k}^i\\right\\|^2\\right] + \n\\frac{\\eta^2}{m^2} K \\cdot \\mathbb{E}\\_t \\left[ \\left\\| \\sum\\_{i=1}^m n_t^i \\right\\|^2\\right]\n\\end{aligned}\n$$\n\nConsidering the quantization noise on each client can be supposed independent, the expectation in the second term is calculated as:\n\n$$\n\\begin{aligned}\n\\mathbb{E}\\_t \\left[ \\left\\| \\sum\\_{i=1}^m n_t^i \\right\\|^2\\right]  = \\sum\\_{i=1}^m \\mathbb{E}\\_t \\left[ \\left\\|  n_t^i \\right\\|^2\\right] + 2\\sum_{i<j} \\mathbb{E}_t\\left[n_t^i n_t^j\\right] = \\sum\\_{i=1}^m ((\\mu\\_N^i)^2 + (\\sigma^i\\_N)^2) + 2\\sum\\_{i<j} \\mu_N^i \\mu_N^j\n\\end{aligned}\n$$\n\nTherefore, $\\Phi$ in Equation (10) changes as\n\n$$\n\\begin{aligned}\n\\Phi =& \\frac{1}{c}\\left[\\frac{L \\eta}{2 m} \\left(\\sigma_L^2 + \\frac{1}{m} \\left( \\sum\\_{i=1}^m  ((\\mu\\_N^i)^2 + (\\sigma^i\\_N)^2) \\right)\\right)   +\\frac{5 K \\eta^2 L^2}{2}\\left(\\sigma_L^2+6 K \\sigma_G^2\\right)  \\right]\n\\end{aligned}\n$$\n\nHowever, the convergence rate does not change, since the quantization noise expectation is usually at 0. \n\nNote that previous convergence result is a special case of this new result. \n\n> **W2: References Not Discussed.**\n\n**Response:** Thanks for the reminder. We will include FedAvg for the standard FL setting in the final version.\n\n> **W3: Some typos.**\n\n**Response:** We will correct these typos in the final version. \n\n> **Q1: Bit-width change for other models on other datasets.**\n\n**Response:** Yes, there are no significant differences among clients but there is a difference between activations and gradients for other models on other datasets. In the table below, we provide the bit-width change process for training ViT-S on CIFAR-10 (200 epochs) and LeNet on CIFAR-100 (2000 epochs) as further evidence. The numbers in brackets indicate the epochs of bit-width change.\n\n| Model | Dataset | Client Idx | Activation | Gradient |\n| ---- | ---- | ---- | ---- | ---- |\n| ViT-S | CIFAR-10 | 2 | (85, 110) | (20, 85) |\n|  | | 6 | (80, 105) | (20, 80) |\n|  |  | 8 | (80, 105) | (20, 75) |\n| LeNet | CIFAR-100 | 20 | (850, 1345) | (170, 825) |\n| | | 60 | (830, 1325) | (150, 830) |\n| | | 80 | (825, 1355) | (140, 820) |\n\n> **Q2: Regarding quantization error as Gaussian noise.**\n\n**Response:** First of all, we emphasize that we no longer assume Gaussian noise for quantization error to achieve the convergence result. We assume that the expectation and variance of the noise distribution on each client exist are well defined and the expectation can be viewed as zero. We further perform experiments with ResNet-18 on CIFAR-10 to support the assumption, where the distribution of quantization noise is concentrated around zero.  \n\nIn the previous result, we made the assumption as in [B1]-[B4] where the Gaussian distribution is assumed to find the optimal clipping value to reduce the quantization loss.\n\nWe will revise the assumption and clarify claims for notations in the final version. \n\n[B1] Ron Banner et al. Scalable methods for 8-bit training of neural networks. NeurIPS 2018. \n\n[B2] Ruizhou Ding et al. Regularizing activation distribution for training binarized deep networks. CVPR 2019. \n\n[B3] Zhezhi He and Deliang Fan. Simultaneously optimizing weight and quantizer of ternary neural network using truncated gaussian approximation. CVPR 2019.\n\n[B4] Xishan Zhang et al. Fixed-point back-propagation training. CVPR 2020.", "claims_and_evidence": "The authors verified the validity of the proposed scheme with comprehensive experiments.", "methods_and_evaluation_criteria": "Yes. The authors leverage reinforcement learning to dynamically determine client bit-widths in federated learning, allowing more flexible and reasonable bit-widths allocation.", "theoretical_claims": "Yes. However, the proof of the theorem in this paper is not rounded enough.", "experimental_designs_or_analyses": "The authors conducted experiments with the CIFAR-10/100 dataset and models of LeNet, ResNet-18, MobileNet-V2, and ViT-S and compared the communication and computation costs, BitOPs, and accuracy under various bit widths. They also checked the effects of local update epochs, data distribution, learning rate decay, etc.", "relation_to_broader_scientific_literature": "This paper introduces reinforcement learning methodology into model compression under federated settings. This new approach reduces overhead in federated learning, and the idea could be explored more widely, for example, in personalized federated learning or channel-wise compression strategy.", "essential_references_not_discussed": "One essential reference, which proposed the standard settings of federated learning and the framework of FedAvg, should be cited: \n\nMcMahan, Brendan, et al. \"Communication-efficient learning of deep networks from decentralized data.\" Artificial intelligence and statistics. PMLR, 2017.", "other_strengths_and_weaknesses": "Strengths: \n1) The core idea, leveraging reinforcement learning to determine the compression strategy in federated learning, is novel, reasonable, and potential. \n2) Comprehensive experiments verify the validity of the proposed methodology. \n\nWeaknesses:\n1) The theoretical proof in the appendix is not rounded enough, though, as stated, it is similar to one reference.\n\n## Update after rebuttal\n\nThe authors gave a rounded analysis as demanded, which makes the theory more generalized. Therefore, I increased the score.", "other_comments_or_suggestions": "Typos:\n1) In Section 4.2, \"Every Thr epochs, the agent on each client ...\".\n2) In Section 4.3, the part of the Balanced reward function, \"Supposng the multiplication of a ...\"\n3) In Section 4.5, \"the theoretical convergence rate is equivalent to the rrate of ...\"", "questions_for_authors": "As for the bit-width change process, is it the same case (as LeNet on CIFAR-10) for other models on other datasets? (There are no significant differences among clients, but there is a difference between activations and gradients). \n\nAs for the proof, it would be better to provide clear claims for notations. Also, is it applicable to regard the quantization error as Gaussian noise under the high heterogeneity of federated learning?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ce7COqMzOo", "reviewer": "Reviewer_umsU", "summary": "The paper introduces Low-Bit Integerized Federated Learning (LBI-FL), a framework designed to reduce both communication and computational costs in Federated Learning (FL) by using quantization techniques. Unlike conventional approaches limited to INT8 precision, LBI-FL dynamically adjusts the bit-width of weights, activations, and gradients during training through reinforcement learning. A trained agent optimizes bit-width allocation by considering factors such as current precision, training stage, and quantization loss. The method generalizes well across different network architectures and non-IID datasets. Authors claim that theoretical analysis confirms that gradient quantization maintains the same convergence rate as FedAvg. Experiments show that LBI-FL achieves 8× communication cost reduction and over 50% fewer BitOPs per client with less than 2% accuracy loss compared to INT8-based low-bit training.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive suggestions. \n\n> **W1: Claims may raise concerns.**\n\n**Response:** Claim i): We use this sentence to emphasize that our LBI-FL can reduce both the overhead in the uplink and downlink communication with low-bit training. In fact, the paper \"Prune at the Clients, Not the Server\" cannot reduce the downlink communication only using client-side pruning and has to resort to accelerated server pruning, which could completely fail in accuracy and loss as mentioned in the paper. For rigidity, we will change the claim to \"existing methods based on quantization\" in the final version. \n\nClaim ii): In lines 19-21 and 55-59, \"low-bit training\" refers to simultaneously quantizing the weights, activations, and gradients. The paper \"IntSGD: Adaptive floatless compression of stochastic gradients\" develops adaptive integer compression operators for distributed SGD. It only quantizes the gradients and does not quantize weights and activations. To our best knowledge, we are the first to achieve \"low-bit training\" in the FL scenario. \n\n\nClaim iii): We have improved the theoretical result by relaxing Assumption 4.2 without affecting the final convergence rate. Instead of assuming the quantization noise to follow a Gaussian distribution with identical variance across all the clients, we now assume only that (a) The gradient quantization noise on each client has a well-defined expectation and variance ($\\mu_N^i$ and $(\\sigma_N^i)^2$ for the $i$-th client), and (b) The expectation $\\mu_N^i$ can be viewed as zero. \n\nBased on this assumption, we provide an updated derivation of the theorem. The noise term does not influence the $A_1$ term in Equation (12). Neglecting the differences across epochs, we reformulate Equation (13) in the appendix as:\n\n$$\n\\begin{aligned}\nA_2 \n& \\le \\frac{\\eta^2}{m^2} \\mathbb{E}\\_t\\left[\\left\\|\\sum\\_{i=1}^m \\sum_{k=0}^{K-1} \\mathbf{g}\\_{t, k}^i\\right\\|^2\\right] + \n\\frac{\\eta^2}{m^2} K \\cdot \\mathbb{E}\\_t \\left[ \\left\\| \\sum\\_{i=1}^m n_t^i \\right\\|^2\\right]\n\\end{aligned}\n$$\n\nConsidering the quantization noise on each client can be supposed independent, the expectation in the second term is calculated as:\n\n$$\n\\mathbb{E}\\_t \\left[ \\left\\| \\sum\\_{i=1}^m n_t^i \\right\\|^2\\right]  = \\sum\\_{i=1}^m \\mathbb{E}\\_t \\left[ \\left\\|  n_t^i \\right\\|^2\\right] + 2\\sum_{i<j} \\mathbb{E}_t\\left[n_t^i n_t^j\\right] = \\sum\\_{i=1}^m ((\\mu\\_N^i)^2 + (\\sigma^i\\_N)^2) + 2\\sum\\_{i<j} \\mu_N^i \\mu_N^j\n$$\n\nTherefore, $\\Phi$ in Equation (10) changes as\n\n$$\n\\Phi = \\frac{1}{c}\\left[\\frac{L \\eta}{2 m} \\left(\\sigma_L^2 + \\frac{1}{m} \\left( \\sum\\_{i=1}^m  ((\\mu\\_N^i)^2 + (\\sigma^i\\_N)^2)  \\right)\\right)   +\\frac{5 K \\eta^2 L^2}{2}\\left(\\sigma_L^2+6 K \\sigma_G^2\\right)  \\right]\n$$\n\nHowever, the convergence rate does not change, since the quantization noise expectation is usually at 0. \n\nNote that previous convergence result is a special case of this new result. \n\n> **W2: Assumption for theoretical claims.**\n\n**Response:** We perform experiments with ResNet-18 on CIFAR-10 to support the assumption (b) in W1 that the expectation $\\mu_N^i$ can be viewed as zero. The distribution of quantization noise is shown to concentrate around zero. \n\n> **W3: Evaluations on more complex architectures.**\n\n**Response:** We have evaluated on larger-scale ResNet50 and ResNet101 on CIFAR-10. The table below shows that our LBI-FL yields less than 1.5\\% performance loss with over 45\\% BitOPs reduction.\n\n| Model | Method | Dice (\\%) | BOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| ResNet50 | FP32 | 85.19 | 258.4G | - |\n| | UI4 | 77.90 | 4.04G | 75 |\n| | UI8 | 84.93 | 16.15G | 0 |\n| | LBI-FL | 83.52 | 8.45G | 47.68 |\n| ResNet101 | FP32 | 85.52 | 492.0G | - |\n| | UI4 | NaN | 7.69G | 75 |\n| | UI8 | 85.05 | 30.75G | 0 |\n| | LBI-FL | 83.55 | 16.31G | 46.96 |\n\nWe further evaluate our LBI-FL by training U-Net for image segmentation on DSB2018. The table below shows that, compared with UI8 training, our LBI-FL obtains about 0.6\\% loss in Dice similarity coefficient (DSC) with over 50\\% reduction of BitOPs. \n\n| Dataset | Method | Dice (\\%) | BOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| DSB2018 | FP32 | 89.55 | 19848G | - |\n| | UI4 | 87.01 | 310.1G | 75 |\n| | UI8 | 89.48 | 1240.5G | 0 |\n| | LBI-FL | 88.84 | 604.9G | 51.27 |\n\n> **W4: References Not Discussed.**\n\n**Response:** We carefully read the two papers and will definitely cite them in the final version. However, they are different from our paper in the contents, as elaborated in W1.\n\n> **Q1: Convergence results without Assumption 4.2 or with a relaxed version.**\n\n**Response:** We have provided a relaxed version of Assumption 4.2. We only assume the expectation and variance of the distribution of the gradient quantization noise on each client exist and the expectation can be viewed as zero, as elaborated in W1. The relaxed assumption does not change the convergence rate in the theorem.", "claims_and_evidence": "In this paper, the authors make several claims that may raise concerns.\n\nThe first statement, found in lines 14-17 on the left side of page 1, reads:  \n*\"Existing compression methods for FL cannot simultaneously reduce the up-link and downlink communication cost and mitigate the computation burden on clients.\"*  \nThis claim is problematic, as there is at least one paper—Meinhardt, Georg, et al. (2024), *\"Prune at the Clients, Not the Server: Accelerated Sparse Training in Federated Learning\"*—that addresses the simultaneous reduction of both communication costs and computational load through client-side pruning.\n\nAnother concerning claim appears in the contribution section:  \n*\"To our best knowledge, this is the first successful attempt to achieve low-bit training FL that evidently reduces the communication overhead and computation cost compared to full-precision and INT8 training.\"*  \nThis assertion should be carefully justified, as there is at least one paper addressing low-bit training in distributed setups, which is not referenced here. Therefore, calling it the \"first successful attempt\" seems unsupported.\n\nMishchenko, Konstantin, et al. \"IntSGD: Adaptive floatless compression of stochastic gradients.\" arXiv preprint arXiv:2102.08374 (2021).\n\n\n\nA further troubling statement is:  \n*\"We demonstrate in theory that federated learning with gradient quantization achieves an equivalent convergence rate to the standard FedAvg algorithm with sufficiently large number of communication rounds and further empirically verify the convergence rate.\"*  \nThis analysis, found in the contribution section, heavily relies on Assumption 4.2, which states that gradient quantization at each client is equivalent to introducing Gaussian noise. This assumption is quite restrictive and not realistic in practical scenarios. In contrast, the analysis of FedAvg does not rely on assumptions about the distribution, making the comparison of convergence rates less valid and the statement potentially misleading.", "methods_and_evaluation_criteria": "The proposed method appears to be well-founded, with the authors employing both theoretical analysis and experimental results to evaluate its effectiveness.", "theoretical_claims": "I have carefully reviewed the proof presented in the appendix. The analysis relies extensively on Assumption 4.2, which essentially reduces the complexity of the proof, making the analysis overly simplistic and trivial. This reliance on such a restrictive assumption undermines the robustness of the theoretical framework. Specifically, the assumption that gradient quantization is equivalent to introducing Gaussian noise at each client is unrealistic and does not reflect the practical dynamics of Federated Learning. Consequently, the current analysis fails to provide a meaningful or comprehensive theoretical understanding of the method's behavior in real-world scenarios. The overly simplistic nature of the proof, due to this assumption, limits its applicability and generalizability to more complex or realistic settings.\n\n===========================================\n\nAfter rebuttal:\n\nAuthors provided the updated analysis as requested, so I increased the score accordingly.", "experimental_designs_or_analyses": "The authors evaluate the proposed method using LeNet (LeCun et al., 1998), ResNet-18 (He et al., 2016), MobileNetV2 (Sandler et al., 2018), and ViT-S (Dosovitskiy et al., 2020) on the CIFAR-10/100 dataset. The agent selects the bit-widths for weights, activations, and gradients from INT4, INT6, and INT8 every five epochs, starting from the 10th epoch. For LeNet, the training process consists of 2000 epochs with 100 clients, where 10% of the clients are selected for updates in each epoch. For the larger networks, training is conducted over 200 epochs with 10 clients, all of whom participate in updates at every epoch. The local update epoch is set to 2, and the learning rate follows a decay of 1.\n\nI appreciate the detailed experimental evaluation; however, conducting experiments on larger models could further strengthen the study. Quantization has a particularly significant impact on large-scale models, where computational and communication efficiency are critical factors. Evaluating the proposed method on more complex architectures would provide deeper insights into its scalability and effectiveness in real-world scenarios.\n\n===========================================\n\nAfter rebuttal:\nAuthors provided additional results, which is valuable.", "relation_to_broader_scientific_literature": "The contributions presented in this paper are relevant to the broader Federated Learning literature, particularly in the context of communication compression in Federated Learning.", "essential_references_not_discussed": "As I mentioned earlier, there are several papers that have not been included:\n\nMeinhardt, Georg, et al. (2024), *\"Prune at the Clients, Not the Server: Accelerated Sparse Training in Federated Learning\"\n\nMishchenko, Konstantin, et al. \"IntSGD: Adaptive floatless compression of stochastic gradients.\" arXiv preprint arXiv:2102.08374 (2021).", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "Please review the previous sections.", "questions_for_authors": "Is it possible for you to obtain convergence results without Assumption 4.2, or with a relaxed version of it?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {"ethical_review_concerns": "N/A"}}, {"review_id": "tZIMDy79LT", "reviewer": "Reviewer_KpQQ", "summary": "The proposed method quantifies weights, activation, and gradients to lower accuracy than INT8 to significantly reduce communication and computational costs, and the proposed LBIFL can reduce communication costs by 8 times compared to full-precision FL. A large number of experiments show that compared with INT8 precision low-bit training, the proposed LBI-FL reduces the average BitOPs per client by more than 50% at a precision loss of less than 2%.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable suggestions and below are our detailed responses to the raised weaknesses and questions. \n\n> **W1: Experiments on different scenarios.**\n\n**Response:** We have made comprehensive evaluations on our LBI-FL, including image classification on CIFAR-10 using diverse architectures of ResNet-18/50/101, MobileNet-V2, and ViT-S and on Tiny-ImageNet using ResNet-18, and image segmentation on DSB2018 using U-Net. In all the evaluations, our LBI-FL achieves acceptable performance (tolerable 1.5\\% loss) with over 45\\% reduction of BitOPs, compared with UI8 training. \n\n| Model | Method | Acc (\\%) | BitOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| ResNet50 | FP32 | 85.19 | 258.4G | - |\n| | UI4 | 77.90 | 4.04G | 75 |\n| | UI8 | 84.93 | 16.15G | 0 |\n| | LBI-FL | 83.52 | 8.45G | 47.68 |\n| ResNet101 | FP32 | 85.52 | 492.0G | - |\n| | UI4 | NaN | 7.69G | 75 |\n| | UI8 | 85.05 | 30.75G | 0 |\n| | LBI-FL | 83.55 | 16.31G | 46.96 |\n\n\n> **W2: Experiments on more tasks and datasets and comparison with advanced compression methods.**\n\n**Response:** i) We train U-Net for Image segmentation on DSB2018. We adopt the image size of 96$\\times$96. The table below shows that, compared with UI8 training, we achieve acceptable performance of about 0.6\\% loss in Dice similarity coefficient (DSC) with over 50\\% reduction of BitOPs.\n\n| Dataset | Method | DICE (\\%) | BitOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| DSB2018 | FP32 | 89.55 | 19848G | - |\n| | UI4 | 87.01 | 310.1G | 75 |\n| | UI8 | 89.48 | 1240.5G | 0 |\n| | LBI-FL | 88.84 | 604.9G | 51.27 |\n\nii) We train ResNet-18 for image classification on Tiny-ImageNet. The table below shows that our LBI-FL achieves over 50\\% reduction of BitOPs with less than 0.1\\% accuracy loss\n\n| Dataset | Method | Acc (\\%) | BitOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| Tiny-ImageNet | FP32 | 35.84 | 457.14G | - |\n| | UI4 | 34.64 | 7.14G | 75 |\n|  | UI8 | 35.21 | 28.57G | 0 |\n| | LBI-FL | 35.13 | 14.05G | 50.81 |\n\niii) We further employ centralized low-bit training method AMPA [D1] in FL for comparison. AMPA uses layer-wise bit-width allocation based on sensitivity measurement during training. Our LBI-FL with RL agents obtains superior performance with evidently reduced BitOPs in training ResNet-18, MobileNet-V2, and ViT-S on CIFAR-10.\n\n[D1] Li Ding et al. AMPA: Adaptive mixed precision allocation for low-bit integer training. ICML 2024.\n\n| Model | Method | Acc (\\%) | BitOPS | RR (\\%) |\n| ---- | ---- | ---- | ---- | ---- |\n| ResNet-18 | AMPA | 84.10 | 3.49G | 51.11 |\n| | LBI-FL | 84.16 | 3.28G | 54.06 |\n| ViT-S | AMPA | 72.54 | 73.08G | 38.79 |\n| | LBI-FL | 72.55 | 60.3G | 49.51 |\n| MobileNet-V2 | AMPA | 87.89 | 9.78G | 46.19 |\n|  | LBI-FL | 89.02 | 8.83G | 51.39 |\n\n> **W3: Discussion on combining pruning and quantification.**\n\n**Response:** This paper focuses on quantization for low-bit training in FL. Our LBI-FL introduces a temporally dynamic bit-width allocation scheme for weights, activations, and gradients, which evolves along the training trajectory. It achieves higher efficiency than UI8 training with great flexibility in diverse FL scenarios.\n\n\nWe will discuss the meaningful topic of combining pruning and quantization such as [D2] in the final version. However, pruning is more difficult to deploy on hardware than quantization and relies on manually tuned hyperparameters such as pruning ratios and threshold values. [D2] only offers results of LeNet and ResNet-20 on CIFAR-10. We will explore to combine pruning with low-bit training (simultaneously quantizing weights, activations and gradients) in future.\n\n[D2] Pavana Prakash et al. IoT device friendly and communication-efficient federated learning via joint model pruning and quantization. IEEE IoT Journal 2022.\n\n> **W4: Figure 1 not referenced.**\n\n**Response:** Thank you. We will include the reference to Figure 1 in the final version.\n\n> **Q1: Can the source code be made public?**\n\n**Response:** We will release the source code upon acceptance. \n\n> **Q2: Difference with other methods like in deep learning.**\n\n**Response:** While low-bit training has been widely studied in conventional deep learning, its direct application to federated learning (FL) is challenging due to the decentralized and heterogeneous nature of FL. In particular, applying a uniform low-bit strategy across all clients can lead to training instability caused by heterogeneity in data distributions and model dynamics. To address this, we propose a aware bit width adaptation framework based on reinforcement learning. Specifically, we introduce an agent that dynamically allocates bit-widths for each client by considering local states, including the current bit-width, training phase, and quantization-induced loss.", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "Experiments are conducted on CIFAR-10 and CIFAR-100 datasets, and it is suggested to add experiments on more different types of federated learning scenarios to verify the effectiveness and scalability of the method in different environments.", "theoretical_claims": "The theory in this paper is proved to be correct, the convergence of the framework is analyzed, and the convergence rate of the framework is deduced, which is proved to be equivalent to the standard FedAvg algorithm. At the same time, the quantization error is analyzed, considering the influence of the noise introduced by gradient quantization on the model updating and convergence, and the quantization error will not have a fundamental impact on the convergence.", "experimental_designs_or_analyses": "The experimental design of the paper is basically reasonable, and the purpose of the experiment is to verify the effectiveness of the proposed method in reducing communication cost and computing cost. CIFAR-10 and CIFAR-100 data sets are selected for verification, and TOP-1 classification accuracy is adopted. The experiment mainly focuses on the image classification task, and the data set is relatively small, and the method comparison in this paper is not compared with some advanced compression methods.", "relation_to_broader_scientific_literature": "The main contributions of this paper are mainly in three areas: federated learning, model compression and reinforcement learning\nFederated learning technology is used to protect privacy, but federated learning faces the limitation of communication and computing resources. Therefore, low-bit quantization technology is applied to federated learning to compress the model and reduce the model size and computing cost. Finally, reinforcement learning is applied to optimize the allocation of bit width. Reinforcement learning provides new scenarios in hyperparameter tuning and network architecture searching.", "essential_references_not_discussed": "For work on the combination of model compression and federated learning, using a combination of model pruning and quantification, the methods proposed in this paper focus on the application of quantitative methods in federated learning, but there may be differences in the comprehensiveness and efficiency of model compression compared with these methods combining pruning and quantification, which may not be fully discussed in this paper.", "other_strengths_and_weaknesses": "In addition, Figure 1 of the article is not referenced elsewhere in the article.", "other_comments_or_suggestions": "no", "questions_for_authors": "1.Can the source code be made public？\n2.The low-bit training is well understand, is any difference with other methd, like in deep learning?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The reviewers identified the novelty of the proposed framework and its contributions to communication-efficient federated learning, and were consistent to accept this paper. It would be beneficial if the responses addressing the reviewers’ questions are added into the final version.
Decision: Accept (poster)