CN116567652B - Omnidirectional super-surface-assisted air calculation energized vertical federal learning method - Google Patents
Omnidirectional super-surface-assisted air calculation energized vertical federal learning method Download PDFInfo
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Abstract
The invention relates to an omnidirectional subsurface assisted air computing energized vertical federal learning method, which is characterized in that an intelligent omnidirectional subsurface reconstruction channel is deployed at the edge of a cell so as to enhance the gain of the channel and reduce the influence caused by inter-cell interference. Meanwhile, the invention utilizes the superposition characteristic of the multiple access channels to aggregate the prediction results of the local equipment in the central server through the air computing technology, thereby effectively reducing the model aggregation speed in vertical federal learning and greatly helping to solve the problem of communication delay.
Description
Technical Field
The invention relates to a communication technology, in particular to an omnidirectional super-surface-assisted air calculation energized vertical federal learning method.
Background
Federal learning is a distributed machine learning approach aimed at enhancing data privacy and security while addressing data islanding problems and reducing reliance on data centers. Through federal learning, multiple participants can jointly train a machine learning model on the premise of protecting respective data privacy. The participants train the model using the local data and then send model parameter updates to the central server for aggregation. Finally, the central server distributes the updated global model parameters to each participant. Federal learning can be classified into horizontal federal learning, vertical federal learning, and federal transfer learning according to the difference of data characteristics and sample IDs. Horizontal federal learning is applicable to scenes with the same feature space among participants but different sample IDs. In other words, the data sets for each participant have the same characteristic columns, but the sample data is different. In horizontal federal learning, gradient or model parameter updates can be directly shared among participants, so that the performance of the overall model is improved while the data privacy is maintained. Vertical federal learning is applicable to scenarios with different feature spaces between participants but identical sample IDs. That is, the data set for each participant contains different columns of features, but the sample data is the same. Due to the differences in data characteristics, gradient or model parameter updates cannot be shared directly between participants. In this case, techniques such as secure multiparty computing (SMPC) are typically employed to ensure that model training information is shared without revealing the original data. Federal transfer learning is a method that accounts for data heterogeneity, allowing for variance in both data characteristics and sample IDs among participants. The method mainly relies on a migration learning technology, and model training is achieved by sharing knowledge between a source domain and a target domain. In federal transfer learning, participants can utilize the data of other participants to boost their own model performance without directly accessing the original data of the other participants.
The present invention will focus mainly on vertical federal learning, as it provides an effective solution for scenes with different feature spaces but identical sample IDs. Vertical federal learning has unique advantages over horizontal federal learning in the field of internet of things, especially when processing cross-domain or cross-organization data. In the internet of things device, characteristic space differences of data are common, and data generated by the device may relate to different sensor types, data sources and application scenes. The feature space of such data may relate to a number of fields such as temperature, humidity, motion, sound, etc. Thus, in such an environment, vertical federal learning helps to exploit the potential of various data features, enabling more accurate model predictions. In addition, internet of things devices are typically deployed in different organizations and geographic areas. In this case, vertical federal learning can help achieve collaborative learning across organizations without sharing the original data. This can avoid privacy disclosure and legal problems that may be caused by data sharing, while achieving better data utilization.
However, deployment of vertical federal learning in real life still presents many challenges, where communication latency is one of the major performance bottlenecks. In the vertical federal learning process, participants need to exchange encrypted intermediate computation results for model training. However, wireless network bandwidth in the present age is becoming increasingly scarce, limiting the speed of data interaction between the various participants, increasing communication delays, especially when the number of participants is high or network conditions are poor. In contrast, in horizontal federal learning, participants need only send gradient or model parameter updates with less communication overhead. Meanwhile, as vertical federal learning requires collaborative training on data of different feature spaces, each participant cannot directly share gradient or model parameter update. Thus, privacy protection techniques such as secure multiparty computing are often required to ensure data security. These techniques, while providing privacy protection, tend to increase communication overhead, resulting in communication delays. In contrast, in horizontal federal learning, participants may directly share gradient or model parameter updates, thereby reducing communication latency. Furthermore, in vertical federal learning, the number of participants is typically low, which means that technical solutions such as device selection will no longer be applicable in vertical federal learning.
However, existing work is still focused mainly on the communication delay problem in horizontal federal learning. In addition, a vertical federal learning system is deployed in a plurality of cells in a real scene, so that the problem of inter-cell interference exists, and the aggregation speed of a model is seriously influenced. To this end, the inventors decided to employ an intelligent omnidirectional subsurface-assisted air-computing-enabled multi-cell vertical federal learning system. The system utilizes the waveform superposition characteristic of the wireless multiple access channel, effectively improves the communication efficiency, uses the intelligent omnidirectional super-surface technology to reconstruct the wireless environment, enhances the channel gain and further reduces the negative influence caused by inter-cell interference.
Disclosure of Invention
Aiming at the problem of communication delay in a vertical federation learning system in a multi-cell wireless communication scene, an omnidirectional super-surface assisted air computing energized vertical federation learning method is provided.
The technical scheme of the invention is as follows: an omnidirectional super-surface assisted air computing energized vertical federal learning method specifically comprises the following steps:
1) Establishing an omnidirectional super-surface auxiliary multi-cell vertical federal learning system: each cell m is provided with a base station, wherein the base stationAnd K in the cell in which the base station is located m A single antenna local edge device jointly trains a machine learning model, and an intelligent omnidirectional super-surface with Q electromagnetic units is placed at the edge of a cell to strengthen signals, and is used for receiving signalsAnd->Representing wireless communication channels from base station m to local edge device k, respectively, from the intelligent omni-directional subsurface to local edge device k, and from the intelligent omni-directional subsurface to local edge device k, the composite channel from local edge device k to base station m may be represented as
Wherein the method comprises the steps ofRepresenting the transmission space of the base station on an omnidirectional subsurface/>Representing the reflection space of the base station on the omnidirectional super surface, theta t And theta (theta) r Respectively an omnidirectional super-surface coefficient matrix in an uplink and a downlink, wherein the superscript H represents the conjugate transpose of the matrix;
2) Initializing: each local edge device k first has model parameters local to itCarrying out random initialization;
3) Local prediction: the local edge equipment k in each cell m calculates the local predicted value of all samples according to the local data set and the current model parameters;
4) Aerial calculation: the local edge equipment sends the local prediction result to the corresponding base station through an air computing technology, and the base station in each cell receives the local prediction result sent by the local edge equipment at the same time, and decodes the local prediction result to obtain an estimated value after aggregation processing;
5) Variable calculation: each base station calculates auxiliary variables according to the estimated valuesAnd transmitting the resulting broadcast to local edge devices within the corresponding cell;
6) And (5) local updating: the local edge device k in each cell m receives and decodes itEstimate of (2)According to the local data set, a gradient descent method is adopted to complete local model iteration, and new model parameters are obtainedSubsequently repeating steps 3) to 6) to start the next iterationTraining.
Further, the machine learning model training method in the omnidirectional subsurface-assisted multi-cell vertical federal learning system in step 1) comprises the following steps:
local edge deviceIn association with base station m, it is assumed that there is one vertically partitioned data set in each cell, where different local edge devices have different dimensional characteristics of the same sample, and cell m contains L m The training set of individual samples is expressed asWherein->Part of the features of sample i representing the local edge device k in cell m, while +.>Then representing the corresponding tag, the base station in each cell m has all tag values +.>While the local edge device k has only the right to access its own local feature set +.>The eigenvector of sample i can be expressed as +.>The goal of vertical federal learning for each cell m is to minimize the following loss function:
wherein w is m Is the local model parameter w of the local edge device k k F (·) is the sampleThe loss function, σ (·) is a continuously differentiable predictive function.
Further, the step 4) is an air calculation concrete method:
by usingRepresenting the objective function that the aerial computation needs to estimate at time slot i, g will be in order to simplify the representation on the symbol m (i) Expressed as g m Will->Denoted as->Assuming that the base stations in each cell are receiving the prediction of the local edge device at the same time, the signal received at base station m can be expressed as
Wherein the method comprises the steps ofIs the transmit scalar at device k, +.>Then it is the noise at base station m, the upper transmit power bound of local device k is P ul The modulated signal received at base station m may be expressed as
Wherein eta m Is a normalization factor that is used to normalize the data,is the beam forming vector of the receiving end at the position of the base station m, and the superscript H represents the conjugate transpose of the matrix;
to solve the phase distortion problem, set
The estimated value of the objective function at base station m can be expressed as +.>Representing the real part;
setting variableObtaining a base station receiving end beam forming vector and an intelligent omnidirectional super-surface phase shift coefficient matrix in an uplink through iteratively solving the following convex optimization problem;
wherein ζ ul Error gap, lambda, representing uplink m Is a given division coefficient of the number of division,representative is a l，j A value at iteration of the t-th round; then sequentially solving a receiving end beam forming vector r at a base station m m Emission scalar b at device k k And values of the uplink phase shift coefficient matrix.
Further, the specific method for local update in the step 6) is as follows:
the signal received by the local edge device k is represented as
Wherein t is m Representing the transmit end beamforming vector at base station m,expressed belowDevice k in the uplink (σ) dl ) 2 Additive white gaussian noise, which is variance; the upper limit of the transmission power at the cell m base station is set to P dl While the receiver scalar at device k in cell m is set to +.>Device k is->Is estimated as (1)
Obtaining a base station transmitting end beam forming vector and an intelligent omnidirectional super-surface phase shift coefficient matrix in a downlink through iterative solution of the following convex optimization problem;
wherein the method comprises the steps ofRepresentative is c m，k The value at the iteration of the t-th round is then sequentially solved to obtain the beamforming vector t of the transmitting end at the position of the base station m m Receiving-side scalar r at device k k And values of a downlink phase shift coefficient matrix; when the local edge device k in each cell receives the estimated value of the data transmitted from the corresponding base station +.>After that, it will be combined with its local dataset +.>To calculate the local gradient of the current number of rounds:
according to the learning rate mu at the current number of rounds t (t) Each local device k will complete local model parameter iterations
The invention has the beneficial effects that: according to the omnidirectional super-surface assisted air computing energized vertical federal learning method, intelligent omnidirectional super-surface reconstruction channels are deployed at the edges of cells, so that the channel gain is enhanced, and the influence caused by inter-cell interference is reduced. Meanwhile, the invention utilizes the superposition characteristic of the multiple access channels to aggregate the prediction results of the local equipment in the central server through the air computing technology, thereby effectively reducing the model aggregation speed in vertical federal learning and greatly helping to solve the problem of communication delay.
Drawings
FIG. 1 is a schematic diagram of an omnidirectional subsurface-assisted airborne computing-enabled vertical federal learning system architecture according to an embodiment of the present invention;
FIG. 2 is a flowchart of an omnidirectional subsurface-assisted air computing-enabled vertical federal learning method provided by an embodiment of the present invention;
FIG. 3 is a diagram of an overhead computing enabled vertical Federal learning system architecture provided in an embodiment of the present invention;
FIG. 4 is a diagram of the error conditions of the method according to the present invention during uplink and downlink signal transmission;
fig. 5 is a diagram showing learning performance of the method according to the present invention in MNIST data set.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
In the present invention, consider an omni-directional subsurface-assisted multi-cell vertical federal learning system, as shown in FIG. 1, with each cell m allocatedA base station, wherein the base stationAnd K in the cell in which the base station is located m A single antenna local edge device jointly trains a machine learning model.
In particular, the deviceBase station m is associated. We then place an intelligent omnidirectional subsurface containing Q electromagnetic units at the cell edge to strengthen the signal. We assume that there is one vertically partitioned data set in each cell, where different devices have different dimensions of features of the same sample. Cell m contains L m The training set of individual samples is denoted +.>Wherein->Part of the features of sample i representing device k in cell m, and +.>Then the corresponding label is represented. The base stations in each cell m have all tag values +.>Whereas device k has only permission to access its own local feature setThe eigenvector of sample i can be expressed as +.>
The goal of vertical federal learning for each cell m is to minimize the following loss function:
wherein w is m Is the local model parameter w of the local edge device k k Is of the complex vector of (2)f (·) is the sample loss function and σ (·) is the continuously differentiable predictive function.
By usingAnd->Wireless communication channels from the base station m to the local edge device k, from the intelligent omni-directional subsurface to the local edge device k, and from the intelligent omni-directional subsurface to the local edge device k are represented, respectively. The composite channel from the local edge device k to the base station m can then be expressed as
Wherein the method comprises the steps ofRepresenting the transmission space of the base station in an omni-directional super-surface, while +.>Representing the reflective space of the base station in an omni-directional subsurface. It should be noted that the intelligent omnidirectional subsurface coefficient matrices in the uplink and downlink are mutually independent, and the coefficient matrices of the uplink and the downlink can be designed respectively. To simplify the representation on mathematical symbols, we will have an omnidirectional super-surface coefficient matrix Θ in the uplink as well as in the downlink t And theta (theta) r Respectively denoted as theta ul And theta (theta) dl 。
As shown in fig. 2, the flow chart of the omnidirectional super-surface assisted air computing energized vertical federal learning method comprises the following experimental steps:
step (a)S101, initializing: each local edge device k first has model parameters local to itRandom initialization is performed.
Step S102, local prediction: in each time slot i e {1,2, …, L m Local edge device k in cell m will predict the local result of the i-th sampleTo the base station m. Assume local edge device k local prediction for all samples +.>Normalized by zero mean and unit variance, i.e.
Step S103, aerial calculation: as shown in fig. 3, the local edge device k sends the local prediction result to the corresponding base station through the air computing technology. The base station m in each cell receives the aggregate value of the local prediction result and decodes the aggregate value to obtain an estimated value
By usingRepresenting the objective function that the aerial computation needs to estimate at time slot i. To simplify the symbology, g will be m (i) Expressed as g m Will->Denoted as->Furthermore, it is also assumed that the base stations in each cell are receiving predictions of the local edge devices at the same time, becauseThe signal received at this base station m can be expressed as
Wherein the method comprises the steps ofIs the transmit scalar at device k, +.>Then it is the noise at base station m. The upper bound of the transmission power of the local device k is P ul . The modulated signal received at base station m may be expressed as
Wherein eta m Is a normalization factorIs the receiving end beam forming vector at the base station m, and the superscript H represents the conjugate transpose of the matrix. To solve the phase distortion problem, set
The estimated value of the objective function at base station m can be expressed as +.>Representing the real part.
Setting variableAnd obtaining a beamforming vector of a base station receiving end in an uplink and a phase shift coefficient matrix of the intelligent omnidirectional super-surface by iteratively solving the following convex optimization problem.
Wherein ζ ul Error gap, lambda, representing uplink m Is a given division coefficient of the number of division,representative is a l，j Values at iteration t. Then the beamforming vector r of the receiving end at the position of the base station m can be sequentially solved m Emission scalar b at device k k And an uplink phase shift coefficient matrix Θ ul Is a value of (2).
Step S104, variable calculation: when the estimated value is obtainedThe base station m will then calculate the auxiliary variable based on this valueAnd broadcast the result to the corresponding edge device +.>To simplify the representation of the mathematical symbol +.>Denoted as G m . Suppose that signal G transmitted by a base station m Again normalized with zero mean and standard deviation.
Step S105, local updating: the signal received by the local edge device k can be expressed as
Wherein t is m Representing the transmit end beamforming vector at base station m,indicating downlink in-deviceIn the preparation k, the sum of (sigma) dl ) 2 Is additive gaussian white noise of variance. The upper limit of the transmission power at the cell m base station is set to P dl While the receiver scalar at device k in cell m is set to +.>For G at device k m Is estimated as (1)
And obtaining a beamforming vector of a base station transmitting end in a downlink and a phase shift coefficient matrix of the intelligent omnidirectional super-surface by iteratively solving the following convex optimization problem.
Wherein the method comprises the steps ofRepresentative is c m，k Values at iteration t. Then the beamforming vector t of the transmitting end at the position of the base station m can be sequentially solved m Receiving-side scalar r at device k k And a downlink phase shift coefficient matrix Θ dl Is a value of (2).
When the local edge device k in each cell receives the estimated primary of the data transmitted from the corresponding base stationAfter that, it will be combined with its local dataset +.>To calculate the local gradient of the current number of wheels
According to the learning rate mu at the current number of rounds t (t) Each local deviceBackup k will complete local model parameter iterations
Fig. 4 shows the error situation of the method in uplink and downlink signal transmission, and shows the influence of the number of antennas, the number of devices and the number of electromagnetic units of the intelligent omnidirectional super-surface in each cell on signal transmission by taking the mean square error between the actual signal value of the transmitting end and the signal estimated value of the receiving end as a performance index. As can be seen from fig. 4, the performance gain of the system becomes larger as the number of electromagnetic units of the intelligent omnidirectional subsurface increases.
Fig. 5 shows learning performance of the method according to the present invention in MNIST data set, and compares with noise-free rational condition, without using intelligent omni-directional super-surface and random phase shift scheme. Wherein a smaller loss value or a higher test set accuracy represents a better model performance. As can be seen from fig. 5, the omnidirectional subsurface auxiliary scheme provided by the invention can obtain a loss function and test accuracy close to the noiseless rational condition, and realizes rapid model aggregation through air calculation, thereby effectively reducing communication delay.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (1)
1. An omnidirectional super-surface assisted air computing energized vertical federal learning method is characterized by comprising the following steps of:
1) Establishing an omnidirectional super-surface auxiliary multi-cell vertical federal learning system: each cell m is provided with a base station, whereinBase stationAnd K in the cell in which the base station is located m A single antenna local edge device jointly trains a machine learning model, and an intelligent omnidirectional super-surface with Q electromagnetic units is placed at the edge of a cell to strengthen signals, and is used for receiving signalsAnd->Representing wireless communication channels from base station m to local edge device k, from the intelligent omnidirectional subsurface to local edge device k, and from the intelligent omnidirectional subsurface to base station m, respectively, the composite channel from local edge device k to base station m may be represented as->
Wherein the method comprises the steps ofRepresenting the transmission space of the base station in an omni-directional super-surface, while +.>Representing the reflection space of the base station on the omnidirectional super surface, theta t And theta (theta) r Respectively an omnidirectional super-surface coefficient matrix in an uplink and a downlink, wherein the superscript H represents the conjugate transpose of the matrix;
2) Initializing: each local edge device k first has model parameters local to itCarrying out random initialization;
3) Local prediction: the local edge equipment k in each cell m calculates the local predicted value of all samples according to the local data set and the current model parameters;
4) Aerial calculation: the local edge equipment sends the local prediction result to the corresponding base station through an air computing technology, and the base station in each cell receives the local prediction result sent by the local edge equipment at the same time, and decodes the local prediction result to obtain an estimated value after aggregation processing;
5) Variable calculation: each base station calculates auxiliary variables according to the estimated valuesAnd transmitting the resulting broadcast to local edge devices within the corresponding cell;
auxiliary variableTo simplify the representation of mathematical symbols, willDenoted as G m ；
6) And (5) local updating: the local edge device k in each cell m receives and decodes itEstimate of +.>According to the local data set, a gradient descent method is adopted to complete local model iteration, and new model parameters are obtained>Repeating the steps 3) to 6) to start the next round of iterative training;
the machine learning model training method in the omnidirectional super-surface auxiliary multi-cell vertical federal learning system in the step 1) comprises the following steps:
local edge deviceIn association with base station m, it is assumed that there is one vertically partitioned data set in each cell, where different local edge devices have different dimensional characteristics of the same sample, and cell m contains L m The training set of individual samples is expressed asWherein->Part of the features of sample i representing the local edge device k in cell m, while +.>Then representing the corresponding tag, the base station in each cell m has all tag values +.>While the local edge device k has only the right to access its own local feature set +.>The eigenvector of sample i can be expressed as +.>The goal of vertical federal learning for each cell m is to minimize the following loss function:
wherein w is m Is the local model parameter w of the local edge device k k F (·) is the sample loss function and σ (·) is the continuously differentiable predictive function;
the specific method for calculating in the air in the step 4) comprises the following steps:
by usingRepresenting the objective function that the aerial computation needs to estimate at time slot i, g will be in order to simplify the representation on the symbol m (i) Expressed as g m Will->Denoted as->Assuming that the base stations in each cell are receiving the prediction of the local edge device at the same time, the signal received at base station m can be expressed as
Wherein the method comprises the steps ofIs the transmit scalar at device k, +.>Then it is the noise at base station m, the upper transmit power bound of local device k is P ul The modulated signal received at base station m may be expressed as
Wherein eta m Is a normalization factor that is used to normalize the data,is the beam forming vector of the receiving end at the position of the base station m, and the superscript H represents the conjugate transpose of the matrix;
to solve the phase distortion problem, set
The estimated value of the objective function at base station m can be expressed as +.> Representing the real part;
setting variableObtaining a base station receiving end beam forming vector and an intelligent omnidirectional super-surface phase shift coefficient matrix in an uplink through iteratively solving the following convex optimization problem;
ζ ul ≥0.
wherein ζ ul Error gap, lambda, representing uplink m Is a given division coefficient of the number of division,representative is a l，j A value at iteration of the t-th round; then sequentially solving a receiving end beam forming vector r at a base station m m Emission scalar b at device k k And values of an uplink phase shift coefficient matrix;
the specific method for the local updating in the step 6) is as follows:
the signal received by the local edge device k is represented as
Wherein t is m Representing the transmit end beamforming vector at base station m,representing the number of the downlink devices k (sigma) dl ) 2 Additive white gaussian noise, which is variance; the upper limit of the transmission power at the cell m base station is set to P dl While the receiver scalar at device k in cell m is set to +.>Device k is->Is estimated as (1)
Obtaining a base station transmitting end beam forming vector and an intelligent omnidirectional super-surface phase shift coefficient matrix in a downlink through iterative solution of the following convex optimization problem;
||t m || 2 ≤p d1
ζ ul ≥0.
wherein the method comprises the steps ofRepresentative is c m，k The value at the iteration of the t-th round is then sequentially solved to obtain the beamforming vector t of the transmitting end at the position of the base station m m Receiving-side scalar r at device k k And values of a downlink phase shift coefficient matrix; when the local edge device k in each cell receives the estimated value of the data transmitted from the corresponding base station +.>After that, it will be combined with its local dataset +.>To calculate the local gradient of the current number of rounds:
according to the learning rate mu at the current number of rounds t (t) Each local device k will complete local model parameter iterations
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