Equipment sending power configuration method for accelerating convergence speed of distributed learning framework

Abstract

A device sending power configuration method for accelerating the convergence speed of a distributed learning framework belongs to the field of communication and comprises the following steps: establishing the distributed learning framework; when entering each training round, each device obtains a channel gain vector to the base station, a receiving beam forming configuration scheme of the base station and a local gradient to be sent; each device sets own sending power by taking amplification of air calculation distortion as a criterion, and concurrently sends a local gradient to the base station by using the set sending power on the same time-frequency resource; the base station aggregates the local gradients of the devices based on the air computing technology to obtain a global gradient of the current training round, and uses the global gradient to update the global model. According to the method, the convergence speed of a distributed learning framework is increased by amplifying the distortion of the gradient aggregation signal based on air calculation. By reducing the sending power of each device in the distributed learning framework, the sending power and communication energy consumption of the devices can be saved while the air calculation distortion is amplified.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a device transmission power configuration method for accelerating the convergence speed of a distributed learning framework. Background Art

[0002] The distributed learning framework in the wireless network includes a base station and multiple devices, where the base station has a global model, and each device has a local data set and a copy of the global model. The process of the distributed learning framework is divided into multiple rounds. In each round, each device uses the data in the local data set and a copy of the global model to calculate the local gradient; then, each device uploads the local gradient to the base station for aggregation to generate a global gradient; then, the base station uses the aggregated global gradient to update the global model; finally, the base station sends the updated global model to each device to update the copy of the global model of each device. The above process is repeated for multiple rounds until the global model of the base station converges, that is, the performance of the global model converges to a predetermined standard, or the maximum number of rounds allowed is reached.

[0003] Multiple transmitters using over-the-air computation (AirComp) technology transmit signals concurrently on the same time-frequency resources, using the superposition characteristics of wireless channels to complete signal-level calculations, so that the receiver directly receives the calculation results of the signals sent by each transmitter. In the distributed learning framework, this technology is often used to aggregate local gradients from each device at the base station.

[0004] The gradient descent algorithm is a basic algorithm for training artificial intelligence (AI) models. In this algorithm, first, the gradient is calculated using data samples and the AI ​​model; then, the updated AI model is obtained by subtracting the product of the learning rate and the gradient from the parameters of the AI ​​model to be updated. In the distributed learning framework, this algorithm is used to update the global model at the base station.

[0005] The prior art closest to the present invention is a device transmission power configuration method based on a distortion suppression criterion (i.e., aiming to minimize the mean square error (MSE) of the AirComp aggregated gradient signal) (reference paper 1 ("Balancing Accuracy and Integrity for Reconfigurable Intelligent Surface-Aided Over-the-Air Federated Learning", author: Zheng Jingheng; Tian Hui; Ni Wanli; Ni Wei; Zhang Ping, IEEE Transactions on Wireless Communications (Volume: 21, Issue 12: December 12, 2022), Pages: 10964-10980, Publication Date: July 13, 2022", URL: https: / / ieeexplore.ieee.org / document / 9829190) and paper 2 ("Federated Learning in Multi-RIS-Aided Systems"). Systems), author: Wanli Ni; Yuanwei Liu; Zhaohui Yang; Hui Tian; Xuemin Shen, IEEE Internet of Things Journal (Volume: 9, Issue 9: June 15, 2022), Pages: 9608-9624, Publication Date: November 24, 2021, URL: https: / / ieeexplore.ieee.org / document / 9626135). In the distributed learning framework using AirComp, the local gradient aggregation based on AirComp takes distortion suppression as the criterion, and it is believed that reducing the distortion of the aggregated local gradient can ensure the convergence of the distributed learning framework. Specifically, most of the existing device transmit power configuration methods based on the distortion suppression criterion require each device to use high transmit power to offset the difference in the uplink channels of each device and suppress the receiving noise, so as to suppress the distortion of the gradient aggregation signal based on AirComp, thereby minimizing the distortion and error of the aggregated gradient signal received at the base station. By analyzing this method, it is found that in order to suppress distortion, MSE needs to be minimized. This means that the value of the normalization factor of the base station should be increased as much as possible. According to the configuration formula for the device transmit power, the increase of the base station normalization factor will lead to an increase in the device transmit power. This shows that the existing device transmit power configuration method based on the distortion suppression criterion requires the device to increase the transmit power to minimize the MSE.

[0006] Some existing research work shows that local gradients in distributed learning frameworks are naturally resistant to model training and do not need to be transmitted overly accurately. Other studies have pointed out that when using the gradient descent algorithm, applying specific artificial interference to the gradient can actually speed up the convergence of the AI ​​model training process. Based on this finding, since the distortion of the gradient aggregation signal based on AirComp is also an interference to the global gradient, it can be inferred that artificially amplifying or utilizing the distortion of the gradient aggregation signal based on AirComp can help speed up the convergence of the distributed learning framework. Therefore, a major disadvantage of the existing device transmit power configuration method based on the distortion suppression criterion is that it is too conservative, that is, it does not fully utilize the convergence acceleration effect brought about by the distortion of the gradient aggregation signal based on AirComp. At the same time, the existing device transmit power configuration method based on the distortion suppression criterion causes the problem of excessive device transmit power, which does not conform to the actual situation of insufficient device transmit power and insufficient energy budget in wireless networks, and is difficult to implement. Summary of the invention

[0007] The present invention is directed to a distributed learning framework that uses over-the-air computation (AirComp) technology to perform local gradient aggregation, and aims to provide a device transmission power configuration method that accelerates the convergence speed of the distributed learning framework, so as to solve the technical problems existing in the existing device transmission power configuration method based on the distortion suppression criterion.

[0008] The present invention accelerates the convergence speed of the distributed learning framework by amplifying the distortion of the gradient aggregation signal based on AirComp. By reducing the transmission power of each device in the distributed learning framework, the transmission power of the device can be saved while amplifying the air calculation distortion, and the communication energy consumption of the distributed learning framework can be saved.

[0009] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0010] The present invention provides a method for configuring device transmission power to accelerate the convergence speed of a distributed learning framework, comprising the following steps:

[0011] Step S1: Establish a distributed learning framework;

[0012] The distributed learning framework includes: K devices and 1 base station;

[0013] Step S2: When entering each training round, each device obtains its channel gain vector to the base station, the base station's receive beamforming configuration scheme and the local gradient to be sent;

[0014] Step S3: Each device sets its own transmit power based on the amplified air-calculated distortion as a criterion, and concurrently sends a local gradient to the base station using the set transmit power on the same time-frequency resource;

[0015] Step S4: The base station aggregates the local gradients of each device based on air computing technology to obtain the global gradient of the current training round, and uses the global gradient to update the global model.

[0016] Furthermore, the calculation formula of the local gradient is:

[0017]

[0018] in, represents the local gradient of device k in the tth training round, represents the gradient operator, Represents the nth data sample in the local data set of device k The corresponding loss function is, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, Represents the local dataset of device k in the tth training round.

[0019] Furthermore, the calculation formula of the transmission power is:

[0020]

[0021] in, represents the transmit power of device k, represents the receive beamforming configuration scheme of the base station, represents the channel gain vector from device k to the base station, represents the non-negative device power scaling factor, represents the conjugate transpose.

[0022] Furthermore, the distortion of the aerial calculation is measured by the mean square error of the global gradient; the mean square error of the aerial calculation is The calculation formula is:

[0023]

[0024] in, represents the non-negative device power scaling factor, represents the base station normalization factor, Indicates the noise intensity.

[0025] Furthermore, the criterion for amplifying the air calculation distortion is: on the premise that the ratio of the device power proportional factor to the base station normalization factor is greater than 1, the device power proportional factor is reduced and the base station normalization factor is simultaneously reduced, so that the MSE increases, thereby amplifying the air calculation distortion.

[0026] Furthermore, the calculation formula of the global gradient is:

[0027]

[0028] in, represents the global gradient of base station aggregation in the tth training round, represents the receiving noise of the base station, represents the base station normalization factor, represents the receive beamforming configuration scheme of the base station, represents the channel gain vector from device k to the base station, represents the conjugate transpose, represents the transmit power of device k, represents the local gradient of device k in the tth training epoch.

[0029] Furthermore, based on the transmission power of device k The configuration scheme of the global gradient of the base station aggregation in the tth training round Further expressed as:

[0030]

[0031] in, Represents the non-negative device power scaling factor.

[0032] Furthermore, the base station updates the global model using a gradient descent formula:

[0033]

[0034] in, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, represents the global model updated in the previous training round broadcasted by the base station in the t-1th training round, represents the learning rate, represents the global gradient of base station aggregation in the tth training round.

[0035] Furthermore, the convergence speed of the distributed learning framework is defined as the expected decrease value of the global loss function between two adjacent training rounds; the mathematical expression of the convergence speed of the distributed learning framework is:

[0036]

[0037] in, represents the global loss function of the tth training round, represents the global loss function of the t-1th training round, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, Represents the global model updated in the previous training round broadcasted by the base station in the t-1th training round.

[0038] Furthermore, the mathematical expression of the global loss function of the t-th training round is:

[0039]

[0040] in, Represents the nth data sample in the local data set of device k The corresponding loss function, D represents the number of data samples in the local dataset.

[0041] The beneficial effects of the present invention are:

[0042] 1. Compared with the existing device transmission power configuration method based on the distortion suppression criterion, the device transmission power configuration method proposed in the present invention artificially amplifies and utilizes the distortion of the gradient aggregation signal based on AirComp to accelerate the convergence speed of the distributed learning framework, reduce the transmission power of the device, and save the communication energy consumption of the device.

[0043] 2. The device transmission power configuration method proposed in the present invention actively reduces the transmission power of the device to amplify the distortion of the gradient aggregation signal based on AirComp, which can save the communication energy consumption of the device. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the distributed learning framework in wireless networks.

[0045] Figure 2 Schematic diagram of the local gradient signal input into the channel by each device in the distributed learning framework in a wireless network, where the horizontal axis is time and the vertical axis is signal amplitude.

[0046] Figure 3 Schematic diagram of the comparison between the global gradient signal output by the channel and aggregated through air calculation and the local gradient signal input by each device to the channel in a distributed learning framework in a wireless network, wherein the solid line represents the global gradient signal output by the channel and aggregated through air calculation, the dotted line represents the local gradient signal input by each device to the channel, the horizontal axis is time, and the vertical axis is signal amplitude.

[0047] Figure 4 A flow chart of a device transmission power configuration method for accelerating the convergence speed of a distributed learning framework provided by the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0049] like Figure 4 As shown, the present invention provides a device transmission power configuration method for accelerating the convergence speed of a distributed learning framework, and its specific implementation process is as follows:

[0050] Step S1: Establish a distributed learning framework;

[0051] like Figure 1 As shown in Figure 1, the distributed learning framework in the wireless network mainly includes: K devices (1,…k,…,K) and 1 base station. In the current t-th training round, each device has a local data set ,… , and the global model updated in the previous training round broadcast by the base station ; Each local data set includes data samples, used to calculate the local gradient of each device ,… .

[0052] Among them, a training round includes a local training cycle and a communication round. The calculation of the local gradient of each device is completed in the local training cycle, and the uploading of the local gradient of each device to the base station is completed in the communication round.

[0053] In the distributed learning framework, each device uploads its local gradient concurrently on the same time-frequency resources, and based on the air computing technology, the local gradients are aggregated at the base station to generate a global gradient. The air computing technology uses the superposition characteristics of the wireless channel to enable each device to transmit local gradients concurrently on the same time-frequency resources, and aggregates the local gradients of the devices at the base station to generate a global gradient.

[0054] It is understandable that due to the influence of wireless channel fading and noise, the global gradient generated by air-based aggregation will be distorted, such as Figure 2 and Figure 3 As shown, the output signal of the wireless channel is greatly distorted in amplitude relative to the input signal. In the traditional distributed learning framework that uses air computing technology to aggregate local gradients, the system design is carried out using the criterion of suppressing air computing distortion. In the present invention, the air computing distortion is deliberately amplified and utilized to act on the global gradient generated by the aggregation, thereby achieving the effect of accelerating the convergence speed of the distributed learning framework. This is the main feature that significantly distinguishes the present invention from other inventions related to distributed learning frameworks.

[0055] The convergence rate of the distributed learning framework is defined as the expected decrease in the global loss function between two adjacent training rounds. Specifically, the global loss function is defined as follows:

[0056]

[0057] in, Represents the nth data sample in the local data set of device k The corresponding loss function; accordingly, the convergence speed of the distributed learning framework can be defined as:

[0058]

[0059] in, represents the global loss function of the tth training round, represents the global loss function of the t-1th training round, represents the global model updated in the previous training round broadcasted by the base station in the tth training round; Represents the global model updated in the previous training round broadcasted by the base station in the t-1th training round.

[0060] like Figure 1 As shown, the base station uses air computing technology to aggregate local gradients to generate global gradients Afterwards, the global model is updated using the gradient descent formula. The gradient descent formula is as follows:

[0061]

[0062] in, Represents the learning rate.

[0063] Step S2: When entering each training round, each device obtains its channel gain vector to the base station, the base station's receive beamforming configuration scheme, and the local gradient to be sent.

[0064] A training round in the distributed learning framework includes a local training cycle and a communication round. Each device calculates a local gradient using a local data set within a local training cycle; then, within a communication round, each device uploads the local gradient to the base station for aggregation to generate a global gradient.

[0065] The length of the local training cycle and the communication round is related to the communication computing capability of each device and needs to be set according to the actual usage scenario. The present invention does not make specific limitations on this.

[0066] When using the local data set to calculate the local gradient, all data samples in the local data set can be used, or only part of the data samples can be used. Specifically, the local gradient of device k Defined as:

[0067]

[0068] in, represents the gradient operator, Represents the local dataset of device k in the tth training round.

[0069] The base station can inform each device of the channel gain vector to the base station and the receive beamforming configuration scheme of the base station in a variety of ways. For example, the base station can send the information to each device by broadcasting, or by polling. The present invention does not make specific limitations on this.

[0070] Step S3: Each device sets its own transmission power based on the amplified air-calculated distortion as a criterion, and concurrently sends local gradients to the base station using the set transmission power on the same time-frequency resources.

[0071] The present invention innovates the distortion suppression criterion generally followed in the model aggregation stage in the existing distributed learning framework into a distortion utilization criterion, and provides a new distributed learning framework design criterion.

[0072] Each device configures its transmission power according to the principle of amplifying the distortion of air-calculated data based on the obtained channel gain vector to the base station and the receive beamforming configuration scheme of the base station. Specifically, let represents the transmit power of device k, then the mathematical expression of the transmit power configuration scheme of device k is:

[0073]

[0074] in, represents the receive beamforming configuration scheme of the base station, represents the channel gain vector from device k to the base station, represents the non-negative device power scaling factor, represents the conjugate transpose.

[0075] The air computation distortion can be measured by the mean square error (MSE) of the global gradient. It can be understood that the larger the MSE, the larger the air computation distortion. Specifically, the symbol represents the mean square error of the aerial calculation, then The specific calculation formula is as follows:

[0076]

[0077] in, represents the base station normalization factor, Indicates the noise intensity.

[0078] In the present invention, on the one hand, the MSE varies with the ratio of the device power proportional factor to the base station normalization factor. Therefore, it can be understood that the distortion criterion for amplifying air calculation is: Under the premise of reducing the equipment power proportional factor And simultaneously reduce the base station normalization factor , which increases the MSE and amplifies the air calculation distortion. Under the premise of reducing the equipment power proportional factor The transmission power of device k can be reduced, thereby saving the device transmission power while amplifying the air computing distortion and saving the communication energy consumption of the distributed learning framework.

[0079] After obtaining the device transmit power configuration scheme, each device sets its transmit power according to the device transmit power configuration scheme, and concurrently sends a local gradient to the base station on the same preset time-frequency resources.

[0080] Step S4: The base station aggregates the local gradients of each device based on air computing technology to obtain the global gradient of the current training round, and finally uses the global gradient to update the global model.

[0081] Since the wireless channel has the superposition characteristic, the base station aggregates the local gradients uploaded by each device as the global gradient. It can be expressed as:

[0082]

[0083] in, Indicates the receiving noise of the base station.

[0084] Furthermore, based on the transmission power of device k Configuration scheme, global gradient It can be further expressed as:

[0085]

[0086] Based on the above formula, it can be understood that the ratio of the device power proportional factor to the base station normalization factor is obtained by amplifying the distortion criterion in the air. Increases, thereby increasing the amplitude of the global gradient and producing greater distortion, which can accelerate the convergence speed of the distributed learning framework.

[0087] The base station updates the global model using the global gradient generated by aggregation. Specifically, the base station can update the global model using the following gradient descent formula:

[0088]

[0089] in, Represents the learning rate.

[0090] Subsequently, the base station broadcasts the updated global model to each device to facilitate the next training round of the distributed learning framework.

[0091] The present invention innovates the distortion suppression criterion commonly followed in the model aggregation stage in the existing distributed learning framework into a distortion utilization criterion. At the same time, based on the inherent invulnerability of local gradients for model training, the present invention reduces the transmission power of each device in the distributed learning framework, artificially amplifies and utilizes the distortion of the gradient aggregation signal based on AirComp, accelerates the convergence speed of the distributed learning framework, and reduces the device transmission power and communication energy consumption.

[0092] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A device transmission power configuration method for accelerating the convergence speed of a distributed learning framework, characterized in that: The following steps are involved: Step S1: Establish a distributed learning framework; The distributed learning framework includes: K devices and 1 base station; Step S2: When entering each training round, each device obtains its channel gain vector to the base station, the base station's receive beamforming configuration scheme and the local gradient to be sent; Step S3: Each device sets its own transmit power based on the amplified air-calculated distortion as a criterion, and concurrently sends a local gradient to the base station using the set transmit power on the same time-frequency resource; Step S4: The base station aggregates the local gradients of each device based on air computing technology to obtain the global gradient of the current training round, and uses the global gradient to update the global model.

2. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1 is characterized in that: The calculation formula of the local gradient is: ， in, represents the local gradient of device k in the tth training round, represents the gradient operator, Represents the nth data sample in the local data set of device k The corresponding loss function is, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, Represents the local dataset of device k in the tth training round.

3. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1 is characterized in that: The calculation formula of the transmission power is: ， in, represents the transmit power of device k, represents the receive beamforming configuration scheme of the base station, represents the channel gain vector from device k to the base station, represents the non-negative device power scaling factor, represents the conjugate transpose.

4. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1, characterized in that: The distortion of the air calculation is measured by the mean square error of the global gradient; the mean square error of the air calculation The calculation formula is: ， in, represents the non-negative device power scaling factor, represents the base station normalization factor, Indicates the noise intensity.

5. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1, characterized in that: The criterion for amplifying the air calculation distortion is: on the premise that the ratio of the device power proportional factor to the base station normalization factor is greater than 1, reduce the device power proportional factor and simultaneously reduce the base station normalization factor, so that the MSE increases, thereby amplifying the air calculation distortion.

6. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1, characterized in that: The calculation formula of the global gradient is: ， in, represents the global gradient of base station aggregation in the tth training round, represents the receiving noise of the base station, represents the base station normalization factor, represents the receive beamforming configuration scheme of the base station, represents the channel gain vector from device k to the base station, represents the conjugate transpose, represents the transmit power of device k, represents the local gradient of device k in the tth training epoch.

7. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 6 is characterized in that: Based on the transmit power of device k The configuration scheme of the global gradient of the base station aggregation in the tth training round Further expressed as: ， in, Represents the non-negative device power scaling factor.

8. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1, characterized in that: The base station updates the global model using the gradient descent formula: ， in, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, represents the global model updated in the previous training round broadcasted by the base station in the t-1th training round, represents the learning rate, represents the global gradient of base station aggregation in the tth training round.

9. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 1, characterized in that: The convergence speed of the distributed learning framework is defined as the expected decrease value of the global loss function between two adjacent training rounds; the mathematical expression of the convergence speed of the distributed learning framework is: ， in, represents the global loss function of the tth training round, represents the global loss function of the t-1th training round, represents the global model updated in the previous training round broadcasted by the base station in the tth training round, Represents the global model updated in the previous training round broadcasted by the base station in the t-1th training round.

10. The device transmission power configuration method for accelerating the convergence speed of a distributed learning framework according to claim 9, characterized in that: The mathematical expression of the global loss function of the tth training round is: ， in, Represents the nth data sample in the local data set of device k The corresponding loss function, D represents the number of data samples in the local dataset.

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