CN116471612A - A Method for Jointly Optimizing Quantization Level and Client Selection in Federated Learning Networks - Google Patents
A Method for Jointly Optimizing Quantization Level and Client Selection in Federated Learning Networks Download PDFInfo
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Abstract
The invention provides a method for jointly optimizing quantization level and client selection in an energy collection type federal learning network. Firstly, constructing a federal learning network model carrying an energy acquisition module; secondly, equivalently replacing the federal learning network training loss as the expected distance between the current weight model and the optimal weight model; thirdly, quantizing the differential weight by adopting a generalized quantization method, and exploring the influence of the differential weight on the quantization optimal rate; then, under the constraint of minimizing energy causality, optimizing the quantization level and the client selection, and constructing a non-convex mixed integer nonlinear optimization problem; finally, the MINLP problem is constructed as a convex optimization problem, which can be solved based on MINLP and the like solvers.
Description
Technical Field
The invention relates to the field of wireless communication, in particular to a design of a wireless federal learning system with an energy acquisition module.
Background
The federal learning network is a research hotspot in the current wireless communication field due to the characteristics of low privacy risk and low transmission cost and the combination of energy acquisition technology. The rapid increase of computing power of the processor and the explosive increase of mobile data mean that the client and the server need to have better information processing capability; the limited nature of radio resources means that the resource allocation capacity needs to be improved.
Scheduling schemes are an important research direction in federal learning. In the training link. And bandwidth and energy resources are reasonably distributed among the clients, so that communication rounds are reduced, and communication quality is improved. Quantization techniques can greatly reduce the cost of wireless resources. Compared with the scheme without quantization, the same convergence speed can be maintained to a large extent as long as the design quantization is proper. If the model weights themselves are passed, the quantization levels should increase at a logarithmic rate. However, if the weight difference is transferred instead, the quantization level may remain unchanged.
And introducing an energy acquisition module into the federal learning network to enable the client device to release the constraint of the wired power supply. The introduction of the energy harvesting module changes the resource allocation mechanism so that the parameters of each round in the system are related to the energy state and the energy arrival characteristics. The change of energy state has an important impact on the client scheduling and quantization level. In the present invention we allow the choice of the level of quantization for each round of federal learning independently from the current energy reserve and reveal the effect of each round of quantization on convergence speed.
Disclosure of Invention
The invention aims to solve the problem of how to provide high energy consumption for model uploading and local computing in a wireless network deploying federal learning. The invention configures an energy acquisition module for the client, uses the obtained energy to schedule the client to perform local calculation to obtain a weight vector, and adopts a generalized quantization method to quantize and upload the weight vector. In consideration of the energy limitation, a federal learning wireless network system with an energy acquisition module is designed, and a method for jointly optimizing the quantization level and the client selection under the system is provided.
The technical scheme adopted by the invention is as follows:
a method for jointly optimizing quantization level and client selection in an energy collection type federal learning network comprises the following steps:
1) Constructing a federal learning network model carrying an energy acquisition module;
2) Equivalently replacing the federal learning network training loss problem with the expected distance problem of the current and optimal weight models;
3) Considering the influence of the weight vector on the quantization level, carrying out weight difference processing on the local weight vector, quantizing the difference weight by adopting a generalized quantization method, and exploring the influence of the weight difference on the quantization optimal rate;
4) For the t+1st round of updating model, K clients are selected for training, and based on a quantization algorithm, the updated local weight vector is differentially quantized to obtain a new round of global weight vector;
5) Under the constraint of minimizing energy causality, optimizing the quantization level and the client selection, and constructing a non-convex mixed integer nonlinear optimization problem;
6) Finally, it is converted into a convex optimization problem, which can be solved based on an MINLP solver.
Furthermore, on the basis of the technical scheme, each step can be further realized in the following specific mode.
The method for constructing the federal learning network model carrying the energy acquisition module in the step 1 is as follows:
wherein F (ω) represents a global loss function in federal learning, M represents the number of clients, F m (ω) represents the loss function of client m.
Further, in the step 2, the method for equivalently replacing the federal learning network training loss problem with the expected distance problem of the current and optimal weight models is as follows:
wherein F (omega) T ) Represented asLoss after T-round global training, F * Representing the optimal loss, ω, under global weight T Representing global weights, ω, after T-rounds * Representing the optimal global weight.
Further, step 3 quantizes the differential weights by using a generalized quantization method, and explores the influence of the differential weights on the quantization level and the influence of the quantization level on the convergence speed as follows:
the method satisfies the unbiased, quantization error is bounded by a function of the number of bits B:
wherein Q (ω) represents a quantization method,the function representing the number of quantization bits is a decreasing convex function.
3.b) based on the loss function L (ω, ζ) L-smooth, μ -strongly convex, client random gradient unbiased and bounded, can be obtained:
wherein,,η t+1 represents the t+1st round learning rate, +.> E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Representing client random gradient varianceAnd f represents the degree of isomerism of the dataset.
3.c) for the t-th round we set the learning rate to beThe boundaries with quantized federal learning satisfy:
wherein the method comprises the steps of E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Representing the upper bound of the client stochastic gradient variance, Γ represents the degree of heterogeneity of the data set.
If the weights are differentially quantized, federal learning can be overlaid onAnd the quantization levels of the different rounds can be arbitrarily chosen as long as the assumption in 3.b) is satisfied.
Further, the method of updating the weight vector in step 4 is as follows:
initializing a selection client with I m,t Representing the participation degree of clients, I m,t =1 means that the client M e {1, …, M } is selected for training on round t. Since only K clients are selected in each round, we must have:
in addition, to ensure the choice is unbiased, the number of times each client participates in training is set to be the same, namely:
and b) broadcasting the central parameter server to the clients selected in the round, and carrying out local updating on the clients.
C) after E local iterations, the local client has a new weight vectorUsing the same quantization level for all clients, the server aggregates the received local weight differences to generate a new weight vector:
wherein omega t The weight vector representing the t-th round,a weight vector representing the kth client in the t+1st round of training, S t+1 The set of clients selected in round t+1, Q (·) represents quantization.
Further, step 5 reconstructs MINLP problem:
wherein,, e represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Represents the upper bound of the random gradient variance of the client, Γ represents the degree of isomerism of the data set, η t The learning rate of the t-th round is shown.
Due toAnd->Is unchanged, and thus can convert the problem into a non-convex MINLP problem, namely:
s.t.
wherein I is m,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t The number of bits representing each weight that client m attempts to use in round t, y represents the upload time, W represents the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
Further, step 6 converts the non-convex MINLP problem into a convex optimization problem, and by solving the convex optimization problem, the solution method for solving the joint optimization quantization level and the client scheduling is:
s.t.
wherein I is m,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t Bit number representing each weight that client m tries to use in the t-th round, B max Is the upper limit of the highest quantization level, gamma denotes the upload time, W denotes the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
The invention has the beneficial effects that: the method for jointly optimizing the quantization level and the client scheduling in the energy collection type federal learning network can optimize the selected clients, the quantization level and the energy consumed by each selected client in each round. The problem that equipment in the traditional network is limited by a limited power supply is solved, and in addition, the accuracy in the data uploading process is improved by the optimization method provided for the network.
Drawings
FIG. 1 is a comparison of training loss of the proposed algorithm with the polling algorithm, myopia algorithm under a non-independent co-distributed MINIST dataset;
FIG. 2 is a comparison of the test accuracy of the proposed algorithm with the polling algorithm, myopia algorithm under a non-independent co-distributed MINIST dataset;
FIG. 3 is a comparison of training loss of the proposed algorithm with the polling algorithm, myopia algorithm under a non-independent co-distributed CIFAR-10 dataset;
FIG. 4 is a comparison of the test accuracy of the proposed algorithm with the polling algorithm, myopia algorithm under a non-independent co-distributed CIFAR-10 dataset.
Detailed Description
The invention provides a method for selecting a jointly optimized quantization level and a client in a federal learning network, which comprises the following steps:
1) The method for constructing the federal learning network model with the energy acquisition module comprises the following steps:
wherein F (ω) represents a global loss function in federal learning, M represents the number of clients, F m (ω) represents the loss function of client m.
2) The method for equivalently converting the federal learning network training loss problem into the expected distance problem of the current and optimal weight models is as follows:
wherein F (omega) T ) Expressed as loss after T-round global training, F * Representing the optimal loss, ω, under global weight T Representing global weights, ω, after T-rounds * Representing the optimal global weight.
3) Considering the influence of the weight vector on the quantization level, carrying out weight difference processing on the local weight vector, quantizing the difference weight by adopting a generalized quantization method, and exploring the influence of the weight difference on the quantization optimal rate;
the method satisfies the unbiased, quantization error is bounded by a function of the number of bits B:
wherein Q (ω) represents a quantization method,the function representing the number of quantization bits is a decreasing convex function.
3.b) based on the loss function L (omega, xi) L-smooth, mu-strong convex, client random gradient unbiased and bounded, can be obtained
Wherein,,η t+1 represents the t+1st round learning rate, +.> E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Representing the upper bound of the client stochastic gradient variance, Γ represents the degree of heterogeneity of the data set.
3.c) for the t-th round we set the learning rate to beThe boundaries with quantized federal learning satisfy:
wherein the method comprises the steps of E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Representing the upper bound of the random gradient variance of the client, Γ represents the heterogeneous range of the data setDegree.
If the weights are differentially quantized, federal learning can be overlaid onAnd the quantization levels of the different rounds can be arbitrarily chosen as long as the assumption in 3.b) is satisfied.
4) For the t+1st round of updating model, K clients are selected for training, and based on a quantization algorithm, the updated local weight vector is differentially quantized to obtain a new round of global weight vector;
initializing a selection client with I m,t Representing the participation degree of clients, I m,t =1 means that the client M e {1, …, M } is selected for training on round t. Since only K clients are selected in each round, we must have:
in addition, to ensure the choice is unbiased, the number of times each client participates in training is set to be the same, namely:
and b) broadcasting the central parameter server to the clients selected in the round, and carrying out local updating on the clients.
C) after E local iterations, the local client has a new weight vectorUsing the same quantization level for all clients, the server aggregates the received local weight differences to generate a new weight vector:
wherein omega t The weight vector representing the t-th round,a weight vector representing the kth client in the t+1st round of training, S t+1 The set of clients selected in round t+1, Q (·) represents quantization.
5) Under the constraint of minimizing energy causality, optimizing quantization level and client selection, and constructing a non-convex mixed integer nonlinear optimization problem:
wherein the method comprises the steps of E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Represents the upper bound of the random gradient variance of the client, Γ represents the degree of isomerism of the data set, η t The learning rate of the t-th round is shown.
Due toAnd->Is unchanged, and thus can convert the problem into a non-convex MINLP problem, namely:
s.t.
wherein I is m,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t The number of bits representing each weight that client m attempts to use in round t, y represents the upload time, W represents the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
6) Finally, the problem is converted into a convex optimization problem, and can be solved based on a solver such as MINLP. The non-convex MINLP problem is converted into a convex optimization problem, and the solution method for solving the joint optimization quantization level and the client scheduling is found by solving the convex optimization problem:
s.t.
wherein I is ,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t Bit number representing each weight that client m tries to use in the t-th round, B max Is the upper limit of the highest quantization level, gamma denotes the upload time, W denotes the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
The patented process of fig. 1 to 4 refers to the process employed in the present invention.
Considering the heterogeneity of data in practical situations, the algorithm uses data which are not independently and uniformly distributed in the MINIST data set. Fig. 1 is a comparison of training loss of the algorithm proposed by the present invention with the polling algorithm and the myopia algorithm under the non-independent and co-distributed MINIST data set, and fig. 2 is a comparison of testing accuracy of the algorithm proposed by the present invention with the polling algorithm and the myopia algorithm under the non-independent and co-distributed MINIST data set. Due to the high heterogeneity of data distribution, the whole training process is slightly unstable and exhibits jagged fluctuations. As can be seen from fig. 1 and 2, the present invention has lower training loss and higher test accuracy compared to the polling algorithm. The invention sets the energy collection module for the client, so that the client has enough energy in the quantization link. Compared with the algorithm, the myopia algorithm has lower performance than the algorithm provided by the invention. The algorithm optimizes the energy utilization to the greatest extent on the basis of ensuring the scheduling fairness, so that the system can adopt a higher quantization level, thereby reducing the training loss and improving the testing precision.
In addition, the algorithm also adopts dependent and equidistributed data under the CIFAR-10 data set. Fig. 3 is a comparison of training loss of the algorithm proposed by the present invention and the polling algorithm and the myopia algorithm under the independent and equidistributed CIFAR-10 data set, and fig. 4 is a comparison of test accuracy of the algorithm proposed by the present invention and the polling algorithm and the myopia algorithm under the independent and equidistributed CIFAR-10 data set. In terms of quantization level, the polling algorithm has lower performance than the polling algorithm due to lower quantization level; in terms of client scheduling, the myopia algorithm performance becomes worst due to the large training bias caused by unfair client selection. Compared with a polling algorithm and a myopia algorithm, the algorithm provided by the patent has better performance.
Claims (11)
1. A method for jointly optimizing quantization levels and client selection in an energy harvesting type federal learning network, comprising the steps of:
1) Constructing a federal learning network model carrying an energy acquisition module;
2) Equivalently replacing the federal learning network training loss problem with the expected distance problem of the current and optimal weight models;
3) Performing weight differential processing on the local weight vector, quantifying differential weight by adopting a generalized quantification method, and exploring the influence of the differential weight on the quantification optimal rate;
4) For the t+1st round of updating model, K clients are selected for training, and based on a quantization algorithm, the updated local weight vector is differentially quantized to obtain a new round of global weight vector;
5) Under the constraint of minimizing energy causality, optimizing the quantization level and the client selection, and constructing a non-convex mixed integer nonlinear optimization problem;
6) Finally, it is converted into a convex optimization problem, which can be solved based on an MINLP solver.
2. The method for selecting a client and a jointly optimized quantization level in an energy harvesting type federal learning network according to claim 1, wherein in step 1, a federal learning network model is constructed:
where F (ω) represents the global loss function in federal learning, M represents the number of clients, F m (ω) represents the loss function of client m.
3. The method for selecting a jointly optimized quantization level and client in an energy harvesting type federal learning network according to claim 1, wherein in step 2, the federal learning network training loss problem is equivalent to the expected distance problem of the current and optimal weight models by:
wherein F (omega) T ) Expressed as loss after T-round global training, F * Representing the optimal loss, ω, under global weight T Representing global weights, ω, after T-rounds * Representing the optimal global weight.
4. The method for selecting a client and a jointly optimized quantization level in an energy harvesting type federal learning network according to claim 1, wherein in step 3, a generalized quantization method is adopted to quantize differential weights, the method satisfies unbiasedness, and quantization errors are defined by a function of the number of bits B:
wherein Q (ω) represents a quantization method,the function representing the number of quantization bits is a decreasing convex function.
5. The method for selecting a client and a jointly optimized quantization level in an energy harvesting federal learning network according to claim 4, wherein in step 3, based on a loss function L (ω, ζ) L-smooth, μ -strongly convex, a client random gradient is unbiased and bounded, it is possible to obtain:
wherein,,represents the t+1st round learning rate, +.> E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Representing the upper bound of the client stochastic gradient variance, Γ represents the degree of heterogeneity of the data set.
6. The method for jointly optimizing quantization levels and client selection in an energy harvesting federal learning network according to claim 5, wherein in step 3, for the t-th round we set the learning rate to beThe boundaries with quantized federal learning satisfy:
wherein the method comprises the steps of2(E-1) 2 EH 2 E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/I>Representing the upper bound of the random gradient variance of the client, Γ representing the degree of isomerism of the data set;
if the weights are differentially quantized, federal learning can be overlaid onAnd the quantization levels of different rounds can be arbitrarily selected as long as the global optimum of the client is satisfied, based on the loss function L (ω, ζ) L-smooth, μ -strongly convex, the random gradient of the client is unbiased and bounded.
7. The method for selecting a client and jointly optimizing quantization levels in an energy harvesting federal learning network according to claim 1, wherein in step 4, the method for updating weight vectors is as follows:
initializing a selection client, I m,t Representing the participation degree of clients, I m,t =1 means that the client M e {1, …, M } is selected for training on round t. Since only K clients are selected in each round, we must have:
in addition, to ensure the choice is unbiased, the number of times each client participates in training is set to be the same, namely:
8. the method of claim 7, wherein in step 4, the central parameter server broadcasts to the clients of the round of selection, and the clients perform local update.
9. The method for selecting a client and jointly optimizing quantization levels in an energy-harvesting federal learning network according to claim 8, wherein in step 4, the local client has a new weight vector after E local iterationsUsing the same quantization level for all clients, the server aggregates the received local weight differences to generate a new weight vector:
wherein omega t The weight vector representing the t-th round,a weight vector representing the kth client in the t+1st round of training, S t+1 The set of clients selected in round t+1, Q (·) represents quantization.
10. The method for selecting a jointly optimized quantization level and client in an energy harvesting federal learning network according to claim 1, wherein in step 5, the reconstructed MINLP problem is:
wherein the method comprises the steps of E represents the selected local iteration number of the client, H represents the upper bound of random gradient descent of the client,/L->Represents the upper bound of the random gradient variance of the client, Γ represents the degree of isomerism of the data set, η t The learning rate of the t-th round is shown.
Due toIs unchanged, and thus can convert the problem into a non-convex MINLP problem, namely:
s.t.
wherein I is m,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t Bit number representing each weight that client m tries to use in the t-th roundUpsilon represents the upload time, W represents the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
11. The method for selecting a joint optimization quantization level and a client in an energy harvesting type federal learning network according to claim 1, wherein in step 6, a non-convex MINLP problem is converted into a convex optimization problem, and a solution for solving the joint optimization quantization level and the client scheduling is found by solving the convex optimization problem:
s.t.
wherein I is m,t Representing the participation degree of clients, I m,t =1 means that at round t, the client M e {1, …, M } is selected for training,represents the normalized quantization error bound, d represents the length of the weight vector, B t Representing quantization level, B m,t Representing clientsm number of bits per weight tried to be used in the t-th round, B max Is the upper limit of the highest quantization level, gamma denotes the upload time, W denotes the bandwidth allocated to each user, χ m,t Representing channel gain between t-th round client m and central parameter server, N 0 Representing the power spectral density of noise in the network, e m,t Representing the energy consumed by the client in the t-th round of training,/for uploading>Representing the energy consumed by client m in one run, E m,t Representing the energy collected at the t-th round.
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| CN117313891A (en) * | 2023-09-26 | 2023-12-29 | 福州大学 | Federated learning aggregation weight design method for wireless network data heterogeneity |
| CN118101501A (en) * | 2024-04-23 | 2024-05-28 | 山东大学 | A communication method and system for heterogeneous federated learning in industrial Internet of Things |
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| CN117313891A (en) * | 2023-09-26 | 2023-12-29 | 福州大学 | Federated learning aggregation weight design method for wireless network data heterogeneity |
| CN118101501A (en) * | 2024-04-23 | 2024-05-28 | 山东大学 | A communication method and system for heterogeneous federated learning in industrial Internet of Things |
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