CN108776926B - Wireless network resource allocation optimal auction method based on deep learning - Google Patents

Wireless network resource allocation optimal auction method based on deep learning Download PDF

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CN108776926B
CN108776926B CN201810581308.8A CN201810581308A CN108776926B CN 108776926 B CN108776926 B CN 108776926B CN 201810581308 A CN201810581308 A CN 201810581308A CN 108776926 B CN108776926 B CN 108776926B
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钱俊
朱琨
王然
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses an optimal auction method for wireless network resource allocation based on deep learning. In conventional resource allocation, the goal of the operator is to maximize social welfare, but for the operator, it focuses more on the income obtained by itself, so the income maximization is more reasonable. In the mechanism, an operator searches out an optimal auction model by adopting a deep learning method and utilizing a deep neural network framework. The operator finally needs to decide an allocation rule and a pricing strategy through a second price auction rule, so that the dynamic allocation of resources is performed, the high efficiency of allocation is realized, and different requirements of users are met.

Description

Wireless network resource allocation optimal auction method based on deep learning
Technical Field
The invention belongs to the technical field of wireless resource allocation in wireless virtualization, and particularly relates to an optimal auction method for wireless network resource allocation based on deep learning, which is mainly used for ensuring efficient and flexible allocation of resources in a virtualized network, meeting the requirements of users, improving the utilization rate of the resources, and reducing the operation cost and expenditure cost, so that the overall economic benefit is improved.
Background
Virtualization technology has been widely used in wired networks for decades, but with the increasing amount of services and traffic in wireless networks, it is necessary to extend virtualization technology into wireless network environments. The basic point of wireless virtualization is to abstract the physical network infrastructure and resources into virtual wireless network resources. Through wireless virtualization, overall resource utilization is improved, capital and operational expenses are greatly reduced, and it may enable small service providers to provide more services for users to choose from, enriching services. Although wireless virtualization technology has great application prospect, it also faces some significant challenges. The most important challenge is resource allocation, where the difficulty is to allocate resources of various mobile network operators to meet the changing demands of the respective users, while at the same time meeting the efficiency of resource allocation.
Auction, a kind of effective resource allocation mechanism. Auction theory has originated from economics, but is now widely used in computer science as a cross-discipline application, such as the auction of spectrum and virtual resources in wireless networks. In a typical auction, there are a buyer, a seller and an auctioneer, and after the auctioneer collects all the bids of the users, the request of the seller and the bid of the buyer are appropriately matched. Ultimately deciding the winners in the auction round and their corresponding payments. The auction mechanism is introduced into the resource allocation of wireless virtualization, and the core problem is to allocate resources efficiently and flexibly, thereby maximizing the revenue of mobile virtual operators.
In the existing work of wireless virtualization resource allocation, the aim of consideration is to maximize social welfare. Since this problem can be easily addressed. In fact, operators are more interested in the revenue they receive from the users. But revenue maximization is very complex, and since the price is not known before calculation, it is difficult for the ordinary analytical methods to solve this problem.
In view of the difficulty of the optimal auction mechanism for revenue maximization, we have adopted deep learning techniques. In recent years, deep learning has received considerable attention because it enables features to be automatically determined. In fact, deep learning employs some gradient descent method, such as a random gradient descent method, and a globally optimal solution can be found. Deep learning works in essence using a multi-layer deep neural network. A typical neural network comprises an input layer, a plurality of hidden layers and an output layer, each hidden layer and the previous layer being connected by a non-linear function. The neural network can iterate continuously until an optimal solution is found. In the invention, the input of the neural network is the evaluation of a plurality of users, the output is the final distribution rule and the pricing rule, and finally, the income maximization is ensured.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art and documents, the invention provides an optimal auction method for wireless network resource allocation based on deep learning, which is mainly used for building a virtual resource dynamic allocation market between a single mobile virtual operator and a plurality of users, so that the problem of resource allocation in a wireless virtualization network is solved. By introducing an auction mechanism and combining with a deep learning technology, the income maximization of an operator is realized under the condition of meeting corresponding constraint conditions.
In order to achieve the purpose, the invention adopts the following technical scheme:
an optimal auction method for deep learning wireless network resource allocation, comprising the following steps:
step 1: all users submit Bids Bids to a controller (operator), and the controller collects the Bids of the users;
step 2: the operator converts the collected Bids into virtual Bids;
and step 3: according to the virtual Bids obtained through calculation, a neural network activation function softmax is used for realizing an allocation rule, and a winner of the round of auction is determined;
and 4, step 4: the operator implements the pricing rules (based on the second price auction rules) using the activation function relu, deciding the final payment for the round of winners;
and 5: the operator calculates its revenue according to the allocation rules and pricing rules, thereby maximizing revenue.
Further, the specific method of step 1 is as follows: assuming that there are n users and 1 mobile virtual network operator, these users want to compete for the operator's resources, but the resources can only be allocated to one user, so this auction model is an auction of a single item. Each user submits one Bid in each auction round, so the total Bid, Bids, { v ═ v1,v2,...,vnIn which v isiRepresenting the user i's bid for the operator resource. The mobile virtual network operator acts as a controller to collect the bids of all users.
Further, in the step 2, the operator converts the obtained Bids into virtual Bids according to the obtained Bids, and the specific details are as follows: for each viWe use the corresponding virtual transfer function φiConvert it into a virtual value
Figure RE-GDA0001737034100000021
To ensure phiiIs strictly monotonously increasing, we have the following design scheme: we use K sets of J linear equations each containing the parameters w and beta, w being the slope of the linear equations,beta is the intercept of the linear equation and to ensure strictly monotonic increase, it is necessary to ensure that the slope w > 0. The calculation formula of the virtual bid is:
Figure RE-GDA0001737034100000031
we base on bid viCalculating all virtual bids
Figure RE-GDA0001737034100000032
What I eventually get is the virtual bid Bids:
Figure RE-GDA0001737034100000033
further, the specific method of step 3 is as follows: we get the virtual bid according to step 2
Figure RE-GDA0001737034100000034
The allocation rules are decided using the softmax activation function in the neural network. The input of the softmax function is
Figure RE-GDA0001737034100000035
The output is the probability of each user being allocated to the resource, and the characteristic of the activation function softmax in the neural network is that the output value is in the range of 0-1. Meanwhile, the resource needs to be distributed to the user with the highest virtual bid to ensure the reasonability of the auction, and then other users are not distributed, namely the user with the highest virtual bid can obtain the resource. The total probability of assignment is denoted by g, so we get:
Figure RE-GDA0001737034100000036
wherein g isiThe probability of the user i being assigned to the operator resource is shown, the parameter k in the formula shows the accuracy of the approximate value, and the larger the value is, the more the approximate value is to the optimal solution, but the optimization is also difficult. So that it is very convenient to select a proper valueIs critical.
Further, in step 4, a basic policy based on a second price auction is adopted to implement the pricing rule. We implement this step using the neural network activation function relu, the input to which is the virtual bid
Figure RE-GDA0001737034100000037
The output is the virtual payment of the user (on the premise of successful allocation to resources), but we must finally convert the virtual payment of the user into the corresponding actual payment. The relu function is characterized in that: when its input value is less than 0, the output value is 0; when its input value is greater than 0, the output equals the input. The specific process is as follows: we calculate for each user i its virtual payment (based on the second price auction rule), i.e. the maximum between the virtual bids of the other users and 0, which can be expressed in particular as:
Figure RE-GDA0001737034100000038
we get a virtual payment for each user. Wherein the relu function may ensure that the virtual payment is non-negative.
Eventually we need to calculate the user's actual payment from the virtual payment:
Figure RE-GDA0001737034100000041
wherein the function
Figure RE-GDA0001737034100000042
Is a virtual transfer function phi corresponding to user iiInverse function of, finally tiThe calculation formula is as follows:
Figure RE-GDA0001737034100000043
further, in step 5, we need to calculate the income of the operator, and based on the results of step 3 and step 4, we can obtain a calculation formula of the income of the operator:
Figure RE-GDA0001737034100000044
wherein, giProbability of allocating to operator resources for user i, and tiIndicating the final actual expenditure of the user on condition of a successful allocation. The ultimate goal of the operator is to maximize revenue.
Has the advantages that: the invention discloses an optimal auction mechanism based on deep learning, wherein a considered model is that a single mobile virtual network operator provides resources, and a plurality of users compete for the resources. The operator aims to maximize his revenue. In the mechanism, operators adopt a deep learning technology and mainly adopt a multi-layer feedforward neural network framework to carry out continuous iteration so as to find out an optimal auction model. The operator can get the optimal allocation rules and pricing strategy according to the optimal auction mechanism, while the pricing strategy is based on the second price auction rule because it can guarantee that the final payment of the user is not negative. The optimal auction mechanism can ensure that the individuality of the user and the dominance strategy incentive are compatible while ensuring the income maximization of the operator, so that the whole auction is real-time trading. The operator carries out dynamic flexible allocation of resources, realizes high efficiency of allocation, and meets different requirements of users.
The optimal auction mechanism of wireless network resource allocation based on deep learning of the invention takes a mobile virtual network operator as a commercial auction seller to participate in market competition, and a plurality of users (auction buyers) compete for resources by submitting bids, and has the following advantages:
1) the resource auction model between a single operator and a plurality of users is considered, so that the income maximization of the operator is realized;
2) the user submits an implicit bid to an operator (auctioneer), and the operator converts the implicit bid into a virtual bid;
3) determining allocation rules and pricing strategies using deep learning techniques;
4) the earnings are maximized, and simultaneously, the rationality of individuals and the incentive compatibility of the dominant strategies are ensured.
Drawings
FIG. 1 is a flow chart of a preferred auction method proposed by the present invention;
fig. 2 to 5 are graphs of experimental results related to four cases a, b, c, and d, respectively.
Detailed Description
The present invention will be further explained with reference to examples.
The invention considers unilateral resource auction among a plurality of users and a single operator, and is different from the traditional method considering social welfare maximization and considering income maximization. The operator sees the resources it owns as a single item, and all users compete for the item. Since the resource can only be allocated to one user, the operator needs to have appropriate decisions, i.e. allocation rules and pricing strategies, so as to ensure that the income of the operator is maximized, and simultaneously, the efficiency of resource allocation is also met, and the needs of the user are met. The auction system is composed of the following components:
1) the mobile virtual network operator provides resources for users to compete;
2) different users estimate the value of the resource according to the demands of the users and bid;
3) collecting the valuations of all users by an auctioneer, and converting the valuations into virtual valuations;
4) in each round of auction, only one user wins, and it will have a corresponding payout;
5) the problem with this optimal auction is that the revenue for the operator is maximized.
The invention is further described with reference to the following figures and examples.
In the actual implementation process, because a deep learning technology is adopted, the bids of users are a plurality of groups of estimates (training data sets), and the implementation process core is divided into the following steps:
step 1: the buyer gives the valuation of the resource according to the degree of the demand of the buyer on the resource and submits the valuation to the operator;
step 2: the operator converts all the valuations into virtual valuations;
and step 3: allocating resources according to the virtual valuation to realize an allocation rule;
and 4, step 4: the operator decides the payment of the winner in the auction, implementing the pricing strategy;
and 5: the operator calculates revenue until the revenue reaches a maximum and the auction round ends.
The above 5 steps are described in detail below:
step 1: in this model we consider 1 operator and n users, the operator acting as an auctioneer at the same time. We describe an estimation first. Each user makes a valuation in a round of auctions, the users asking the auctioneer operator for their one valuation as the actual bid:
v＝{v1,v2,...,vn}
vithe larger the value of the demand of the user i on the resources owned by the operator, the higher the demand of the user i on the resources.
Step 2: after step 1 is completed, i.e. after the operator has collected all the user estimates, they are converted into virtual estimates, where we use K sets of equations, each set containing J linear equations, to ensure a virtual transfer function phiiIs strictly monotonically increasing, each linear equation containing a slope w>0 and intercept β. Each user corresponds to a virtual conversion function, and the conversion formula is as follows:
Figure RE-GDA0001737034100000061
and step 3: after obtaining the virtual estimates according to step 2, we need to calculate the probability g that each user gets the resourceiNamely:
Figure RE-GDA0001737034100000062
κ is a parameter in the activation function softmax, which determines the approximation of the result to an optimal value, the larger the value, the higher the approximation, but it is also difficult to optimize.
And 4, step 4: having obtained the virtual estimate according to step 2, we need to calculate the corresponding payout for the winner, thereby implementing the pricing strategy. The method mainly comprises two processes:
a. calculating a virtual payment for the user:
Figure RE-GDA0001737034100000063
the comparison with 0 is because it is guaranteed that the value of the virtual payment is not negative.
b. Calculating the final actual payment of the user:
Figure RE-GDA0001737034100000064
therefore, tiWhat is shown is the cost that user i actually needs to pay on the premise that it is successfully allocated to the resource.
And 5: the probability of resource allocation is obtained in step 3, the payment fee of the user is obtained in step 4, and the income of the operator needs to be calculated, and the formula is as follows:
Figure RE-GDA0001737034100000065
in fact, deep learning requires multiple sets of test data (evaluation samples) during operation. We denote the number of data sets (number of estimates) by L, and the samples of estimates for each user for the resource obey a known distribution. With S ═ v(1),...,v(L)Denotes the actual evaluation samples of all users, where
Figure RE-GDA0001737034100000071
Indicating the estimate of the resource by the nth user. We get backThe income calculation formula is as follows:
Figure RE-GDA0001737034100000072
in fact, because there are multiple parameters in the virtual function, the neural network calculates the corresponding revenue R under different parameters (the parameters refer to the slope and intercept in the virtual conversion function), and performs continuous iteration to find the optimal and suitable parameters, thereby maximizing the revenue.
In the experimental part, we use a deep learning method based on the tenserflow library, and we set the learning rate to be 0.01 and the iteration number to be 1000. We can set the number of test data sets L to 1000 and set different numbers of users to observe different revenue results. In the virtual transfer function, we can use 5 sets of 10 linear equations each (K5, J10). In addition, a parameter k in the distribution function softmax, which determines the final optimization result, is set to be 50 and 100, and different experimental results are observed. The estimate samples for each user are subject to a known distribution, which may be the same or different. In general, we can set vi～U[0,1](the estimate of each user obeys a uniform distribution of 0 to 1) or vi～U[0,i](the estimate of user i obeys a uniform distribution of 0 to i).
We consider mainly the following four cases:
a.3 users (n ═ 3), each user obeying vi～U[0,1]；
b.3 users (n ═ 3), each user obeying vi～U[0,i]；
c.5 users (n-5), each user obeying vi～U[0,1]；
d.5 users (n-5), each user obeying vi～U[0,i]。
Fig. 2 to 5 are graphs of experimental results related to four cases, a, b, c and d, respectively. Looking at the experimental result graph, we can find that the income obtained based on the deep learning (DL-based) is always higher than the income of the traditional auction method (SPA-second price auction) under the condition of different user numbers and distribution.
The optimal auction mechanism can realize the income maximization of operators, and simultaneously can ensure the individuality of all users and the compatibility of the dominance strategy incentives, and the specific description is as follows:
1) individuality: the SPA-0 scheme is adopted in the pricing scheme, and the final actual payment of a winner is an estimation value of resources smaller than the actual payment, so that the benefit of a buyer is ensured to be positive all the time, and the individuality of the buyer is ensured;
2) the prevailing strategy encourages compatibility: all users in the auction submit their bids really without considering other users, thereby maximizing the benefits of themselves.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. An optimal auction method for wireless network resource allocation based on deep learning is characterized by comprising the following steps:
1) collecting the evaluation values of the n users to the wireless network resources in L bids to form a training sample set S ═ v(1),...,v(L)Therein of
Figure FDA0002961255760000011
Representing the evaluation of the wireless network resources by the n users in the ith bid;
2) estimate v of each time of all usersiConverting it into a virtual estimate using a virtual transfer function phi i
Figure FDA0002961255760000012
viRepresenting an estimate of the radio network resource by user i;
3) based on a set of virtual estimates
Figure FDA0002961255760000013
Calculating the probability g of obtaining the wireless network resource distributed by each user ii；
4) Based on a set of virtual estimates
Figure FDA0002961255760000014
Computing virtual payments for user i
Figure FDA0002961255760000015
According to virtual payment
Figure FDA0002961255760000016
Calculating the actual payment ti，
5) Calculating operator revenue
Figure FDA0002961255760000017
6) Training a neural network by using a training sample set, wherein the output of the neural network is gi(v(l)) And ti(v(l)) The goal is to maximize the operator income R, the training is finished when the iteration times reach the set times, the model parameters and the neural network model are determined, otherwise, the model parameters are updated, and the steps 2) to 6) are repeated;
7) and inputting the new evaluation value into the neural network model in the new round of bidding to obtain the optimal auction result of the current round of bidding.
2. The optimal auction method for wireless network resource allocation based on deep learning of claim 1, wherein in step 2), the virtual transfer function is:
Figure FDA0002961255760000018
wherein K, J represents a linear equation
Figure FDA0002961255760000019
There are K sets of J linear equations each, w is the slope of the linear equation and β is the intercept of the linear equation.
3. The method for optimal auction of wireless network resource allocation based on deep learning of claim 1, wherein in step 3), the probability g of the wireless network resource isiThe calculation formula of (2) is as follows:
Figure FDA0002961255760000021
where κ is a parameter in the activation function softmax.
4. The optimal auction method for wireless network resource allocation based on deep learning of claim 1, wherein in step 4), the virtual payment is made
Figure FDA0002961255760000022
The calculation formula is as follows:
Figure FDA0002961255760000023
5. the optimal auction method for wireless network resource allocation based on deep learning of claim 2, wherein the actual payment t isiThe calculation formula of (2) is as follows:
Figure FDA0002961255760000024
wherein the function
Figure FDA0002961255760000025
Is a virtual transfer function phiiToA function.
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