In the age of the development of artificial intelligence, we face the challenge on how to obtain high-quality data set for learning systems effectively and efficiently. Crowdsensing is a new powerful tool which will divide tasks between the data contributors to achieve an outcome cumulatively. However, it arouses several new challenges, such as incentivization. Incentive mechanisms are significant to the crowdsensing applications, since a good incentive mechanism will attract more workers to participate. However, existing mechanisms failed to consider situations where the crowdsourcer has to hire capacitated workers or workers from multiregions. We design two objectives for the proposed multiregion scenario, namely, weighted mean and maximin. The proposed mechanisms maximize the utility of services provided by a selected data contributor under both constraints approximately. Also, extensive simulations are conducted to verify the effectiveness of our proposed methods.
With the rapid development of the hand-held mobile devices, mobile crowdsensing [
With the limited budget, workers may be reluctant to participate, if the offered price is too low. Offering a high price to workers may result in lower outcome. We will use a powerful tool from the algorithmic game to ensure both the efficiency and workers’ incentivization.
The mechanism design is a tricky issue for the crowdsourcer with budget constraint, since designing a budget constraint allocating scheme needs understanding its payoff to workers, which is also related to the allocating scheme itself. Most existing works aim at maximizing the efficiency of crowdsensing by hiring workers in a single region. Nevertheless, with some geographical limitations, the crowdsourcer is necessary to procure service from workers in multiple regions to perform tasks and consider the interactions of different regions. Consider a crowdsourcer with a hard budget who wants to estimate the residential information in Eastern Asia which consisted of five countries, China, Japan, South Korea, North Korea, and Mongolia. Due to the geographical limitation, the crowdsourcer has to hire workers in each country to perform tasks separately. Furthermore, the populations or the area of the territories of five countries are different. Thus, the crowdsourcer has to design mechanisms to allocate proper budgets to each region and considers the incentives for workers from different regions.
In this paper, we introduce and study a new scenario, where the crowdsourcer or buyer wants to buy service in a macroregion which is composed of several nonoverlapped microregions. The crowdsourcer will get a utility for each microregion, respectively, and aggregate results in each microregion to get a final result. We introduce and study two optimization goals when combining results of each microregion, namely, weighted mean and maximin. Under the first model, we define the crowdsourcer’s utility as the weighted mean of utility obtained in each microregion. Under the second model, the crowdsourcer’s utility is defined as the minimum utility obtained in all microregions. Compared with single region settings, our multiple region setting leads to more useful solutions in practice. By this work, we proposed an incentive mechanism for the weighted mean model firstly, which consists of a task allocation algorithm and a worker compensation algorithm. Then, we extend the proposed mechanism to the maximin model.
The main of our paper can be summarized as follows:
A major contribution of this work is introducing a new problem, multiregion crowdsensing. Two objectives are introduced to measure the utility of multiregion crowdsensing. Although we study our problem in the context of crowdsensing, the framework and solution proposed in this paper can be applied to a broad range of domains, such as procurement and resource allocation For a multiunit budget-feasible mechanism, we propose a novel method via a proportional share allocation rule instead of the random sampling method applied in [
In recent years, the mobile crowdsensing system has a wide range of application in our daily life [
Budget-feasible incentive mechanism design, which was initially studied by Singer [
In our setting, a crowdsourcer or buyer wants to procure service in a macroregion, which is composed of
Let
This paper studies the service procurement with strategic players, and each worker will report his cost strategically in order to maximize his benefit. Let
Since the utility in each microregion is calculated, respectively, we need to know the quota of procured service in each microregion. We use
The crowdsourcer will get a final result by combining the outcomes in each microregion. Two optimization objectives are introduced, namely,
Problem: weighted mean maximization.
Objective: maximize
Subject to:
In the maximin model, the global benefit of the crowdsourcer is calculated by the minimum of the accuracy rate achieved in all microregions.
Problem: minimum maximization.
Objective: maximize
Subject to:
We use
Due to the fact that the worker
A single-parameter multiunit domain, a normalized auction
The first condition is trivial and could be obtained via Myerson’s lemma [
Thus, the lemma holds.
We expect our designed auctions are
Based on Myerson’s well-known lemma [
First, we would like to introduce a greedy but nonmonotone selecting rule. Then, we modify this rule to make it monotone. Given a set of procured service
Our greedy algorithm selects a group of services one by one. In each stage
If there are multiple candidate workers, we sort them lexicographically. For each
We choose workers as candidates iteratively until the budget constraint is exceeded. Formally, we have
This allocation rule is a variation of the proportional share rule which is the basis for mechanisms under a budget. Observing that if
Given a sorted list if if
With
Since With
No two services from the same region intersect with each other in
The greedy selection principle is monotone.
For each service
For each microregion, each worker’s units are placed in
Assume that worker
Therefore, we obtain
Thus, each service will be allocated with a lower cost declaration, and the monotonicity achieved.
Through the greedy selecting principle, we get a candidate set, denoted by
Let
Sort workers like
Due to the optimality, we have
Next,
Combining the above inequalities, which imply
Then, we obtain
Based on the concept of notation
From inequalities (
Thus, we have
Finally, we get
However, one can show that simply selecting max
1: Input: a set of workers 2: Output: a set of winning worker 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15:
Algorithm
We prove this lemma through contradiction. With a cost vector If If
Thus, it does not violate the budget constraint, and the worker
Now, we move to our payment scheme which is presented in Algorithm
We can show that the payment for the selected workers can be bounded.
If
We assume that the mechanism will select first
We assume that
1: Input: a set of workers 2: Output: a payment profile of workers 3: 4: 5: 6: return 7: 8: 9: 1. Order the workers in region 10: 2. Order all services except from worker 11: 3. For each 12: 4. Get the last position 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 5. 25: 26: return 27:
Furthermore, we have
Combining these two inequalities, we have
It is a contradiction, because
With the previous lemma, we still do not know whether worker
The threshold reported cost
Suppose
For any
By the lexicographical rule,
Since
It is trivial to have
Moreover, we have
It is obvious to know in all 3 cases, service
According to Lemma
The payment to all workers in worker compensation algorithm is upper bounded by
By Lemma
That is, it is upper bounded by
Now, we have the following theorem.
The weighted mean mechanism is truthful, budget feasible, individual rational and tractable.
Weighted mean multiunit multiregion budget-feasible mechanism achieves a constant ratio approximation:
Drawing from the proof of Theorem
In the weighted mean model, the buyer will perform a single auction to allocate tasks and compensate workers from all micro-regions. However, in the maximin, the buyer will allocate budget
1: 2: Run task allocation 3: Run worker compensation 4: 5: Aggregate the outcome from each microregion.
Maximin mechanism is truthful, budget feasible, individual rational, and computationally efficient.
Since mechanisms performed in each microregion are truthful, budget feasible, individual rational, computationally efficient, and independent from each other, multiregion maximin mechanism is also truthful, budget feasible, individual rational, and computationally efficient.
With payment algorithm
Use
For any
For the set
Let
In the maximin model, the mechanism achieves a constant approximation ratio:
Based on the definition of the maximin problem, we get
Since the single-region performance is guaranteed in Corollary
Since we have known
Thus, we have
Then, we have
It is hard to get the bidding data of workers directly; thus, it is necessary for us to infer the cost profile via historical cost information. Drawing from [
Cost information with numbers of friends.
We compare our designed auctions (
We will present the results of the winner ratio, firstly. Since the simulation results of the three crowdsourcer’s valuations are similar, we just present the results of
Results on weighted mean model.
Winner ratio
Utility
Utility
Results on maximin model.
Winner ratio
Utility
Utility
In this work, we introduce and study the multiregion crowdsensing problem and design two models for the multiregion crowdsensing. We propose a novel multiunit budget-feasible mechanism to solve problems. Our designed mechanisms are budget feasible, truthful, and individual rational and have a constant approximation ratio. Extensive simulations demonstrate the effectiveness of our solution.
The data adopted to support the findings of this manuscript are available from all authors upon request.
The authors declare that there is no conflict of interest regarding the publication of this paper.
Yu Qiao: the contribution of Yu Qiao is to provide the idea of the paper. Also, he finished the proof and wrote the paper. Jun Wu: the contribution of Jun Wu is to improve the idea and help the first author to finish the proof. Hao Cheng: the contribution of Hao Cheng is to conduct the experiments of the paper. Zilan Huang: the contribution of Zihang Huang is to conduct the experiments of the paper. Qiangqiang He: the contribution of Qiangqiang He is to depict the figures in the editable format in the paper after acceptance. Chongjun Wang: the contribution of Chongjun Wang is to improve the idea and help the first author to finish the proof.
This paper is supported by the National Key Research and Development Program of China (Grant No. 2016YF-B1001102), the National Natural Science Foundation of China (Grant Nos. 61502227 and 61876080), the Fundamental Research Funds for the Central Universities (No. 020214380040), and the Collaborative Innovation Center of Novel Software Technology and Industrialization at Nanjing University.