Enhancing Campaign Design in Crowdfunding: A Product Supply Optimization Perspective

1 Introduction

With the rapid development of the Internet, crowdfunding, which provides a revolutionary way to support ideas and campaigns across a wide range of domains (e.g. technology, film, art), has rapidly risen in popularity [Gerber and Hui, 2013]. It was estimated that the global crowdfunding industry has raised more than US$34 billion for millions of campaigns in 2015, and this market share may have surpassed venture capital in the year of 2016 [Barnett, 2015].

When launching a campaign (project) on crowdfunding platforms, like Kickstarter and Indiegogo, the creators (individuals or startups) want to solicit as many funds as possible or expand their awareness from investors (i.e., backers, contributors, buyers) by carefully showing their stories, goals

∗Corresponding author.

(funding amount), reward options (often vowing future products) and so on. Even though, statistics show that only around 40% of the campaigns succeed in reaching their pledged goals [Li et al., 2016]. Therefore, predicting the success rate of a campaign and inferring the impacts of specific factors on investor decision (e.g., the campaign descriptions, the social networks of creators) have become research hotspots.

Since the investors in crowdfunding are sufficiently heterogeneous in product valuations, a campaign usually offers a variety of rewards in the form of perks [Hu et al., 2015] for soliciting more funds. For instance, as shown in Figure 1, the creator of this campaign divided her budget and offered a line of perks with different levels of prices (e.g. $129), product rewards (e.g. one headphone) and the claimed product supply (e.g. 500 for Perk 1) to maximize the expected funding or awareness. However, the problem of how to automatically help creators optimally divide their budgets according to the market states, i.e. by optimizing the product supply of each perk, remains pretty much open. Indeed, it is very challenging to recommend an appropriate product supply to each perk in a campaign. First, the choice of the product supply for each perk is limited due to the entire budget of one campaign. Second, it is difficult to estimate the return and risk before the campaign is finished, since the investments are potentially affected by many static and temporal factors, such as the perk or campaign descriptions and the funding dynamics.

To address these challenges, in this paper, we propose a novel solution to automatically recommend the optimal product supply to each pre-defined perk (including the prices and the reward products are given) so as to maximize the expected return and minimize the risk of the campaign, simultaneously. Along this line, inspired by the modern portfolio theory [Markowitz, 1952; Wang and Zhu, 2009], we first define it as a constrained portfolio optimization problem, where the constraint is the budget of the campaign. Then, considering the relevance and heterogeneity among the perks when attracting investments, we propose a trace-norm multi-task learning method to estimate the future return for each campaign. In this way, the risk on the settings of product supply to the perks/campaigns could also be estimated. Next, by solving the optimization problem with Alternating Optimization Method, the optimal product supply can be recommended to each perk in a new campaign. Finally, we conduct extensive experiments on the real-world crowdfunding data that was crawled from Indiegogo.com. The results clearly prove that the optimized product supply can help improve the future performance of campaigns significantly, and meanwhile, our multi-task learning method could more precisely estimate the investment (risk) of each campaign setting. To the best of our knowledge, this is the first comprehensive attempt at assisting creators to enhance the performance of newly proposed campaigns, with a focus on optimizing the product supply from a data-driven way, and this idea can also be applied on optimizing other features of the campaign.

2 RelatedWork

The related studies can be grouped into three categories: Crowdfunding, Portfolio Selection and Multi-task Learning.

Crowdfunding. Since the vast majority of crowdfunding platforms follow the "all or nothing" rule, most of the studies in this category focus on predicting the funding results, i.e., whether a campaign will succeed or not [Li et al., 2016], what factors influence the result [Lu et al., 2014; Mitra and Gilbert, 2014], and the contribution behaviors [Zhao et al., 2017]. For instance, [Li et al., 2016] formulated the campaign success prediction as a survival analysis problem and applied the censored regression-based solution. To explore the influenced features, [Mitra and Gilbert, 2014] found that the description language used in the campaign also has surprising predictive power, and even accounting for 58.56% of the variance around successful funding. Recently, [Zhao et al., 2017] used a sequential approach to model market state of funding projects (e.g., hot and cold), and further predicted the bidding behaviors. With the success of crowdfunded campaigns, it is important to understand what drives people to either create or fund these campaigns. For instance, the desire to raise funds and expand awareness of the products are two of the major motivations of creators, according to the interviews given by [Gerber and Hui, 2013]. In [Hu et al., 2015] , the authors also claimed that the investors are sufficiently heterogeneous in their product valuations, and the creator should offer a line of products in the campaign. These studies all contribute some novel insights on campaign/perk design. Though it is also possible for the creators to get help from the manual instructions 1 , to the best of our knowledge, the problem of how to automatically help creators design more attractive campaigns according to current market status, e.g., by optimizing the product supply of each perk, remains pretty much open.

1 https://www.indiegogo.com/partners

Portfolio Selection. Modern portfolio theory is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given risk, and it is built upon the seminal work of Markowitz [Markowitz, 1952]. Indeed, researchers are very much interested in investigating new methods from diverse perspectives (e.g. developing novel approaches for quickly selecting portfolios) to extend/improve this theory [Shen et al., 2015], and the portfolio analysis has become an important method in finance and economics. For instance, [Luo et al., 2011] viewed each investee as a portfolio of investors, and evaluated the risk of an investee based on risk preferences of investors. Similar ideas inspired by portfolio selection have also been adopted in other domains, e.g., solving hard computational problems [Silverthorn and Miikkulainen, 2010], information retrieval [Wang and Zhu, 2009] and loan recommendation [Zhao et al., 2016].

Multi-task Learning. Multi-task learning (MTL) performs well in classification and regression by considering the related tasks simultaneously and utilizing the cross-task information [Caruana, 1998; Xu et al., 2015]. Among existing MTL methods, the regularization-based multi-task learning is one of the main research directions. These methods share the similar framework but choose different regularization terms (e.g. L1-norm) according to the task relationships [Zhou et al., 2011]. Since MTL usually results in improved learning efficiency and prediction accuracy, it has been used in various fields, i.e., stock selection [Ghosn and Bengio, 1997], dynamic trajectory regression [Huang et al., 2014], real estate prediction [Zhu et al., 2016], and natural language processing [Collobert andWeston, 2008].

3 Product Supply Optimization

In this section, we first detail the problem of product supply optimization in crowdfunding, and then show the way of solving this problem by a constrained portfolio selection and multi-task learning. For better illustration, Table 1 lists some mathematical notations, the transverse line distinguishes the input and output variables, where the variables in upper part are given (input variables), and the rest variables need to be learnt (output variables).

In crowdfunding, what the creators are concerned most is the success of their campaigns. In this paper, we aim to assist these creators to enhance the performance of their newly proposed campaigns by optimizing the product supply of each perk. Specifically, the problem can be defined as:

Problem Formulation. Given the entire budget Bi from the creator to campaign i, the perk settings (including the class number of perks ni in this campaign, the prices Pi = {pi1, pi2, ..., pini }, the manually set/claimed product numbers Si = {si1, si2, ..., sini } and the rewards Ei = {ei1, ei2, ..., eini } of the perks), and some other features (like campaign descriptions), our goal is to get the optimal product supply S′ i = {s′i1 , s′i2 , ..., s′ini } of the perks, which can bring the maximum expected return with minimum risk for the target campaign.

where ρi is a heuristic parameter, B′i is the cost of campaign i under the product supply S′ i , and it can be measured by B′i ≈ ∑ni j=1 s′ij eij. Similarly, the claimed budget Bi is Bi ≈ ∑ni j=1 sijeij. The constraint condition is the cost B′i after optimizing could not exceed the expect cost of the creator. In this paper, pij in Pi is the price for the investors to contribute on one product in perk j (e.g. pi1 and pi2 for the two perks in Figure 1 are $129 and $6450, respectively), and eij in Ei is the reward/payback that the creator should provide to the investors (e.g. ei1 and ei2 for the two perks in Figure 1 are 1x Vinci and 50x Vinci, respectively) after the campaign success. For simplicity, we assume that the creator has enough number of rewards eij for each product supply s′ij , as long as the budget constraint is satisfied.

Now let us use an example for depicting the research problem intuitively. We suppose the campaign in Figure 1 contains only 2 (ni) perks whose price Pi = {$129, $6450} and the product numbers preset by the creator are Si = {500, 20}, respectively. We hope to recommend a more suitable product number setting S′ (e.g. {400, 30}) to replace this Si for making the campaign even more successful.

Computation of Returni. According to the findings in previous studies, the motivations/goals for creators launching campaigns are mainly classified into two categories: raising enough money and expanding awareness of the products (boosting their brands) [Brown et al., 2016; Gerber and Hui, 2013]. Thus, the expected return of campaign i can be measured by:

where c′ij in C ′ i (C ′ i = {c′i1 , c′i2 , ..., c′ini }) is the number of investments of j-th perk in campaign i under the product supply setting S′ i . hij measures the motivation of the campaign, i.e., hij = 1 if the creator mainly try to influence more people and hij = pij if she aims to collect more money. We should also note that, there may be more sophisticated choices of hij , e.g. by balancing between pij and 1. However, this is not the major focus of this paper, and we will leave it for future study.

Computation of Riski. Besides the budgets from creators, the product supply of each perk is also constrained by the number of potential investors in the market. For instance, if the number of investments cij is much smaller than the estimation c′ij , the product rewards are overstocked by the creator, and vice versa. Indeed, since the number of investors can not be perfectly estimated, the future return of a new campaign is actually unknown and Eq. (2) is computed with uncertainty/risk. In finance, risk is usually measured by (co)variance of the investments (e.g. stocks) [Markowitz, 1952; Wang and Zhu, 2009]. Correspondingly, in crowdfunding, the risk of setting product supply as Si for campaign i can be estimated by the variance of the returns:

Therefore, summarizing Eq. (1) for all the campaigns:

where M is the number of campaigns. Obviously, as a portfolio of investment choices in the platform, every campaign (perk) is related to others (e.g. the competitors will have an influence on the final investment volume). Thus, instead of computing independently, the risk in Eq. (4) should be measured more precisely by exploiting this kind of relevance.

Multi-task Learning. In this paper, considering the number of investments of a perk is related to other perks even other campaigns, we propose such a measurement by the trace-norm multi-task learning method. Specifically, instead of a formal definition on the correlation/relevance among different campaigns, we automatically learn the risk of the portfolio from a data-driven way:

where × denotes the cross product of two vectors. All perks in the campaigns are now clustered into L learning tasks based on their characteristics. For the t-th task, the input comprises (Xt, Ct, ht), where Xt ∈ Rmt×d is the input matrix for the t-th task with mt perks and d features, i.e. Xij is the feature vector of the j-th perk in campaign i. While label Ct ∈ Rmt×1 is the corresponding target vector (i.e. entries from C, under the product supply setting S), and similarly, vector ht contains the motivations of these perks. W = [W1,W2, ...,WL] is a d × L weight matrix, containing the importance/coefficient of each feature to one task. Obviously, the estimated value in t-th task is C ′t = XtW ⊤ t , and the estimated number of investments in j-th perk of campaign i is c′ij = XijW ⊤ tij . Different choices of regularization terms may reflect different task relationships [Zhu et al., 2016]. Without loss of generality, in this study, we formulate our model by trace norm, which is given by the sum of the singular values: ||W||∗ = ∑t (σt(W)), for capturing the task relationship by constraining the parameter vectors of different tasks to share a low dimensional subspace.

We can rewrite the Returni in Eq. (4) in this multi-task learning way. Thus, the optimization problem becomes:

Here, Xij is represented by Xij=< s′ij , X-s′ ij >, where s′ij is the optimized product supply and X-s′ ij stores other features of this perk except s′ij . Similarly, matrix Wt is also split two parts, W s′ t and W -s′ t . Note that index tij indicates the j-th perk in campaign i belongs to the t-th task.

Product Supply Optimization. In summary, given the campaigns/perks and their features X, for solving the product supply optimization problem, we first put these perks into different learning tasks, and then learn the W and S′ based on the training ones by solving Eq. (6). Thus, the optimal S′ i for each testing campaign can be computed by only maximizing the expected return.

Please note the difference between Eq. (6) and (7), i.e. for the new campaign in test, the risk is unknown without any investment records. Finally, S′ i (i.e. the output of Eq. (7)) is recommended to the creator when she is publishing this campaign. The entire flowchart of the framework is illustrated in Figure 2. Now, we show the way of solving Eq. (6).

Optimization Algorithm. Before solving Eq. (6), we should first put the perks into L different learning tasks. Indeed, there are a number of methods for task partition according to the features X of perks. The details of the task partition and the features of perks will be shown in the experiments. Here, we propose to solve Eq. (6) by the Alternating Optimization Method, which is similar to the Block Coordinate Descent method [Wright and Nocedal, 1999], the variable is optimized alternatively with the other variables fixed. Because Eq. (6) is continuous and separately convex, the alternating optimization algorithm is convergent. Please refer to Algorithm 1 for the holistic method, and the detailed gradients of W and S′ are shown as (Here, we simply fix hij = 1 for better illustration):

In Algorithm 1, B is each campaign's budget and S is the product supply claimed by creators. Since each s′ij is a part (an entry) of the feature matrix X, X should be updated whenever s′ij changes. We should also note that we update W for each task, and update S′ for each perk. In each iteration step, we adopt Accelerated Gradient (AG) method to update W and S′ for achieving the optimal rate of convergence by specifying the stepsize policy, and we use projection method to satisfy the constrains.

During the implement, we first update W for each task. For task t which contains nt campaigns, each campaign has D dimensional features, so the computational complexity is O(n2t D2 ). Then we update S′ and X, and the computational complexity can be regard as O(1) compared to the complexity in updating W, so the overall computational complexity is O(n2kD2N), where k is the index of the task that has the biggest n2k . That is, the algorithm should be stopped when the changing of W or S′ is less than a threshold (i.e. tolW or tolS′ ) or the iteration reaches a maximum number N. In practice, we set tolW(tolS′ ) as 1.0e-5, and set N as 1.0e5 , which we think is of high-quality enough.

Algorithm 1 Alternating Optimization Method

Input: X, C, S, B, N, tolW , tolS′ Output: W, S′ 1: set S′ = S,W0 = 0 2: for k = 1 to N do 3: UpdateW based on Eq. (8), 4: Update S′ based on Eq. (9), 5: Update X by replacing S′ . 6: 7: Break 8: end if 9: end for

if stopping criteria is satisfied then 10: return W, S′

4 Experiments

In this section, we provide empirical validation on a realworld dataset that we crawled from one famous crowdfunding platform in America, i.e. Indiegogo.com.

Dataset Description. Our experimental data includes the campaign information, perk information, and some mutual records of creators and investors 2 . For instance, it contains 14,143 launched campaigns for more than 18 billion funds (including 98,923 perks, on average 7 perks in one campaign) and their funding information from July 2011 to May 2016 with 217,156 investors, 1,862,097 investment records.

2 This data will be publicly available after the paper acceptance.

Here, we remove the unfinished campaigns because their investment volume still changes. To observe how each algorithm behaves at different sparsity levels, we construct different sizes of training sets from 50% to 80% of the campaigns with the increasing step at 10%, and we name the four pairs of training and testing sets as D#1, D#2, D#3 and D#4.

Feature Extraction. We extract 23 features from the campaign level and 9 features from the perk level, and the details of them are illustrated in Table 2. We can see the features are very heterogeneous, including numerical ones (e.g., perk price, goal), categorical ones (e.g., category, location) and text (e.g., campaign description, perk description). For data preprocessing and constructing the feature matrix X, we first transform categorical data into N binary-valued features (numerical ones) using one-hot encoding (i.e. dummy feature). Meanwhile, the doc2vec method [Le and Mikolov, 2014] is adopted to convert textual data into numerical vectors, e.g., the perk description is represented by a 10 dimension vector, and the campaign title and the campaign description are turned into 5 and 100 dimension vectors separately. To explore how these features affect the investment volume prediction, we group them into four integrations:

• NP: Mainly contains numerical perk features.
• NTP: Besides features in NP, textual features of perks are also included.
• NPC: Besides features in NP , there are also the numerical campaign features.
• NTPC: Besides features in NPC, campaign textual fea-
• tures and perk textual features are also included.

Therefore, the relationship among the feature integrations is NP ⊆ NTP ⊆ NTPC, NP ⊆ NPC ⊆ NTPC, and generally, the feature matrix X of the following experiments is constructed based on all of the features, i.e. NTPC. We should also note that the proposed product supply optimization approach is a general framework and it is open to some other features.

Task Partition. In MTL, we should put perks into different tasks. Considering that, products with near prices are more related than distant ones, we propose to split perks into different tasks according their prices, i.e. the perks with the similar prices will be put into the same task. Without loss of generality, we generate 7 tasks (L = 7) whose price ranges (in $) (from task T1 to task T7) are (0, 10], (10, 20], (20, 30], (30, 40], (40, 50], (50, 200], and (200,+∞), respectively. Actually, our solution is a general framework which is open to different task partition methods[Liu et al., 2011].

Parameter Setting. Firstly, we show the way of computing budgets B′i and Bi. As we can see from Figure 1, the reward eij in crowdfunding is usually the product or some other stuff of the project, therefore, it is very hard to directly compute B′i and Bi based on eij (Please refer to Section 3 for detailed information). Luckily, in the marketing literature, it is usually assumed that the price positively influences the perception of product (reward) quality, that is eij ∝ pij [Dodds and Monroe, 1985], and the unit cost of the product with a quality eij is e2ij /2 [Guo and Zhang, 2012; Hu et al., 2015] which can be further represented as θp2ij /2, where θ is a parameter. Therefore, in the following experiments we define B′i = 12 θ ∑ni j=1 s′ij p2ij and Bi = 12 θ ∑ni j=1 sijp2ij .

Parameter ρij represents the risk preferences of creators, here we simply define ρij as a uniform value since it is hard to quantify risk preference for each creator with limited data records. Parameter λ is learned through cross validation.

Evaluations on Multi-task Learning. Before proving the effectiveness of the entire framework of product supply optimization, we first show the performance of MTL on measuring the risk (predicting the future investment volume) of each campaign (Eq. (5)). We adopt RMSE and nMSE as the metrics as they are widely used in MTL [Xu et al., 2015; Zhu et al., 2016]. For the RMSE and nMSE, the smaller the value, the better the performance. We also choose several state-of-the-art regressions for comparison [Zhu et al., 2016]:

• Linear Regression (LR): training a linear regression model for predicting the investment volume.
• Ridge: LR with L2-norm regularizer.
• Lasso: LR with L1-norm regularizer.
• Support Vector Regression (SVR): training a Support Vector Regression model.
• SVR with sigmoid kernel (SigmoidSVR): Support Vector Regression with sigmoid kernel.

The experimental results of our MTL method and the baselines on four data splits are shown in Figure 3. Due to space limitation, we only show the results with hij = 1. We can see that MTL method consistently performs the best on all splits in terms of two evaluation metrics, which clearly validates the effectiveness of our multi-task learning method. Also, the SigmoidSVR is the worst which proves that investment volume prediction is more likely a linear regression instead of a nonlinear regression. We also show the performance of each method in terms of different feature integrations, and the results are given in Figure 4. We can have the following observations. First, the more features contains, the better performance of trace-normMTL is, but this kind of phenomenon is not obvious in other methods (baselines). We think the reason is that trace-norm MTL method constrains the learning model from different tasks to share a low-dimension subspace to capture the task/campaign relevance. The more features are applied, the better the shared subspace can be learnt, and then the more clear the task relevance is. Second, the performance improvement is significant from NTP to NPC, and to NTPC on MTL method, which indicates the campaign features are very effective in improving the prediction accuracy on investment volume, and carefully describing the campaign is really crucial for the success of creator [Mitra and Gilbert, 2014].

Figure 6: An illustration of several important features.

Task Correlations and Feature Study. To intuitively illustrate the utilities of MTL, we compute the Jaccard similarity 3 among the rows (tasks) in W. The results are shown in Figure 5, where we can see that the tasks with the similar price ranges are usually more similar, and task T1 and task T7 are the most distinctive ones. One step further, Figure 6 gives several important features in W, where feature importance is measured based on the summary of the absolute value of each feature at all the tasks. Since we use vectors to express the textual features, there are multiple dimensions belong to one feature. Indeed, the features about campaign/perk description are generally more important than others for predicting the investment volume of the campaign, as shown in Figure 6.

Evaluations on Product Supply Optimization. Indeed, there are no related studies on the task of product supply optimization in crowdfunding, and we treat the investment volumes of the campaigns (e.g. ∑ni j=1 cijhij) under the manually claimed numbers S as a baseline. Since the aim of our framework is using S′ to improve these investment volumes (e.g. ∑ni j=1 c′ij hij), the difference between these two different kinds of investment volumes can be adopted as metrics. For instance, we define the metric

3 The similarity is computed by summarizing the number of features, whose absolute value in two rows of W are both larger than the mean value.

"Growth Num" as ∑Mi=1 (∑ni j=1 c′ij hij - ∑ni j=1 cijhij)/M, and define "Growth Rate" as the average of (∑ni j=1 c′ij hij - ∑ni j=1 cijhij)/(∑ni j=1 cijhij).

Without loss of generality, we only report the results on the 60%-40% data split (D#2), and our optimization algorithm converges quickly by only 26 iterations (on average). The final experimental results with ρij = 0.05 are shown in Table 3, where we take both the two motivations/goals of the creators into consideration. The "Num of Money" motivation measures the amount of raised money when hij = pij and the "Num of Investors" motivation stands for the number of investors when hij = 1. From this table we can see that the optimization of the product supply structure does improve the return of the campaigns, given so many other features fixed. For instance, after optimization, each campaign is expected to attract an average of extra $208 (or 6 investors), which accounts for 2.79% (4.43%) of its current return. The number in each bracket (.) in Table 3 is the variance. After investigating the data carefully, we found that (∑ni j=1 c′ij hij - ∑ni j=1 cijhij) > 0 for more than 87.1% of the campaigns, which means most of the product supply of the campaigns should be optimized.

Actually, the expected return for each creator can be even more impressive if we simply change the setting of ρij (in Eq. (6)) when selecting portfolios. However, high return always associates with high risk. As shown in Figure 7, when ρij becomes larger, not only the expected return rate but also the risk of the optimized product supply will go higher. In practice, the creators can select this parameter manually based on their risk preferences, or we can automatically make a recommendation based on historical records.

Case Study. In Table 4, we present a case study of the product supply optimization results on two real campaigns, Pon 4 and The Wipy 5 . Specifically, Price(in $) is the price of each perk, S is the claimed/given product supply number and S′ is the optimized/recommended number (Without loss of generality, we set hij = 1 for outputting S′ ). Let's take campaign Pon as an exmaple. From this table we can see that the creator of Pon simply sets the same supply number (i.e. 100) to each perk. In contrast, our optimization method can detect the variance of investors (e.g. more investors will be interested in the perk with price $35 and there are few of investors interest in the highest price $85) and make the product supply more reasonable. Note that the number of investors can be found in the webpage of these campaigns.

5 Conclusion

In this paper, we presented a focused study on enhancing the funding performance of newly proposed campaigns in crowdfunding by optimizing the product supply of perks. Inspired by the modern portfolio theory, we first defined it as a constrained portfolio optimization problem. Under this definition, we then proposed a multi-task learning way of estimating the future return for each campaign and measuring the risk of the product supply settings, considering the relevance among the perks when attracting investments. Finally, the solutions for the optimization problem were recommended to creators as the optimal product supply setting. The experimental results on a real-world dataset showed that the optimized product supply can help the campaign get more investments. We hope this study could lead to more future work on optimizing other important features for campaign design in crowdfunding.

Acknowledgements

This research was partially supported by grants from the National Science Foundation for Distinguished Young Scholars of China (Grant No. 61325010), the National Natural Science Foundation of China (Grants No. 61672483 and U1605251), the Anhui Provincial Natural Science Foundation(No 1708085QF140), and the Fundamental Research Funds for the Central Universities. Qi Liu gratefully acknowledges the support of the Youth Innovation Promotion Association of CAS (No. 2014299) and the MOE-Microsoft Key Laboratory of USTC.

4 https://www.indiegogo.com/projects/pon-the-puncturelesspush-pin-photography

5 https://www.indiegogo.com/projects/the-wipy-the-internet-ofthings-of-the-future-wifi