Bandit strategies in social search: the case of the DARPA red balloon challenge
- Haohui Chen^{1, 2}Email author,
- Iyad Rahwan^{3} and
- Manuel Cebrian^{1}
Received: 16 December 2015
Accepted: 26 May 2016
Published: 6 June 2016
Abstract
Collective search for people and information has tremendously benefited from emerging communication technologies that leverage the wisdom of the crowds, and has been increasingly influential in solving time-critical tasks such as the DARPA Network Challenge (DNC, also known as the Red Balloon Challenge). However, while collective search often invests significant resources in encouraging the crowd to contribute new information, the effort invested in verifying this information is comparable, yet often neglected in crowdsourcing models. This paper studies how the exploration-verification trade-off displayed by the teams modulated their success in the DNC, as teams had limited human resources that they had to divide between recruitment (exploration) and verification (exploitation). Our analysis suggests that team performance in the DNC can be modelled as a modified multi-armed bandit (MAB) problem, where information arrives to the team originating from sources of different levels of veracity that need to be assessed in real time. We use these insights to build a data-driven agent-based model, based on the DNC’s data, to simulate team performance. The simulation results match the observed teams’ behavior and demonstrate how to achieve the best balance between exploration and exploitation for general time-critical collective search tasks.
Keywords
crowdsourcing exploration exploitation misinformation disinformation social search bandit problem1 Introduction
Crowdsourcing, the use of the Internet to solicit contributions from large groups of people, has been shown to be very effective in time-critical tasks, ranging from manhunts [1–3], to influenza detection [4], to crisis-mapping [3, 5, 6]. However, time-critical crowdsourcing tasks often reward the collection of new information, but ignore the efforts of verification. Crowds tend to explore new information but seldom verify it autonomously, and exploration effort often dominates. This causes information overload, where misinformation (caused by error) and disinformation (caused by deliberate malice) conceal true information [7], posing a significant challenge to crowdsourcing. In the context of disaster response, while online social media is a highly-effective crowdsourcing tool, it also makes it nearly costless to spread false information [8]. Misinformation has impeded search and rescue operations [5], and sometimes it can go as far as harming innocent people. For example, during the manhunt for the Boston Marathon bombers, the crowd wrongly identified one missing student, Sunil Tripathi, as a suspect. It subsequently emerged that he had died days before the bombings, yet misinformation was spread in 29,416 tweets [9]. Scholars have identified this problem and paid attention to the detection of false information. Gupta et al. [8] and Boididou et al. [10] building up on Canini et al. [11]’s work, use contents and corresponding authors’ profiles to classify false information, and achieve relatively high accuracy. However, in reality, information arrives from various channels, e.g. phone calls, text messages or online social media. Therefore, there is no universal method of processing the information and even classifying it in a short period of time. This paper does not attempt to build a classifier or a universal strategy for discriminating misinformation or disinformation from correct entries. Rather, we assume that, based on the discussion above, the success of a time-critical task requires not just exploring new information (exploration) but also verification (exploitation). Given that an individual or organization has limited resources, exploration and exploitation are regarded as two competing processes [12]. Therefore, this paper explores how to balance exploration and exploitation in time-critical crowdsourcing tasks.
We use DARPA Network Challenge (DNC) as the study case. In 2009, DARPA launched a competition, which aims to evaluate the power of social networks and media in mobilizing crowds. Ten red weather balloons were placed at undisclosed locations throughout the United States. Participating teams or personnel competed to be the first one to locate all the red balloons and win a prize of $40,000 [13]. This paper revisits the full submission history of individual teams, and statistically analyses why high-ranking teams topped the challenge. We found that a large number of false locations were submitted across the teams. Moreover, some of the false locations were submitted concurrently by more than one team, which implies that some teams were using similar sources of information or, as stated by Smith [14], attacks were organized during the competition. As the veracity of sources strongly influences the quality of information [3], to succeed in the DNC, a team must strike a balance between exploring new sources and exploiting the most reliable ones. We assume that the DNC can be modelled as a Multi-Armed Bandit (MAB) problem [15, 16], which implies that solutions for other MAB problems could also be effective. Employing empirical studies of MAB problems, we develop agent-based simulation models to study performance of alternative strategies and to assess the optimal one.
2 Statistics
There were a total of 42 registered teams in the competition. In addition, there was a large amount of anonymous submissions. We assign all anonymous submissions to a virtual team called Anonymous (the complete submission history can be found in [17] and a video illustrating submissions over time is shown in Additional file 1). A submission may contain up to ten locations, and each location comprises a pair of longitude and latitude for a purported balloon. Every team could submit multiple entries while waiting for the previous ones to be validated by DARPA. For each submission DARPA returned the number of correct locations that submission contained. However, the mechanism used by DARPA to screen submissions is not known, neither is the time needed to validate each submission.
Variables of clusters
Variable | Description |
---|---|
a_{submission} | Submission count: how many submissions the cluster had |
a_{balloon} | Balloon count: how many reported locations the cluster had |
a_{team} | Team count: how many teams submitted locations belonging to the cluster |
a_{appear} | Appearance time: the earliest appearance time of the cluster |
a_{disappear} | Disappear time: the latest appearance time of the cluster |
a_{lasting} | Lasting time: a_{disappear} - a_{appear} |
a_{half-submission} | Half-life submissions: time elapsed to reach half of all submissions for the cluster. It’s the different to the appearance time a_{appear}: if the cluster only has 1 submission, the value is 0 |
a_{half-balloon} | Half-life balloons: time elapsed to reach half balloons |
a_{half-team} | Half-life teams: time it took for the cluster to be detected by half of the teams that report it over the course of the challenge |
- 1.
Most teams managed to discriminate correct information and false information.
- 2.
Teams changed their strategies over time to acquire more information from more sources, which increases the chances of receiving false information.
- 3.
Malicious attacks were not organized until the white-hot stage, and most of them did not last a long time.
- 4.
There are a few confusing false clusters that have similar characteristics as correct clusters.
3 Simulation
3.1 Multi-armed bandit (MAB) problem
According to DARPA [13], teams expanded their sources of information as the challenge progressed, e.g. purchased information from other teams or obtained from Twitter’s posts. Retrieving information from new sources can be seen as a form of exploration, while verifying the existing information sources is exploitation. We assume that exploration and exploitation are two competing processes [12], due to limited resource (mainly time) each team has. This implies that at in each trial, teams need to make a choice between submitting the information from what they consider the most reliable sources (exploitation) and submitting from another source (exploration), so this kind of social search problem could be modelled as a MAB problem.
The conventional MAB problem is a problem in which one gambler facing multiple slot machines, each of which has an unknown probability distribution of rewards, needs to decide (a) which machines to play, (b) the order of play, and (c) the number of times to play each machine, to maximize rewards [15, 16]. The player should spend a portion of the limited budget to explore every machine (or some of them) to estimate the distribution of rewards, and then use the remaining budget to exploit the ones with highest expectations.
An adaptive allocation rule to attain the asymptotic lower bound for the regret when the reward distributions are the one-parameter exponential family was proposed by Lai and Robbins in [16]. Based on their work, Agrawal and Hedge [21] expanded the problem and introduced switching cost to the MAB problem attaining the asymptotic lower bound for the regret as well. Switching cost occurs along with the exploration of different machines. It discourages frequent switching, which also applies to a number of practical problems, e.g. oil exploration [22], research and development [23], and website morphing [24, 25]. Other variations of MAB problem have been studied, with various objectives. Hauser et al. [24] explored when the best website morphing time is (switching to another website layout style) to increase consumer’s purchase probability. In online shortest path problems, the objectives are to minimize delays occurring in network links which are unknown at first but become more predictable over time [26, 27].
In a social search problem discussed in this paper, the objective is to minimize the time required to find all key information (all correct locations in this study). We propose a general MAB model to solve time-critical social search tasks: Given k people and a set of opinions M, where each person j espouses \(s_{j} \in M\) opinions, a player, who has access to each of the k opinionated people and has heard opinions W. Consider the following process: a player sequentially selects a person, j, and verifies an opinion in \(s_{j} \in W\). If the information is true, the player receives payoff 1, and otherwise receives nothing. The objective is to minimize W when payoff meets a certain threshold.
- 1.
The sources are regarded arms. In DNC, trading with other teams is regarded as one kind of sources.
- 2.
The reliability of a source can be estimated by submitting certain pieces of the information provided by the source. In DNC, some teams submitted a single location to validate it through DARPA. It could be an effective submission strategy, if not an optimal one, because submitting more than one could be confusing if the score from the feedback is less than the numbers of locations in the submission.
- 3.
The switching cost \(t_{\mathrm{switch}} \times d\) occurs when a team explores d sources and each time it takes \(t_{\mathrm{switch}}\) to get access to a new source, e.g. negotiation time with other teams when trading locations. We assume that the switching cost is one-off in DNC, which means switching to the explored sources would not generate additional cost.
- 4.
Each submission is a trial. The cost \(t_{\mathrm{submission}} \times n\) occurs when a team submits n times and each time it takes \(t_{\mathrm{submission}}\) to wait for the feedback.
- 5.
A team receives payoff 1, only if the submission is correct and unobserved before.
- 6.
The objective is to minimize the total search cost \(t_{\mathrm{search}} = t_{\mathrm{submission}} \times n+ t_{\mathrm{switch}} \times d\) when finding all key information, that is payoff = 10. Moreover, key information could be repeated in different sources.
We consider the following set of strategies, which were previously studied in relation to MAB: ϵ-greedy and its variants, interval estimation (referred as IntEstim in the following), SoftMax, and POKER [28, 29]. As the winning criteria of the DNC is discovering all correct locations, so in an ideal case, where team can submit all 10 correct locations within only 10 trials, the number of trials is 10. However, in reality, the number of submissions is higher than the number of sources, due to the dominating number of false locations over correct ones (Figure 2). In such case, MAB’s heuristic algorithms ϵ-greedy and interval estimation strategy are applied as both are proven to be promising strategies [28, 29]. However, we don’t consider SoftMax strategy [30] and the POKER strategy [28] and their variants, as the former underperforms other strategies and the latter does not suit in this case where there are more trials than arms [28]. Overall, we test 4 strategies: basic ϵ-greedy, ϵ-first, ϵ-decreasing, and IntEstim.
The ϵ-greedy strategy and its variants have common greedy behaviors where the best arm (the one of highest rewards expectation based on acquired knowledge) is always pulled except when a (uniformly) random action is taken [28]. The basic ϵ-greedy strategy defines a fixed value of ϵ, which is the probability that a random arm is selected in the next trial. The ϵ-first strategy tends to explore in the first \(\epsilon~\mbox{N}\) trials, and exploit the best arms in the remaining \((1- \epsilon)~\mbox{N}\) trials. As the estimation for the rewards distribution of each arm becomes more accurate over time, a fixed ϵ would possibly make the exploration at later stage inefficient. As an improvement, a more adaptive greedy strategy called ϵ-decreasing strategy was proposed, where the value of ϵ decreases as the experiment progresses, resulting in highly explorative behavior at the beginning, but highly exploitative behavior at the end [29]. Different to fixing ϵ in the former two cases, ϵ-decreasing strategy requires a user to fine-tune the parameter c, which controls the decreasing rate of ϵ, to achieve approximate optimal solution. According to the Theorem 3 of [29], let Δ be the difference between the expectation \(\mu^{*}\) of the best arm and the expectation μ of the second best arm. The decreasing ϵ is defined as \(\varepsilon\stackrel{\mathrm{def}}{=} \min \{ 1 , \frac{c k}{n \Delta^{2}} \}\), where k is the number of arms, and n is the number of trials. The larger the value of c, the slower the ϵ decreases, the more exploration is performed.
3.2 Experiment settings
In theory, the number of sources during a time-critical social search could be unlimited, since participating teams are free to explore Twitter feeds, Facebook groups, online forums, personal contacts and any other type of sources without restrictions. New sources could be acquired at any stage of the challenge. Teams have no a priori knowledge of the number of sources available. However, the course of the DNC demonstrated that teams accumulate all key information from limited number of sources, which they also trade with each other. To reflect this, and to simplify the experiment, we assume that all information M (correct and false) is provided by a fixed number \(k = (20, 40, \ldots, 80)\) of sources that are equally accessible by any team.
- I.
Locations in M (regardless whether correct or false) are uniformly distributed between k sources;
- II.
Locations in M (regardless whether correct or false) are normally distributed between k sources, and
- III.
Correct clusters are set to contain the same number of locations (10 locations of each), so that \(L_{c} = ( l_{1}^{1}, \ldots, l_{1}^{10} ), \ldots, ( l_{10}^{1}, \ldots, l_{10}^{10} )\), and correct locations are normally distributed in k sources.
3.3 Results
In a randomized dataset (setting I), all sources tend to have similar reliability. Therefore, exploration oriented strategy or exploitation oriented strategy would not be significantly different. The experimental results confirm this assumption, with no strategy standing out from the others, and the \(t_{\mathrm{search}}\) converges at approximately 950 minutes (\(k=20\), \(t_{\mathrm{switch}}=20\)).
However, in setting III of the simulation, where all correct clusters have equal number of locations, the switching cost dominates the variances of the total search time (see Section C of Additional file 2). A team would probably collect all ten correct locations from a small number of sources. Therefore, the highly exploitative ϵ-greedy strategy and its variants outperform the IntEstim strategy by switching less. Given that the highly exploitative ϵ-greedy strategy and its variants achieve overall promising performance in setting II and III, they should also be adopted in a more general social search problem with unknown rewards distribution.
In conclusion, the results suggest that there would be no universal optimal strategy for time-critical social search tasks of different rewards distributions. Even though the IntEstim strategy outperforms others in the case of DNC, it could generate higher switching cost than the others on average. While in the cases where switching cost is higher than verification cost, the IntEstim strategy could result in an undesired solution. On the other hand, highly exploitative greedy behaviors could guarantee minimum number of switches, while performance is only marginally downgraded. Therefore, in general time-critical social search tasks where rewards distribution and switching cost is usually unknown, we suggest adopting highly exploitative ϵ-greedy strategy and its variants.
4 Discussions and conclusions
To the best of the authors’ knowledge, it is impossible to understand the strategies of an individual team given that only a few of them were interviewed after the competition [33]. Moreover, it is not clear how much information each team collected and how reliable this information was. Through the analysis of the submission history, we found that the dominant teams do not necessarily submit the most or have the best verification ability. However, it is the combination of both that leads to success in the competition. When exploration and exploitation are regarded as two competing processes, teams need to balance between exploration of new sources and exploitation of the most reliable ones to gain advantage. As this competition can be seen as a MAB problem, we assume that solutions of other MAB problems could also be effective in this case. Firstly, we propose a general form of the MAB model for handling the time-critical social search problem where multiple information sources are presenting possibly inaccurate information; secondly, we extended it to adapt to the context of DNC. Agent-based simulations of different strategies are performed to obtain the optimal one for DNC. The result suggests that, in a situation where some key information is rare (known only to a few sources), the IntEstim strategy outperforms the others on average, no matter what confidence level is defined. It also agrees with the findings of other studies [28] that ϵ-greedy strategy and its variants have very similar performance, and making ϵ decreasing would not improve that. On the other hand, if all key information has similar number of appearances, highly exploitative ϵ-greedy strategy and its variants could be the most promising strategies. Given that general time-critical social search problems usually have unknown reward distribution and switching cost, we suggest adopting highly exploitative ϵ-greedy strategy and its variants.
The experiment is performed in only three settings: I - correct locations are randomly distributed across sources, II - correct locations are normally distributed across sources, and III - correct locations have equivalent appearances and they are normally distributed across sources. However, in reality, the distribution of misinformation is unknown beforehand. Therefore, highly exploitative ϵ-greedy strategy and its variants might not work in other cases. It implies that more works need to be done in analysis of the distribution of misinformation in other time-critical crowdsourcing tasks.
Switching cost is unavoidable in practical problems. However, in time-critical social search tasks, little has been done in research about the cost of exploring new sources, or the relationships between switching cost and verification cost. Further analysis about them should be performed.
Even though the result of this study cannot be directly applied in other time-critical crowdsourcing tasks, it provides insights into how to strike a balance between exploration and exploitation. For example, during the crowdsourced manhunt event for the Boston Marathon bombers, the authorities should have observed that misinformation dominated useful information from the very beginning [9], and the self-correcting crowd hardly deterred it. Therefore, attentions should be paid to the discussion threads or Twitter feeds that continually deliver useful information that advanced the search.
Declarations
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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