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Incentivize Crowd Labeling under Budget Constraint Qi Zhang, Yutian Wen, Xiaohua Tian, Xiaoying Gan, Xinbing Wang Shanghai Jiao Tong University, China

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2 Outline Introduction to Crowdsourcing Mechanism Problem Formulation and Mechanism Setting Mechanism Analysis Performance Evaluation 2

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Background Crowdsourcing systems leverage human wisdom to : perform tasks, such as: Image classification Character recognition Data collection 3

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Types of Tasks Types of Tasks Tasks can be divided into two categories: Structured Structured response format Binary choice Multiple choice Real Value Unstructured Unstructured response format Logo design 4

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5 Motivating Example Example: Image classification Workers Allocation CrowdsourcingPlatform Task Dog Dog Cat Cat Dog Inference Algorithm Dog

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6 Framework: Reverse Auction (1)Tasks (2)Bids (3)Winning bids determination ( 4)Winning bids ( 6)Payments (5)Answers

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7 Major Challenges(1) To design a successful crowdsourcing system Task Allocation (winning bids) Tasks should be allocated evenly Payment Determination: Must provide proper incentives (monetary rewards) Inference Algorithm: Should improve overall accuracy Should address the diversity of the crowd

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8 Major Challenges(2) We need to model on Diverse task difficulty Dog or Cat Older than 30 or Not Diverse worker quality Cat

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9 Model on Tasks(1) We focus on binary choice tasks Each task is a 0 – 1 question (Assumption) Each worker is uniformly reliable Task Soft Label Probability that the task is labeled as 1( by a reliable worker) Crowd Label 0 or 1

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10 Model on Tasks(2) The soft label is viewed as a random variable drawn from Beta distribution Update parameters (a,b) by Bayes rule Inference The task is inferred as 1 Prior Parameters Prior Posterior Likelihood More than half agree

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11 Framework: Reverse Auction The platform publicizes a set of binary tasks Workers reply with a set of bids Each bid is a task-price pair (Allocation) The platform sequentially decide winning bids (Payment) Winning workers provide labels and get payment

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12 Crowdsourcing Platform Utility After observing all crowd labels, the distribution is updated as Platform Utility: KL Divergence between the initial and the final distribution

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13 Problem Formulation We want: Platform utility maximization under budget constraint Individual rationality Truthful about the cost Truthful bid Untruthful bid Computation Efficiency

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14 Allocation Scheme (1) The task allocation(winning bid determination) is sequential : Candidate selection one candidate a round Proportional rule check Answer collection & Soft label update The allocation scheme repeats the 3 steps until Remaining bids Candidate Discard Winning bid All bids Discard Winning bids

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15 Allocation Scheme (2) The candidate selection is greedy The largest platform utility gain per unit price Platform utility gain: PU Gain Price Candidate Updated distribution Current distribution

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16 Allocation Scheme (3) Proportional rule check Soft label update Collect the answer from the winning bid Update the soft label according to Bayes rule price budget fraction ratio

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17 Allocation Scheme (5) Candidate selection Proportional rule check Soft label update Computationally efficient !

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18 Payment Scheme(1) p(C) = max {b1,b2, b3, b4} Winning bids {A, B, C} Discard {D, E, F} Kick out C { A,B,D,E,F } Winning bids {A, B, D, E} Discard {F} C b1 b2 b3 b4 b1 is the minimum price that bid C can replace bid A

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19 Payment Scheme(2) (Proposition)The winning bid C is paid threshold payment. p(C) C’s payment, b(C) C’s bid if b(C) < p(C), C is a winning bid if b(C) > p(C), C is discarded p(C)=max { b1, b2, b3, b4} Winning bids {A, B, D, E} C b1 b2 b3 b4

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20 Payment Scheme(3) (Proposition)The incentive mechanism is truthful Each bid has a cost Workers will truthfully reveal the cost as asked price Why? Proof: Threshold payment + Greedy candidate Selection

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21 Individual Rationality (Proposition)The incentive mechanism is individual rational The utility of a winning bid is nonnegative Proof ： Let us consider the winning bid C 1.C is the 3 rd winning bid. 2.The first 2 bids are the same 3.b3 is the minimum price that bid C can replace the new 3 rd bid (D) It is true that b3 > b(c) ！ p(C) = max {b1, b2, b3, b4}, p(C) > b3 p(C) > b(C) New Winning bids {A, B, D, E} b1 b2 b3 b4 { A, B, C} Original wining bids

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22 Budget Feasibility (Proposition, Payment Bound) Payment to each winning bid is upper bounded by Proportional rule: Set

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23 Performance Evaluation(1) Benchmark 1.Untruthful Allocation: Workers’ cost is public information 2.Random Allocation: Candidate selection is random TruthfulRunning Time Platform Utility Benchmark 1 High Benchmark 2 Low My Mechanism High

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24 Performance Evaluation(2) Metric 1 : Platform Utility Platform utility vs. Budget Price of Truthfulness Gain over random allocation

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25 Performance Evaluation(3) Metric 2 : Budget Utilization Payment / Budget Budget utilization gain Over random allocation

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Thank you ! Presented by : Qi Zhang

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