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Online Policies for Efficient Volunteer Crowdsourcing

Our Contributions:

• Introduce the online volunteer notification problem
• Develop online policies with constant factor guarantees
• Provide hardness results
• Test policies on datasets from FRUS

How can we use nudging mechanisms to engage volunteers efficiently while avoiding excessive notifications? Motivated by a collaboration with (FRUS)

Authors: Vahideh Manshadi and Scott Rodilitz (Yale School of Management) Paper: https://arxiv.org/abs/2002.08474

Online Volunteer Notification Problem

Challenging Objective: maximize expected # of completed tasks over 𝑈 periods (submodular in notified subset)

We can notify each volunteer every two days 𝑕 2 = 1

Donation Volunteer

time today tomorrow

𝑤 𝑣 𝑡 arrives w.p. 𝜇𝑡,1 𝑡′ arrives w.p. 𝜇𝑡′,2 𝑞𝑤,𝑡 𝑞𝑣,𝑡 𝑞𝑣,𝑡′

• 𝑊: set of volunteers and 𝑇: set of task types
• Task arrival: At time t task 𝑡 becomes available w. p. 𝝁𝒕,𝒖 (σ𝑡∈𝑇 𝜇𝑡,𝑢 ≤ 1)
• Volunteer state (active/inactive): Initially active.
• Match prob.: If active & notified about 𝑡, volunteer 𝑤 responds w. p. 𝒒𝒘,𝒕
• If an active volunteer is notified, she becomes inactive for 𝜐 periods
• Inter-activity time distribution: 𝑕 𝜐

Goal: design online notification policies that perform well compared to a “clairvoyant benchmark” Example:

• Parameterized based on minimum discrete hazard rate of inter-activity time distribution:

Summary of Theoretical Results

Theorem [Upper Bound]: If 𝑟 = 1/𝑜 for some integer 𝑜, no online policy can achieve better than

𝑛𝑗𝑜

1 2−𝑟 , 1 + 𝑟 + 𝑟(1−𝑟)(1−𝑓−1) (1+q)log(1−𝑟) of our benchmark.

Theorem [Lower Bound]: There exists a non- adaptive randomized online policy that achieves at least 1 − Τ

1 𝑓 1 2−𝑟 of our benchmark.

Competitive ratio

𝑟 q = min

𝜐

𝑕(𝜐) 1 − 𝐻(𝜐 − 1)

Sparse Notification Policy (SNP)

Key Idea: Sparsify an ex-ante solution 𝒚∗ by solving a sequence of “low-dimensional” DPs

𝑧𝑤,𝑡,𝑢 = ቊ𝑦𝑤,𝑡,𝑢

∗

Reward of notifying 𝑤 about 𝑡 at 𝑢 ≥ Reward of not notifying 𝑤 at 𝑢

𝑞𝑤,𝑡 ෑ

1≤𝑣≤𝑤−1

1 − 𝑞𝑣,𝑡 𝑧𝑣,𝑡,𝑢 + ෍

𝑢+1≤𝜐≤𝑈

𝑕 𝜐 − 𝑢 𝑲𝒘,𝝊

𝐾𝑤,𝑢+1

Solution of higher ranked DP’s

Offline Phase: Artificially rank volunteers. Starting with 𝑤 = 1 and 𝑢 = 𝑈,

Expected future number of rescues completed by 𝑤 (if active at 𝜐)

Online Phase: If task 𝑡 arrives at time 𝑢, notify volunteer 𝑤 with prob. 𝑧𝑤,𝑒,𝑢

SNP vs. FRUS Current Practice

Fraction of benchmark

𝐾𝑤,𝑢 = σ𝑡∈𝑇 𝑧𝑤,𝑡,𝑢 +(1 − 𝑧𝑤,𝑡,𝑢)

(Reward of notifying 𝑤 about 𝑡 at 𝑢) (Reward of not notifying 𝑤 at 𝑢)