A General Framework for Budgeted Threshold Incentives on Request

Zhuolin Wu; Chengrui Zhu; Wenhua Nie; Kenny Ye Liang; Junming Lin; Haiyang Li; Zhilin Li; Wenjia Geng; Zeyu Wu; Yinan Wu; Jinghua Hao; Renqing He

arXiv · 2609.29724

A General Framework for Budgeted Threshold Incentives on Request

Zhuolin Wu·Chengrui Zhu·Wenhua Nie·Kenny Ye Liang·Junming Lin·Haiyang Li·Zhilin Li·Wenjia Geng·Zeyu Wu·Yinan Wu·Jinghua Hao·Renqing He

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Abstract

On-demand delivery platforms pay riders through incentive activities whose tiers are set from recent completions of riders with a similar history. Operators request such plans for changing periods, rider populations, payment rules and budgets, often for holidays or bad weather, where randomized trials are scarce and take months to collect. We present a request-driven framework that composes four stages (conditional prediction, population reduction, trajectory integration and budget allocation) through seven replaceable modules that exchange conditional trajectory laws, whose award probabilities and award-marked moments give payment and uplift for any activity rule. A response-correction step reweights trajectories from abundant no-offer history to match the moments of a short pilot. We prove that, on a fixed plan menu and given the stage errors, the end-to-end value loss is bounded by the sum of four stage terms, and that for every stage there are instances on which omitting it leaves an error floor the others cannot remove. On 3,000 riders over 45 weekly origins, all 127 windows of a week are answered 11.04x faster with identical scenarios and at most 0.92% value lost by the allocation. On 24 new controlled response laws, the response correction with a one-week pilot lowers regret by 51.2% relative to a trial with the same nominal randomized rider-weeks, and a four-week pilot with exact summation comes within +0.007 of an 18-week trial. In registered studies where windows, populations, rules and binding budgets change from request to request, the framework's regret is below that of a trial with the same nominal rider-weeks and below dose interpolation of the same pilot data, and reusing its one-off preparation answers 60 requests 14.1x and 2.70x faster with identical answers. Against a nine-offer trial fitted with the framework's own dose curve, one-week regret is 0.055 lower.

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Zhuolin Wu, Chengrui Zhu, Wenhua Nie, Kenny Ye Liang, Junming Lin, Haiyang Li, Zhilin Li, Wenjia Geng, Zeyu Wu, Yinan Wu, Jinghua Hao, Renqing He. 2026-09-24. A General Framework for Budgeted Threshold Incentives on Request. https://arxiv.org/abs/2609.29724

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