Adaptive Multi-Round Allocation with Stochastic Arrivals

2026-05-12

AI Summary

This work addresses the multi-round allocation of homogeneous resources under budget constraints and stochastic individual recommendation efficacy. The authors propose a dynamic programming approach based on a population-level proxy value function, which leverages marginal survival probabilities to design a single-round greedy policy. By constructing a proxy function that depends only on the remaining budget and the size of the active frontier, and integrating it with a truncated probability generating function, the method efficiently circumvents the intractability of Bellman recursion caused by high-dimensional stochastic frontiers. Theoretical analysis provides an error decomposition bound under model misspecification, and the algorithm achieves polynomial time complexity in the total budget. Empirical evaluation on real-world recruitment data demonstrates the method’s effectiveness and robustness.

Abstract

We study a sequential resource allocation problem motivated by adaptive network recruitment, in which a limited budget of identical resources must be allocated over multiple rounds to individuals with stochastic referral capacity. Successful referrals endogenously generate future decision opportunities while allocating additional resources to an individual exhibits diminishing returns. We first show that the single-round allocation problem admits an exact greedy solution based on marginal survival probabilities. In the multi-round setting, the resulting Bellman recursion is intractable due to the stochastic, high-dimensional evolution of the frontier. To address this, we introduce a population-level surrogate value function that depends only on the remaining budget and frontier size. This surrogate enables an exact dynamic program via truncated probability generating functions, yielding a planning algorithm with polynomial complexity in the total budget. We further analyze robustness under model misspecification, proving a multi-round error bound that decomposes into a tight single-round frontier error and a population-level transition error. Finally, we evaluate our method on real-world inspired recruitment scenarios.

Problem

• sequential resource allocation
• stochastic arrivals
• adaptive recruitment
• diminishing returns
• multi-round allocation

Innovation

• adaptive allocation
• stochastic arrivals
• surrogate value function
• dynamic programming
• diminishing returns