Adaptive Multi-Round Allocation with Stochastic Arrivals

This paper studies a sequential resource allocation problem motivated by adaptive network recruitment, where limited resources must be distributed over multiple rounds to individuals with uncertain referral capacity. The authors develop a population-level surrogate value function and an exact dynamic programming approach using truncated probability generating functions to address the intractability of the multi-round setting. The resulting algorithm achieves polynomial-time planning complexity and includes robustness guarantees under model misspecification. Empirical evaluations on realistic recruitment scenarios demonstrate the effectiveness of the proposed method for large-scale stochastic allocation problems.