Adaptive Multi-Round Allocation with Stochastic Arrivals

TL;DR

This paper develops a polynomial-time dynamic programming approach for multi-round resource allocation with stochastic arrivals, using a surrogate value function to handle complexity and analyzing robustness under model misspecification.

Contribution

It introduces a population-level surrogate value function for multi-round stochastic allocation, enabling efficient planning and robustness analysis.

Findings

Exact greedy solution for single-round allocation based on marginal survival probabilities.

Polynomial complexity dynamic programming algorithm for multi-round planning.

Robustness bounds under model misspecification with empirical evaluation.

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.