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.

翻译：我们研究了一个由自适应网络招募所驱动的顺序资源分配问题，其中有限的相同资源预算必须在多轮中分配给具有随机推荐能力的个体。成功的推荐会内生性地产生未来的决策机会，而对一个个体分配更多资源则表现出边际收益递减。我们首先证明，单轮分配问题基于边际生存概率允许一个精确的贪心解。在多轮设置中，由于边界上随机、高维的演化，所得到的贝尔曼递归是难以处理的。为了解决这一问题，我们引入了一个仅依赖于剩余预算和边界大小的群体级替代价值函数。该替代函数通过截断概率生成函数实现了一个精确的动态规划，从而得到了一个总预算多项式复杂度的规划算法。我们进一步分析了模型误设下的鲁棒性，证明了一个多轮误差界，该误差界可以分解为紧的单轮边界误差和群体级转移误差。最后，我们在基于真实场景的招募情景中评估了我们的方法。