Adaptive Multi-Round Allocation with Stochastic Arrivals
For researchers in sequential decision-making and resource allocation, this work provides a tractable solution to a previously intractable multi-round allocation problem with stochastic arrivals.
This paper tackles a sequential resource allocation problem with stochastic arrivals and diminishing returns, introducing a population-level surrogate value function that enables an exact dynamic program with polynomial complexity. The method achieves robust performance under model misspecification, with a multi-round error bound decomposing into single-round frontier and population-level transition errors.
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.