基于在线社会福利函数的资源分配
Online Social Welfare Function-based Resource Allocation
AI总结：
本文提出基于社会福利函数的在线学习算法SWF-UCB，通过单调性性质实现最优福利界推断，适用于多种SWF家族，实现近最优的后悔界并支持推断应用。
摘要：
在许多现实世界场景中，一个集中决策者必须在多个时间步中反复将有限资源分配给一个群体。获得资源的个体会获得一些随机效用；为了表征群体层面的分配影响，将个体的预期效用通过社会福利函数（SWF）进行汇总。我们正式定义了这一设定，并提出了一个通用的置信序列框架，用于基于SWF的在线学习和推断，适用于任何单调、凹凸且利普希茨连续的SWF。我们的关键发现是，单调性本身足以将置信序列从个体效用提升到任何时候都有效的最优福利界上。在此基础上，我们提出了SWF-UCB，一种不依赖特定SWF的在线学习算法，其达到近最优的$\tilde{O}(n+\sqrt{nkT})$后悔（对于每个时间步T，k个资源分配给n个个体）。我们将在三个规范不同的SWF家族上实例化我们的框架：加权幂均值、Kolm和辛普森，为每个提供定制的 oracle 算法。实验确认了$\sqrt{T}$的扩展，并揭示了k和SWF参数之间的丰富交互。该框架自然支持推断应用，如序列假设检验、最优停止和政策评估。
英文摘要：
In many real-world settings, a centralized decision-maker must repeatedly allocate finite resources to a population over multiple time steps. Individuals who receive a resource derive some stochastic utility; to characterize the population-level effects of an allocation, the expected individual utilities are then aggregated using a social welfare function (SWF). We formalize this setting and present a general confidence sequence framework for SWF-based online learning and inference, valid for any monotonic, concave, and Lipschitz-continuous SWF. Our key insight is that monotonicity alone suffices to lift confidence sequences from individual utilities to anytime-valid bounds on optimal welfare. Building on this foundation, we propose SWF-UCB, a SWF-agnostic online learning algorithm that achieves near-optimal $\tilde{O}(n+\sqrt{nkT})$ regret (for $k$ resources distributed among $n$ individuals at each of $T$ time steps). We instantiate our framework on three normatively distinct SWF families: Weighted Power Mean, Kolm, and Gini, providing bespoke oracle algorithms for each. Experiments confirm $\sqrt{T}$ scaling and reveal rich interactions between $k$ and SWF parameters. This framework naturally supports inference applications such as sequential hypothesis testing, optimal stopping, and policy evaluation.
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