Online Social Welfare Function-based Resource Allocation

2026-02-01

AI Summary

This work addresses the challenge of effectively aggregating individual stochastic utilities to optimize collective welfare in multi-round resource allocation under arbitrary monotonic, concave, and Lipschitz-continuous social welfare functions (SWFs). The key contribution is a novel confidence sequence framework that, for the first time, establishes that monotonicity alone suffices to lift individual utility confidence sequences to anytime-valid bounds on social welfare. Building on this insight, the authors propose the SWF-UCB algorithm, which unifies treatment across diverse SWFs—including weighted power means, Kolm, and Gini—achieving a near-optimal regret bound of $\tilde{O}(n + \sqrt{nkT})$. Empirical evaluations confirm the predicted $\sqrt{T}$ scaling and uncover intricate interactions between resource availability and SWF-specific parameters.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• resource allocation
• social welfare function
• online learning
• stochastic utility
• sequential decision-making

Innovation

• social welfare function
• confidence sequences
• online learning
• regret minimization
• resource allocation