Online Social Welfare Function-based Resource Allocation

TL;DR

This paper introduces a general framework for online resource allocation based on social welfare functions, providing confidence bounds, a near-optimal learning algorithm, and applications to inference tasks.

Contribution

It formalizes SWF-based online learning, develops confidence sequences for welfare bounds, and proposes SWF-UCB for near-optimal regret in resource allocation.

Findings

Confidence sequences valid for any monotonic, concave, Lipschitz SWF.

SWF-UCB achieves near-optimal regret of ten+b7b7b7T.

Experiments demonstrate b7b7 scaling and interactions between resources and SWF parameters.

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.