# Online Social Welfare Function-based Resource Allocation

arXiv: https://arxiv.org/abs/2602.01400 · HTML: https://mlsanity.com/paper/2602.01400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Fairness of Exposure in Stochastic Bandits](https://mlsanity.com/paper/2103.02735/) (2021)
- [Restless-UCB, an Efficient and Low-complexity Algorithm for Online Restless Bandits](https://mlsanity.com/paper/2011.02664/) (2020)
- [An Axiomatic Theory of Provably-Fair Welfare-Centric Machine Learning](https://mlsanity.com/paper/2104.14504/) (2021)
- [Fairness and Welfare Quantification for Regret in Multi-Armed Bandits](https://mlsanity.com/paper/2205.13930/) (2022)
- [Learning Social Welfare Functions](https://mlsanity.com/paper/2405.17700/) (2024)
- [p-Mean Regret for Stochastic Bandits](https://mlsanity.com/paper/2412.10751/) (2024)
- [Stochastic Bandits for Egalitarian Assignment](https://mlsanity.com/paper/2410.05856/) (2024)
- [Revisiting Social Welfare in Bandits: UCB is (Nearly) All You Need](https://mlsanity.com/paper/2510.21312/) (2025)

## Abstract (arXiv)

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 tildeO(n+√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 √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.