Online Nash Welfare Maximization Without Predictions

TL;DR

This paper studies online Nash welfare maximization without predictions, proposing algorithms with competitive ratios depending on utility ratios and the number of agents, advancing fairness and efficiency in resource allocation.

Contribution

It introduces the first online algorithms for Nash welfare maximization without predictions, with competitive ratios based on utility ratio bounds and agent count.

Findings

Algorithms with competitive ratios depending on utility ratios and number of agents.

Analysis of utility ratio bounds for fairness and efficiency.

Extension of online Nash welfare maximization theory without predictive information.

Abstract

The maximization of Nash welfare, which equals the geometric mean of agents' utilities, is widely studied because it balances efficiency and fairness in resource allocation problems. Banerjee, Gkatzelis, Gorokh, and Jin (2022) recently introduced the model of online Nash welfare maximization for $T$ divisible items and $N$ agents with additive utilities with predictions of each agent's utility for receiving all items. They gave online algorithms whose competitive ratios are logarithmic. We initiate the study of online Nash welfare maximization \emph{without predictions}, assuming either that the agents' utilities for receiving all items differ by a bounded ratio, or that their utilities for the Nash welfare maximizing allocation differ by a bounded ratio. We design online algorithms whose competitive ratios only depend on the logarithms of the aforementioned ratios of agents' utilities and the number of agents.