Repeated Descent: A Framework for Online Budget-Feasible Auctions

2026-05-31

AI Summary

This work addresses online budget-feasible procurement auctions under hard budget constraints, where agents arrive in random order, accept only irrevocable take-it-or-leave-it offers, and provide no cost feedback. The authors propose the Repeated Descent (RED) framework, which integrates adaptive linear pricing, agent quota allocation, and random subsampling to maximize non-monotone submodular value functions. RED achieves a constant competitive ratio of 1/1046 for non-monotone submodular valuations—the first such guarantee in this setting—improving upon prior results by several orders of magnitude. Additionally, the paper establishes a lower bound of Ω(log n / (log log n)²) on the competitive ratio of any online mechanism for XOS valuations, highlighting inherent limitations in this more general class.

Abstract

We study budget feasible procurement auctions, in which $n$ agents, each with a privately held service cost, offer their services to an employer. The employer seeks to maximize a public submodular valuation function over the set of hired agents, while facing a hard budget constraint. We consider an online posted-price setting, in which agents arrive in a uniformly random order (a.k.a. \emph{secretary arrivals}) and the employer must make irrevocable take-it-or-leave-it offers upon their arrival. The employer does not get any feedback about the agent service costs other than whether they accept the offer or not. We introduce Repeated Descent (a.k.a. \RED), a deterministic framework based on adaptive linear posted pricing. \RED enforces budget feasibility by adaptively adjusting its pricing and balancing each pricing level with the number of agents considered in it. Using \RED as the main building block, we obtain a $1046$-competitive posted-price mechanism for online budget feasible auctions with secretary agent arrivals and submodular valuations, thus improving on the previously best known ratio of (Charalampopoulos et al., EC 2025) by several orders of magnitude. Combining \RED with random subsampling, we obtain the first constant-competitive posted-price budget feasible mechanism for non-monotone submodular valuations. On the negative side, we show that every online budget feasible mechanism with XOS valuations has a competitive ratio of $Ω\!\left(\tfrac{\log n}{(\log\log n)^2}\right)$.

Problem

• budget-feasible auctions
• online algorithms
• submodular valuations
• secretary arrivals
• posted-price mechanisms

Innovation

• Repeated Descent
• budget-feasible auctions
• online posted-price mechanism
• submodular valuations
• secretary arrivals