Repeated Descent framework slashes auction budget waste by orders of magnitude

A team of computer scientists from the National Technical University of Athens — Andreas Charalampopoulos, Dimitris Fotakis, and Thanos Tolias — has released a new framework called Repeated Descent (RED) that tackles one of the hardest problems in algorithmic economics: online budget-feasible procurement auctions. In these auctions, an employer wants to hire agents (each with a private cost) to maximize a public submodular valuation function, all while staying under a hard budget. Agents arrive in random order (secretary model), and the employer must make irrevocable, take-it-or-leave-it offers without knowing their costs.

RED is a deterministic framework based on adaptive linear posted pricing. It enforces budget feasibility by dynamically adjusting prices and balancing each pricing level with the number of agents considered at that level. The main result: RED achieves a 1046-competitive posted-price mechanism for online budget-feasible auctions with secretary arrivals and submodular valuations, improving the previous best ratio (from Charalampopoulos et al., EC 2025) by several orders of magnitude. When combined with random subsampling, RED yields the first constant-competitive mechanism for non-monotone submodular valuations. On the negative side, the authors prove that any online budget-feasible mechanism for XOS valuations has a competitive ratio of Ω(log n / (log log n)^2), highlighting the limitations of the approach. The paper is available on arXiv (2606.01142) and is relevant for economists, platform designers, and anyone working on online allocation with budgets.