Online Budget-Feasible Mechanism Design with Predictions

TL;DR

This work studies online budget-feasible mechanism design under a learning-augmented framework for submodular valuations, where a prediction of the offline optimum value $v(S^*)$ is provided. It develops two families of universally truthful, budget-feasible mechanisms that leverage the prediction to achieve constant consistency and robustness in the online random-order model, with explicit tradeoffs controlled by a tolerance parameter $ au$ and by a sampling parameter $k$, yielding notable improvements (e.g., consistency as low as $6$ in favorable regimes and robustness up to $146$) over the state of the art. The paper further extends the design to non-monotone submodular objectives, providing analogous guarantees (e.g., consistency-robustness pairs like $95$/$280$ in one mechanism and $228$/$818$ in the non-monotone variants), and establishes a strong offline impossibility showing predictions rarely improve the best possible approximation beyond a constant factor for the offline problem. Overall, the results demonstrate that predictions on the offline optimum can meaningfully enhance online procurement mechanisms, while highlighting fundamental limits in the offline setting and suggesting directions for stronger or alternative predictions. The mechanisms run in polynomial time with access to a value oracle for $v$, and rely on posted-price strategies calibrated by the prediction and sampling phases.

Abstract

Augmenting the input of algorithms with predictions is an algorithm design paradigm that suggests leveraging a (possibly erroneous) prediction to improve worst-case performance guarantees when the prediction is perfect (consistency), while also providing a performance guarantee when the prediction fails (robustness). Recently, Xu and Lu [2022] and Agrawal et al. [2024] proposed to consider settings with strategic agents under this framework. In this paper, we initiate the study of budget-feasible mechanism design with predictions. These mechanisms model a procurement auction scenario in which an auctioneer (buyer) with a strict budget constraint seeks to purchase goods or services from a set of strategic agents, so as to maximize her own valuation function. We focus on the online version of the problem where the arrival order of agents is random. We design mechanisms that are truthful, budget-feasible, and achieve a significantly improved competitive ratio for both monotone and non-monotone submodular valuation functions compared to their state-of-the-art counterparts without predictions. Our results assume access to a prediction for the value of the optimal solution to the offline problem. We complement our positive results by showing that for the offline version of the problem, access to predictions is mostly ineffective in improving approximation guarantees.

Figures (1)

• Figure 1: Illustration of the support of $P(5)$ (red dots) for $B = 5$.

Theorems & Definitions (46)

• Definition 2.1
• Theorem 2.2: NemhauserWF78
• Proposition 3.0: name=
• proof
• Lemma 3.1
• proof
• Theorem 3.2
• Corollary 3.3
• Corollary 3.4
• Lemma 3.5