Eliciting Truthful Feedback for Preference-Based Learning via the VCG Mechanism

2025-10-20

AI Summary

This paper studies resource allocation under strategic agents with unknown, misreportable cost functions, aiming to minimize social cost. We propose a novel framework integrating preference learning with the VCG mechanism: D-optimal query design elicits agents’ ordinal preferences; maximum-likelihood estimation infers their implicit cost parameters; and the inferred costs are embedded into a VCG-based allocation rule to ensure incentive compatibility and individual rationality. Theoretically, we establish that the social cost estimation error is Õ(K⁻¹/²) after K queries, and in the online T-round setting, the algorithm achieves Õ(T²/³) sublinear regret. The method supports both one-shot and dynamic allocation, simultaneously guaranteeing approximate optimality, truthfulness, and computational tractability. Numerical experiments demonstrate its effectiveness and robustness in power demand-response applications.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study resource allocation problems in which a central planner allocates resources among strategic agents with private cost functions in order to minimize a social cost, defined as an aggregate of the agents' costs. This setting poses two main challenges: (i) the agents' cost functions may be unknown to them or difficult to specify explicitly, and (ii) agents may misreport their costs strategically. To address these challenges, we propose an algorithm that combines preference-based learning with Vickrey-Clarke-Groves (VCG) payments to incentivize truthful reporting. Our algorithm selects informative preference queries via D-optimal design, estimates cost parameters through maximum likelihood, and computes VCG allocations and payments based on these estimates. In a one-shot setting, we prove that the mechanism is approximately truthful, individually rational, and efficient up to an error of $ ilde{mathcal O}(K^{-1/2})$ for $K$ preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of $ ilde{mathcal O}(T^{2/3})$ after $T$ rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.

Problem

• Allocating resources among strategic agents with private costs
• Incentivizing truthful reporting of unknown cost functions
• Minimizing social cost through preference-based learning mechanism

Innovation

• Combining preference-based learning with VCG payments
• Using D-optimal design for informative preference queries
• Estimating costs via maximum likelihood with VCG allocations