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

TL;DR

This paper introduces a mechanism combining preference-based learning with VCG payments to incentivize truthful reporting in resource allocation problems with strategic agents, achieving near-truthfulness and efficiency.

Contribution

It proposes a novel algorithm that integrates D-optimal design, maximum likelihood estimation, and VCG payments to address strategic misreporting in preference-based resource allocation.

Findings

Mechanism is approximately truthful and efficient with limited preference queries.

Guarantees asymptotic truthfulness and sublinear regret in online settings.

Validated through a demand response case study in electricity markets.

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 $\tilde{\mathcal O}(K^{-1/2})$ for $K$ preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of $\tilde{\mathcal O}(T^{2/3})$ after $T$ rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.