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

Leo Landolt, Anna Maddux, Andreas Schlaginhaufen, Saurabh Vaishampayan, Maryam Kamgarpour

TL;DR

The paper addresses resource allocation with private costs by eliciting truthful preference feedback using a VCG-based mechanism. It blends preference-based learning under a Bradley–Terry model with D-optimal query design and maximum-likelihood estimation to infer agent costs, then uses VCG payments to incentivize truthful reporting. The authors prove approximate truthfulness and efficiency in the one-shot setting with a learning error that decays as $\tilde{\mathcal O}(K^{-1/2})$, and establish sublinear welfare regret $\tilde{\mathcal O}(T^{2/3})$ in an online, multi-round setting. A numerical case study on demand response in local electricity markets demonstrates convergence to socially efficient allocations while mitigating strategic misreporting.

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.

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

TL;DR

The paper addresses resource allocation with private costs by eliciting truthful preference feedback using a VCG-based mechanism. It blends preference-based learning under a Bradley–Terry model with D-optimal query design and maximum-likelihood estimation to infer agent costs, then uses VCG payments to incentivize truthful reporting. The authors prove approximate truthfulness and efficiency in the one-shot setting with a learning error that decays as , and establish sublinear welfare regret in an online, multi-round setting. A numerical case study on demand response in local electricity markets demonstrates convergence to socially efficient allocations while mitigating strategic misreporting.

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 for preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of after rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.
Paper Structure (38 sections, 6 theorems, 65 equations, 2 figures, 2 tables, 3 algorithms)

This paper contains 38 sections, 6 theorems, 65 equations, 2 figures, 2 tables, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Related work
  3. Contributions
  4. Notation
  5. BACKGROUND AND PROBLEM FORMULATION
  6. Auctions
  7. Preference model
  8. Problem formulation
  9. ONE-SHOT GAME: ALGORITHM AND ANALYSIS
  10. Algorithm components
  11. Cost estimation.
  12. Optimal design.
  13. VCG mechanism.
  14. Algorithm
  15. Theoretical guarantees
  16. ...and 23 more sections

Key Result

Lemma 1

Under Assumption as:linear-cost, supppose for each agent $i$, the planner selects $K>d(d+1)/2$ queries by $\textsc{D-Optimal-Design}(K)$. If the agents provide truthful preference feedback $\bar{\mathcal{D}}_i = \{(x_{i,k}, \bar{y}_{i, k})\}_{k=1}^K$, then with probability at least $1-\delta$, with $\epsilon_K(\delta) \in \tilde{\mathcal{O}}\left( d \sqrt{\log(1/\delta) / K}\right)$.

Figures (2)

  • Figure 1: Impact of misreporting on a given agent's utility in the one-shot game under (a) the pay-as-bid mechanism and (b) the VCG mechanism. We show the utility gain $u_i(\hat{a}(\mathcal{D}_i,\mathcal{D}_{-i})) - u_i(\hat{a}(\bar{\mathcal{D}}_i,\mathcal{D}_{-i}))$ across independent runs, with the worst-case outcome highlighted.
  • Figure 2: Mechanism's performance in terms (a) social cost gap $J(\hat{a}(\bar{\mathcal{D}}))-J(a^*)$ in the one-shot game and (b) average welfare regret $R^w(T)/T$ in the multi-round game. Both are normalized by the optimal social cost $J(a^*)$.

Theorems & Definitions (12)

  • Definition 1: Bradley--Terry model
  • Lemma 1
  • Definition 2: VCG mechanism
  • Theorem 1
  • Theorem 2
  • Lemma 2: schlaginhaufen2025efficient, Lemma A.1
  • Lemma 3
  • proof
  • proof
  • proof
  • ...and 2 more