Learning Truthful Mechanisms without Discretization

Yunxuan Ma, Steven Wang, Zhijian Duan, Yukun Cheng, Xiaotie Deng

Keywords: Automated Mechanism Design, Differentiable Economics, Deep Learning, First-Order Algorithm

TL;DR: This paper introduces a discretization-free algorithm to learn optimal truthful mechanisms.

Abstract:

This paper introduces TEDI (Truthful, Expressive, and Dimension-Insensitive approach), a discretization-free algorithm to learn truthful and utility-maximizing mechanisms. We apply TEDI to an auction scenario involving reproducible goods with production costs and supply exceeding demand.
Existing learning-based approaches often rely on discretization of outcome spaces to ensure truthfulness, which leads to inefficiency with increasing problem size. To address this limitation, we formalize the concept of \emph{pricing rules}, defined as functions that map outcomes to prices. Based on this concept, we propose a novel menu mechanism, which can be equivalent to a truthful direct mechanism under specific conditions.
The core idea of TEDI lies in its parameterization of pricing rules using Partial GroupMax Network, a new network architecture designed to universally approximate partial convex functions. To learn optimal pricing rules, we develop novel training techniques, including \emph{covariance trick} and \emph{continuous sampling}, to derive unbiased gradient estimators compatible with first-order optimization.
Theoretical analysis establishes that TEDI guarantees truthfulness, full expressiveness, and dimension-insensitivity.
Experimental evaluation in the studied auction setting demonstrates that TEDI achieves strong performance, competitive with or exceeding state-of-the-art methods.

This work presents the first approaches to learn truthful mechanisms without outcome discretization, thereby enhancing algorithmic efficiency. The proposed concepts, network architecture, and learning techniques might offer potential value and provide new insights for automated mechanism design and differentiable economics.

Area: Learning and Adaptation (LEARN)

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Submission Number: 344