Machine Learning-Powered Combinatorial Clock Auction

TL;DR

This paper designs an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries and introduces an efficient method for determining the demand query with the highest clearing potential, for which the paper provides a theoretical foundation.

Abstract

We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, several papers have recently proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most important information from bidders. However, from a practical point of view, the main shortcoming of this prior work is that those designs elicit bidders' preferences via value queries (i.e., ``What is your value for the bundle $\{A,B\}$?''). In most real-world ICA domains, value queries are considered impractical, since they impose an unrealistically high cognitive burden on bidders, which is why they are not used in practice. In this paper, we address this shortcoming by designing an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries (i.e., ``At prices $p$, what is your most preferred bundle of items?''). We make two key technical contributions: First, we present a novel method for training an ML model on demand queries. Second, based on those trained ML models, we introduce an efficient method for determining the demand query with the highest clearing potential, for which we also provide a theoretical foundation. We experimentally evaluate our ML-based demand query mechanism in several spectrum auction domains and compare it against the most established real-world ICA: the combinatorial clock auction (CCA). Our mechanism significantly outperforms the CCA in terms of efficiency in all domains, it achieves higher efficiency in a significantly reduced number of rounds, and, using linear prices, it exhibits vastly higher clearing potential. Thus, with this paper we bridge the gap between research and practice and propose the first practical ML-powered ICA.

Figures (2)

• Figure 1: Scaled prediction vs. true plot of a trained mMVNN via \ref{['alg:train_on_dqs']} for the national bidder in the MRVM domain (see \ref{['sec:experiments']}).
• Figure 2: Efficiency path plots in SATS for ML-CCA and CCA both after clock bids (solid lines) and raised clock bids (dashed lines). Averaged over 100 runs including a 95% CI. The dashed black vertical line indicates the value of $Q^{\textrm{\tiny init}}$.

Theorems & Definitions (10)

• Definition 1: Multiset MVNN
• Theorem 1: Multiset Universality
• proof
• Definition 2: Indirect Utility and Revenue
• Definition 3: Clearing Prices
• Theorem 2
• proof
• Remark 1: Constraint \ref{['eq:app:corollary_constraint']}
• Theorem 3
• proof