Bayesian Optimization-based Combinatorial Assignment
This addresses the problem of efficient resource allocation in combinatorial auctions for domains like spectrum auctions, representing an incremental improvement over prior machine learning-based elicitation methods.
The paper tackles the challenge of combinatorial assignment, where bundle space grows exponentially, by proposing a Bayesian optimization-based mechanism (BOCA) that models uncertainty over unelicited bundles to improve preference elicitation. Results show BOCA achieves higher allocative efficiency than state-of-the-art approaches in spectrum auction domains.
We study the combinatorial assignment domain, which includes combinatorial auctions and course allocation. 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-based preference elicitation algorithms that aim to elicit only the most important information from agents. However, the main shortcoming of this prior work is that it does not model a mechanism's uncertainty over values for not yet elicited bundles. In this paper, we address this shortcoming by presenting a Bayesian optimization-based combinatorial assignment (BOCA) mechanism. Our key technical contribution is to integrate a method for capturing model uncertainty into an iterative combinatorial auction mechanism. Concretely, we design a new method for estimating an upper uncertainty bound that can be used to define an acquisition function to determine the next query to the agents. This enables the mechanism to properly explore (and not just exploit) the bundle space during its preference elicitation phase. We run computational experiments in several spectrum auction domains to evaluate BOCA's performance. Our results show that BOCA achieves higher allocative efficiency than state-of-the-art approaches.