Multi-objective Optimization Methods for Allocation and Prediction

In this thesis we focus on two different aspects of auctions and we employ techniques and methods from both operations research and computer science. _First,_ we study the allocation of tasks to agents at the end of an auction. Usually, tasks are allocated in such a way that minimizes the total cost for the auctioneer. This allocation is optimal in a one-shot auction, but if the auction is repeated, this can have negative consequences for the results in the long run. Therefore, we consider a fair allocation, which costs slightly more in a one-shot auction, but has positive effects on the participation level of agents and the total cost for the auctioneer in repeated auctions. _Second,_ we consider the auction design. How an auction is set up, like which tasks should be auctioned first, or what the starting price should be, impacts the result. Usually there are experts who know what has occurred in previous auctions and how a future auction should be designed in order to obtain the best results. However, historical auctions can obtain so much information that experts overlook things. We use a combination of machine learning and optimization models to extract information from historical auctions and use this information to help design future auctions for better results

Auction optimization using regression trees and linear models as integer programs

In a sequential auction with multiple bidding agents, the problem of determining the ordering of the items to sell in order to maximize the expected revenue is highly challenging. The challenge is largely due to the fact that the autonomy and private information of the agents heavily influence the outcome of the auction.The main contribution of this paper is two-fold. First, we demonstrate how to apply machine learning techniques to solve the optimal ordering problem in sequential auctions. We learn regression models from historical auctions, which are subsequently used to predict the expected value of orderings for new auctions. Given the learned models, we propose two types of optimization methods: a black-box best-first search approach, and a novel white-box approach that maps learned regression models to integer linear programs (ILP), which can then be solved by any ILP-solver. Although the studied auction design problem is hard, our proposed optimization methods obtain good orderings with high revenues.Our second main contribution is the insight that the internal structure of regression models can be efficiently evaluated inside an ILP solver for optimization purposes. To this end, we provide efficient encodings of regression trees and linear regression models as ILP constraints. This new way of using learned models for optimization is promising. As the experimental results show, it significantly outperforms the black-box best-first search in nearly all settings