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

White-box optimization from historical data

Contains fulltext : 122450.pdf (preprint version ) (Open Access)BENELEARN 2013: Proceedings of the 22nd Belgian-Dutch Conference on Machine Learning, Nijmegen, 3 june 201

Participation behavior and social welfare in repeated task allocations

Task allocation problems have focused on achieving one-shot optimality. In practice, many task allocation problems are of repeated nature, where the allocation outcome of previous rounds may influence the participation of agents in subsequent rounds, and consequently, the quality of the allocations in the long term. We investigate how allocation influences agents' decision to participate using prospect theory, and simulate how agents' participation affects the system's long term social welfare. We compare two task allocation algorithms in this study, one only considering optimality in terms of costs and the other considering optimality in terms of primarily fairness and secondarily costs. The simulation results demonstrate that fairness incentivizes agents to keep participating and consequently leads to a higher social welfare

Fair task allocation in transportation

Task allocation problems have traditionally focused on cost optimization. However, more and more attention is being given to cases in which cost should not always be the sole or major consideration. In this paper we study a fair task allocation problem in transportation where an optimal allocation not only has low cost but more importantly, it distributes tasks as even as possible among heterogeneous participants who have different capacities and costs to execute tasks. To tackle this fair minimum cost allocation problem we analyze and solve it in two parts using two novel polynomial-time algorithms. We show that despite the new fairness criterion, the proposed algorithms can solve the fair minimum cost allocation problem optimally in polynomial time. In addition, we conduct an extensive set of experiments to investigate the trade-off between cost minimization and fairness. Our experimental results demonstrate the benefit of factoring fairness into task allocation. Among the majority of test instances, fairness comes with a very small price in terms of cost

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

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