Strategic algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 193-201).Classical algorithms from theoretical computer science arise time and again in practice. However,a practical situations typically do not fit precisely into the traditional theoretical models. Additional necessary components are, for example, uncertainty and economic incentives. Therefore, modem algorithm design is calling for more interdisciplinary approaches, as well as for deeper theoretical understanding, so that the algorithms can apply to more realistic settings and complex systems. Consider, for instance, the classical shortest path algorithm, which, given a graph with specified edge weights, seeks the path minimizing the total weight from a source to a destination. In practice, the edge weights are often uncertain and it is not even clear what we mean by shortest path anymore: is it the path that minimizes the expected weight? Or its variance, or some another metric? With a risk-averse objective function that takes into account both mean and standard deviation, we run into nonconvex optimization challenges that require new theory beyond classical shortest path algorithm design. Yet another shortest path application, routing of packets in the Internet, needs to further incorporate economic incentives to reflect the various business relationships among the Internet Service Providers that affect the choice of packet routes. Strategic Algorithms are algorithms that integrate optimization, uncertainty and economic modeling into algorithm design, with the goal of bringing about new theoretical developments and solving practical applications arising in complex computational-economic systems.(cont.) In short, this thesis contributes new algorithms and their underlying theory at the interface of optimization, uncertainty and economics. Although the interplay of these disciplines is present in various forms in our work, for the sake of presentation we have divided the material into three categories: 1. In Part I we investigate algorithms at the intersection of Optimization and Uncertainty. The key conceptual contribution in this part is discovering a novel connection between stochastic and nonconvex optimization. Traditional algorithm design has not taken into account the risk inherent in stochastic optimization problems. We consider natural objectives that incorporate risk, which tum out equivalent to certain nonconvex problems from the realm of continuous optimization. As a result, our work advances the state of art in both stochastic and in nonconvex optimization, presenting new complexity results and proposing general purpose efficient approximation algorithms, some of which have shown promising practical performance and have been implemented in a real traffic prediction and navigation system. 2. Part II proposes new algorithm and mechanism design at the intersection of Uncertainty and Economics. In Part I we postulate that the random variables in our models come from given distributions. However, determining those distributions or their parameters is a challenging and fundamental problem in itself. A tool from Economics that has recently gained momentum for measuring the probability distribution of a random variable is an information or prediction market. Such markets, most popularly known for predicting the outcomes of political elections or other events of interest, have shown remarkable accuracy in practice, though at the same time have left open the theoretical and strategic analysis of current implementations, as well as the need for new and improved designs which handle more complex outcome spaces (probability distribution functions) as opposed to binary or n-ary valued distributions. The contributions of this part include a unified strategic analysis of different prediction market designs that have been implemented in practice.(cont.) We also offer new market designs for handling exponentially large outcome spaces stemming from ranking or permutation-type outcomes, together with algorithmic and complexity analysis. 3. In Part III we consider the interplay of optimization and economics in the context of network routing. This part is motivated by the network of autonomous systems in the Internet where each portion of the network is controlled by an Internet service provider, namely by a self-interested economic agent. The business incentives do not exist merely in addition to the computer protocols governing the network. Although they are not currently integrated in those protocols and are decided largely via private contracting and negotiations, these economic considerations are a principal factor that determines how packets are routed. And vice versa, the demand and flow of network traffic fundamentally affect provider contracts and prices. The contributions of this part are the design and analysis of economic mechanisms for network routing. The mechanisms are based on first- and second-price auctions (the so-called Vickrey-Clarke-Groves, or VCG mechanisms). We first analyze the equilibria and prices resulting from these mechanisms. We then investigate the compatibility of the better understood VCG-mechanisms with the current inter-domain routing protocols, and we demonstrate the critical importance of correct modeling and how it affects the complexity and algorithms necessary to implement the economic mechanisms.by Evdokia Velinova Nikolova.Ph.D