A Typed Language for Truthful One-Dimensional Mechanism Design

We first introduce a very simple typed language for expressing allocation algorithms that allows automatic verification that an algorithm is monotonic and therefore truthful. The analysis of truthfulness is accomplished using a syntax-directed transformation which constructs a proof of monotonicity based on an exhaustive critical-value analysis of the algorithm. We then define a more high-level, general-purpose programming language with typical constructs, such as those for defining recursive functions, along with primitives that match allocation algorithm combinators found in the work of Mu'alem and Nisan [10]. We demonstrate how this language can be used to combine both primitive and user-defined combinators, allowing it to capture a collection of basic truthful allocation algorithms. In addition to demonstrating the value of programming language design techniques in application to a specific domain, this work suggests a blueprint for interactive tools that can be used to teach the simple principles of truthful mechanism desig

05011 Abstracts Collection -- Computing and Markets

From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve

Second-price auctions with reserve play a critical role for modern search engine and popular online sites since the revenue of these companies often directly de- pends on the outcome of such auctions. The choice of the reserve price is the main mechanism through which the auction revenue can be influenced in these electronic markets. We cast the problem of selecting the reserve price to optimize revenue as a learning problem and present a full theoretical analysis dealing with the complex properties of the corresponding loss function. We further give novel algorithms for solving this problem and report the results of several experiments in both synthetic and real data demonstrating their effectiveness.Comment: Accepted at ICML 201

Multi-objective optimization in graphical models

Many real-life optimization problems are combinatorial, i.e. they concern a choice of the best solution from a finite but exponentially large set of alternatives. Besides, the solution quality of many of these problems can often be evaluated from several points of view (a.k.a. criteria). In that case, each criterion may be described by a different objective function. Some important and well-known multicriteria scenarios are: · In investment optimization one wants to minimize risk and maximize benefits. · In travel scheduling one wants to minimize time and cost. · In circuit design one wants to minimize circuit area, energy consumption and maximize speed. · In knapsack problems one wants to minimize load weight and/or volume and maximize its economical value. The previous examples illustrate that, in many cases, these multiple criteria are incommensurate (i.e., it is difficult or impossible to combine them into a single criterion) and conflicting (i.e., solutions that are good with respect one criterion are likely to be bad with respect to another). Taking into account simultaneously the different criteria is not trivial and several notions of optimality have been proposed. Independently of the chosen notion of optimality, computing optimal solutions represents an important current research challenge. Graphical models are a knowledge representation tool widely used in the Artificial Intelligence field. They seem to be specially suitable for combinatorial problems. Roughly, graphical models are graphs in which nodes represent variables and the (lack of) arcs represent conditional independence assumptions. In addition to the graph structure, it is necessary to specify its micro-structure which tells how particular combinations of instantiations of interdependent variables interact. The graphical model framework provides a unifying way to model a broad spectrum of systems and a collection of general algorithms to efficiently solve them. In this Thesis we integrate multi-objective optimization problems into the graphical model paradigm and study how algorithmic techniques developed in the graphical model context can be extended to multi-objective optimization problems. As we show, multiobjective optimization problems can be formalized as a particular case of graphical models using the semiring-based framework. It is, to the best of our knowledge, the first time that graphical models in general, and semiring-based problems in particular are used to model an optimization problem in which the objective function is partially ordered. Moreover, we show that most of the solving techniques for mono-objective optimization problems can be naturally extended to the multi-objective context. The result of our work is the mathematical formalization of multi-objective optimization problems and the development of a set of multiobjective solving algorithms that have been proved to be efficient in a number of benchmarks.Muchos problemas reales de optimización son combinatorios, es decir, requieren de la elección de la mejor solución (o solución óptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Además, la mejor solución de muchos de estos problemas es, a menudo, evaluada desde varios puntos de vista (también llamados criterios). Es este caso, cada criterio puede ser descrito por una función objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes: · En optimización de inversiones se pretende minimizar los riesgos y maximizar los beneficios. · En la programación de viajes se quiere reducir el tiempo de viaje y los costes. · En el diseño de circuitos se quiere reducir al mínimo la zona ocupada del circuito, el consumo de energía y maximizar la velocidad. · En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor económico. Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es difícil o imposible combinar todos ellos en un único criterio) y están en conflicto (es decir, soluciones que son buenas con respecto a un criterio es probable que sean malas con respecto a otra). Tener en cuenta de forma simultánea todos estos criterios no es trivial y para ello se han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el cómputo de soluciones óptimas representa un importante desafío para la investigación actual. Los modelos gráficos son una herramienta para la represetanción del conocimiento ampliamente utilizados en el campo de la Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gráficos son grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Además de la estructura gráfica, es necesario especificar su (micro-estructura) que indica cómo interactúan instanciaciones concretas de variables interdependientes. Los modelos gráficos proporcionan un marco capaz de unificar el modelado de un espectro amplio de sistemas y un conjunto de algoritmos generales capaces de resolverlos eficientemente. En esta tesis integramos problemas de optimización multi-objetivo en el contexto de los modelos gráficos y estudiamos cómo diversas técnicas algorítmicas desarrolladas dentro del marco de los modelos gráficos se pueden extender a problemas de optimización multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo gráfico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, ésta es la primera vez que los modelos gráficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimización cuya función objetivo está parcialmente ordenada. Además, mostramos que la mayoría de técnicas para resolver problemas monoobjetivo se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalización matemática de problemas de optimización multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo de problemas. Además, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks

A Primal-Dual Analysis of Monotone Submodular Maximization

In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This problem and its special case, the maximum $k$-coverage problem, have a wide range of applications in various fields including operations research, machine learning, and economics. While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate may be used in practice to certify much stronger guarantees than the worst-case $(1-1/e)$ approximation factor