Results 1 
8 of
8
Playing games with approximation algorithms
 In Proceedings of the 39 th annual ACM Symposium on Theory of Computing
, 2007
"... Abstract. In an online linear optimization problem, on each period t, an online algorithm chooses st ∈ S from a fixed (possibly infinite) set S of feasible decisions. Nature (who may be adversarial) chooses a weight vector wt ∈ R n, and the algorithm incurs cost c(st, wt), where c is a fixed cost fu ..."
Abstract

Cited by 27 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In an online linear optimization problem, on each period t, an online algorithm chooses st ∈ S from a fixed (possibly infinite) set S of feasible decisions. Nature (who may be adversarial) chooses a weight vector wt ∈ R n, and the algorithm incurs cost c(st, wt), where c is a fixed cost function that is linear in the weight vector. In the fullinformation setting, the vector wt is then revealed to the algorithm, and in the bandit setting, only the cost experienced, c(st, wt), is revealed. The goal of the online algorithm is to perform nearly as well as the best fixed s ∈ S in hindsight. Many repeated decisionmaking problems with weights fit naturally into this framework, such as online shortestpath, online TSP, online clustering, and online weighted set cover. Previously, it was shown how to convert any efficient exact offline optimization algorithm for such a problem into an efficient online algorithm in both the fullinformation and the bandit settings, with average cost nearly as good as that of the best fixed s ∈ S in hindsight. However, in the case where the offline algorithm is an approximation algorithm with ratio α> 1, the previous approach only worked for special types of approximation algorithms. We show how to convert any offline approximation algorithm for a linear optimization problem into a corresponding online approximation algorithm, with a polynomial blowup in runtime. If the offline algorithm has an αapproximation guarantee, then the expected cost of the online algorithm on any sequence is not much larger than α times that of the best s ∈ S, where the best is chosen with the benefit of hindsight. Our main innovation is combining Zinkevich’s algorithm for convex optimization with a geometric transformation that can be applied to any approximation algorithm. Standard techniques generalize the above result to the bandit setting, except that a “Barycentric Spanner ” for the problem is also (provably) necessary as input. Our algorithm can also be viewed as a method for playing large repeated games, where one can only compute approximate bestresponses, rather than bestresponses. 1. Introduction. In the 1950’s
A LearningBased Approach to Reactive Security
"... Abstract. Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our gametheo ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our gametheoretic model follows common practice in the security literature by making worstcase assumptions about the attacker: we grant the attacker complete knowledge of the defender’s strategy and do not require the attacker to act rationally. In this model, we bound the competitive ratio between a reactive defense algorithm (which is inspired by online learning theory) and the best fixed proactive defense. Additionally, we show that, unlike proactive defenses, this reactive strategy is robust to a lack of information about the attacker’s incentives and knowledge. 1
A new proof of the ellipsoid algorithm
, 2011
"... Linear programming is described by Howard Karloff as “the process of minimizing a linear objective function, subject to a finite number of linear equality and inequality constraints”. Linear optimization is one of the main tools used in applied mathematics and economics. It finds applications in fi ..."
Abstract
 Add to MetaCart
Linear programming is described by Howard Karloff as “the process of minimizing a linear objective function, subject to a finite number of linear equality and inequality constraints”. Linear optimization is one of the main tools used in applied mathematics and economics. It finds applications in fields ranging from image processing to logistic distribution of goods. The first algorithm that was used to solve linear programs was the Simplex Method. Other popular algorithms are the Interior Point Methods. In 1979, Leonid Khachiyan invented the first ever polynomialtime algorithm to solve linear programs, the Ellipsoid Algorithm (see [13] for the first appearance). The algorithm is based on the geometry of ellipsoids and how a sequence of progressively smaller ellipsoids contains convex sets. Its ability to run in polynomialtime makes the Ellipsoid Algorithm an important theoretical tool that can be used as the basis of many other algorithmic applications in various fields. In my senior thesis, I will present the details of the Ellipsoid Algorithm and my work
Maxmin Spanning trees
"... An alternate proof of NashWilliamsTutte Theorem via ..."
(Show Context)
Approximation Algorithms Going Online
, 2007
"... In an online linear optimization problem, on each period t, an online algorithm chooses st ∈ S from a fixed (possibly infinite) set S of feasible decisions. Nature (who may be adversarial) chooses a weight vector wt ∈ R n, and the algorithm incurs cost c(st, wt), where c is a fixed cost function tha ..."
Abstract
 Add to MetaCart
In an online linear optimization problem, on each period t, an online algorithm chooses st ∈ S from a fixed (possibly infinite) set S of feasible decisions. Nature (who may be adversarial) chooses a weight vector wt ∈ R n, and the algorithm incurs cost c(st, wt), where c is a fixed cost function that is linear in the weight vector. In the fullinformation setting, the vector wt is then revealed to the algorithm, and in the bandit setting, only the cost experienced, c(st, wt), is revealed. The goal of the online algorithm is to perform nearly as well as the best fixed s ∈ S in hindsight. Many repeated decisionmaking problems with weights fit naturally into this framework, such as online shortestpath, online TSP, online clustering, and online weighted set cover. Previously, it was shown how to convert any efficient exact offline optimization algorithm for such a problem into an efficient online bandit algorithm in both the fullinformation and the bandit settings, with average cost nearly as good as that of the best fixed s ∈ S in hindsight. However, in the case where the offline algorithm is an approximation algorithm with ratio α> 1, the previous approach only worked for special types of approximation algorithms. We show how to convert any efficient offline αapproximation algorithm for a linear optimization problem into an efficient algorithm for the corresponding online problem, with average cost not much larger than α times that of the best s ∈ S, in both the fullinformation and the bandit settings. Our main innovation is in the fullinformation setting:
A Learning Perspective on Selfish Behavior in Games
, 2009
"... Computer systems increasingly involve the interaction of multiple selfinterested agents. The designers of these systems have objectives they wish to optimize, but by allowing selfish agents to interact in the system, they lose the ability to directly control behavior. What is lost by this lack of ..."
Abstract
 Add to MetaCart
Computer systems increasingly involve the interaction of multiple selfinterested agents. The designers of these systems have objectives they wish to optimize, but by allowing selfish agents to interact in the system, they lose the ability to directly control behavior. What is lost by this lack of centralized control? What are the likely outcomes of selfish behavior? In this work, we consider learning dynamics as a tool for better classifying and understanding outcomes of selfish behavior in games. In particular, when such learning algorithms exist and are efficient, we propose “regretminimization” as a criterion for selfinterested behavior and study the systemwide effects in broad classes of games when players achieve this criterion. In addition, we present a general transformation from offline approximation algorithms for linear optimization problems to online algorithms that achieve low regret.
4. TITLE AND SUBTITLE
, 2010
"... Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments ..."
Abstract
 Add to MetaCart
(Show Context)
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,