On sparse approximations to randomized strategies and convex combinations
TLDR
An approximation lemma is presented and it is shown that in all cases arbitrary probability vectors can be replaced by sparse ones (with only logarithmically many positive entries) without losing too much performance.About:
This article is published in Linear Algebra and its Applications.The article was published on 1994-03-01 and is currently open access. It has received 135 citations till now. The article focuses on the topics: Sparse approximation & Convex combination.read more
Citations
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Proceedings ArticleDOI
Playing large games using simple strategies
TL;DR: The existence of ε-Nash equilibrium strategies with support logarithmic in the number of pure strategies is proved and it is proved that if the payoff matrices of a two person game have low rank then the game has an exact Nash equilibrium with small support.
Proceedings ArticleDOI
Randomized rounding without solving the linear program
TL;DR: A new technique called oblivious rounding is introduced a variant of randomized rounding that avoids the bottleneck of first solving the linear program, which yields more efficient algorithms and brings probabilistic methods to bear on a new class of problems.
Proceedings ArticleDOI
Progress in approximate nash equilibria
TL;DR: A polynomial algorithm is given for computing an ε-approximate Nash equilibrium in 2-player games with ε ≈ .38; the algorithm computes equilibria with arbitrarily large supports.
Posted Content
Randomized Rounding without Solving the Linear Program
TL;DR: In this article, the authors explore how to avoid the time bottleneck for randomized rounding algorithms for packing and covering linear programs (either mixed integer linear programs or linear programs with no negative coefficients).
Book ChapterDOI
A note on approximate nash equilibria
TL;DR: A simple, linear-time algorithm is given, examining just two strategies per player and resulting in a -approximate Nash equilibrium in any 2-player game, and it is shown that an approximation of is possible contingent upon a graph-theoretic conjecture.
References
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Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Book
The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
Book ChapterDOI
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
TL;DR: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady.