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2,442
Beyond Logarithmic Bounds in Online Learning
"... We prove logarithmic regret bounds that depend on the loss L ∗ T of the competitor rather than on the number T of time steps. In the general online convex optimization setting, our bounds hold for any smooth and expconcave loss (such as the square loss or the logistic loss). This bridges the gap be ..."
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Cited by 3 (2 self)
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We prove logarithmic regret bounds that depend on the loss L ∗ T of the competitor rather than on the number T of time steps. In the general online convex optimization setting, our bounds hold for any smooth and expconcave loss (such as the square loss or the logistic loss). This bridges the gap
Logarithmic Bounds on an Algorithm for Asymmetric TSP
, 2005
"... In 1982 Frieze, Galbiati and Maffioli (Networks 12:2339) published their famous algorithm for approximating the TSP tour in an asymmetric graph with triangle inequality. They show that the algorithm approximates the TSP tour within a factor of log 2 n. We construct a family of graphs for which the ..."
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In 1982 Frieze, Galbiati and Maffioli (Networks 12:2339) published their famous algorithm for approximating the TSP tour in an asymmetric graph with triangle inequality. They show that the algorithm approximates the TSP tour within a factor of log 2 n. We construct a family of graphs for which the algorithm (with some implementation details specified by us) gives an approximation which is log 2 n/(2+o(1)) times the optimum solution. This shows that the analysis by Frieze et al. is tight up to a constant factor and can hopefully give deeper understanding of the problem and new ideas in developing an improved approximation algorithm.
Logarithmic Bounds for Infinite Prandtl Number Rotating Convection
 J. Math. Phys
, 2000
"... this paper is to provide a similar bound in the rotating case, allowing for finite values of E. As we shall see the correction vanishes as E !1, and we recover the above logarithmic bound even for rather strong rotation (E R ..."
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Cited by 4 (1 self)
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this paper is to provide a similar bound in the rotating case, allowing for finite values of E. As we shall see the correction vanishes as E !1, and we recover the above logarithmic bound even for rather strong rotation (E R
Logarithmic bounds for translationinvariant equations in squares
 Int. Math. Research Not
"... ar ..."
Logarithmic bounds on Sobolev norms for time dependent linear Schröinger equations
 Comm. Part. Di . Eq
, 2008
"... 1. Introduction and statement of the theorem 2. Periodic approximations and Floquet solutions 3. Some a priori estimates ..."
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Cited by 12 (0 self)
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1. Introduction and statement of the theorem 2. Periodic approximations and Floquet solutions 3. Some a priori estimates
Finitetime analysis of the multiarmed bandit problem
 Machine Learning
, 2002
"... Abstract. Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy’s success in addressing ..."
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Cited by 817 (15 self)
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to grow at least logarithmically in the number of plays. Since then, policies which asymptotically achieve this regret have been devised by Lai and Robbins and many others. In this work we show that the optimal logarithmic regret is also achievable uniformly over time, with simple and efficient policies
Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm
 Machine Learning
, 1988
"... learning Boolean functions, linearthreshold algorithms Abstract. Valiant (1984) and others have studied the problem of learning various classes of Boolean functions from examples. Here we discuss incremental learning of these functions. We consider a setting in which the learner responds to each ex ..."
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Cited by 773 (5 self)
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algorithms are available that make a bounded number of mistakes, with the bound independent of the number of examples seen by the learner. We present one such algorithm that learns disjunctive Boolean functions, along with variants for learning other classes of Boolean functions. The basic method can
Lower Bounds for Discrete Logarithms and Related Problems
, 1997
"... . This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is ..."
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Cited by 288 (11 self)
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. This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element
Strengths and weaknesses of quantum computing
, 1996
"... Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both solv ..."
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Cited by 381 (10 self)
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Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both
A Parallel Repetition Theorem
 SIAM Journal on Computing
, 1998
"... We show that a parallel repetition of any twoprover oneround proof system (MIP(2, 1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The constant in the exponent (in our analysis) depends only on the original probability of error and on the t ..."
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Cited by 362 (9 self)
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We show that a parallel repetition of any twoprover oneround proof system (MIP(2, 1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The constant in the exponent (in our analysis) depends only on the original probability of error
Results 1  10
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2,442