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The LastStep Minimax Algorithm
 Pages 279 290 of: Proc. 11th International Conference on Algorithmic Learning Theory
, 2000
"... We consider online density estimation with a parameterized density from an exponential family. In each trial t the learner predicts a parameter t . Then it receives an instance x t chosen by the adversary and incurs loss ln p(x t j t ) which is the negative loglikelihood of x t w.r.t. the predict ..."
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Cited by 17 (3 self)
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.r.t. the predicted density of the learner. The performance of the learner is measured by the regret dened as the total loss of the learner minus the total loss of the best parameter chosen oline. We develop an algorithm called the Laststep Minimax Algorithm that predicts with the minimax optimal parameter assuming
Minimax Programs
 University of California Press
, 1997
"... We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting spec ..."
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Cited by 482 (5 self)
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special case and present an efficient algorithm for its solution. 1 Introduction Over the last fifty years, thousands of problems of practical interest have been formulated as a linear program. Not only has the linear programming model proven to be widely applicable, but ongoing research has discovered
Achievability of Asymptotic Minimax Regret in Online and Batch Prediction
"... The normalized maximum likelihood model achieves the minimax coding (logloss) regret for data of fixed sample size n. However, it is a batch strategy, i.e., it requires that n be known in advance. Furthermore, it is computationally infeasible for most statistical models, and several computationally ..."
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, no online strategy can be asymptotically minimax. We prove that this holds under a slightly stronger definition of asymptotic minimaxity. Our numerical experiments support the conjecture about nonachievability by so called laststep minimax algorithms, which are independent of n. On the other hand, we show
No Free Lunch Theorems for Optimization
, 1997
"... A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performan ..."
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Cited by 961 (10 self)
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issues addressed include timevarying optimization problems and a priori “headtohead” minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems’ enforcing of a type of uniformity over all algorithms.
The adaptive LASSO and its oracle properties
 Journal of the American Statistical Association
"... The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain sc ..."
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Cited by 683 (10 self)
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as well as if the true underlying model were given in advance. Similar to the lasso, the adaptive lasso is shown to be nearminimax optimal. Furthermore, the adaptive lasso can be solved by the same efficient algorithm for solving the lasso. We also discuss the extension of the adaptive lasso
MediaBench: A Tool for Evaluating and Synthesizing Multimedia and Communications Systems
"... Over the last decade, significant advances have been made in compilation technology for capitalizing on instructionlevel parallelism (ILP). The vast majority of ILP compilation research has been conducted in the context of generalpurpose computing, and more specifically the SPEC benchmark suite. At ..."
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Cited by 966 (22 self)
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suite that has been designed to fill this gap. This suite has been constructed through a threestep process: intuition and market driven initial selection, experimental measurement to establish uniqueness, and integration with system synthesis algorithms to establish usefulness.
The Nonstochastic Multiarmed Bandit Problem
 SIAM JOURNAL OF COMPUTING
, 2002
"... In the multiarmed bandit problem, a gambler must decide which arm of K nonidentical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the tradeoff between exploration (trying out ..."
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Cited by 491 (34 self)
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round payoff of the strategy at the rate O((logN)1/2T−1/2). Finally, we apply our results to the problem of playing an unknown repeated matrix game. We show that our algorithm approaches the minimax payoff of the unknown game at the rate O(T−1/2).
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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policy. Large applications of reinforcement learning (RL) require the use of generalizing function approximators such neural networks, decisiontrees, or instancebased methods. The dominant approach for the last decade has been the valuefunction approach, in which all function approximation effort goes
A LastStep Regression Algorithm for NonStationary Online Learning
"... The goal of a learner in standard online learning is to maintain an average loss close to the loss of the bestperforming single function in some class. In many realworld problems, such as rating or ranking items, there is no single best target function during the runtime of the algorithm, instea ..."
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Cited by 2 (1 self)
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stead the best (local) target function is drifting over time. We develop a novel laststep minmax optimal algorithm in context of a drift. We analyze the algorithm in the worstcase regret framework and show that it maintains an average loss close to that of the best slowly changing sequence of linear
Weighted LastStep MinMax Algorithm with Improved SubLogarithmic Regret
"... In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster [12] proposed a laststep minmax algorithm which was somewhat simpler than the algorithm of Vovk [26], yet with the same regret. In ..."
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In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster [12] proposed a laststep minmax algorithm which was somewhat simpler than the algorithm of Vovk [26], yet with the same regret
Results 1  10
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