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A Minimax Strategy for Global Optimization
"... A computationally expensive multimodal optimization problem is considered. After an optimization loop it is desirable that the optimality gap, i.e., the difference between the best value obtained and the true optimum, is as small as possible. We define the concept of maximum loss as being the sup ..."
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the supremum of the optimality gaps over a set of functions, i.e., the largest possible optimality gap assuming that the unknown objective function belongs to a certain set of functions. The minimax strategy for global optimization is then to—at each iteration—choose a new evaluation point
The minimax strategy for gaussian density estimation
 In COLT
, 2000
"... We consider online density estimation with a Gaussian of unit variance. In each trial t the learner predicts a mean θt. Then it receives an instance xt chosen by the adversary and incurs loss 1 2 (θt − xt) 2. The performance of the learner is measured by the regret de£ned as the total loss of the l ..."
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Cited by 10 (2 self)
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of the learner minus the total loss of the best mean parameter chosen offline. We assume that the horizon T of the protocol is £xed and known to both parties. We give the optimal strategies for both the learner and the adversary. The value of the game is 1 2X2 (ln T − ln ln T + O(ln ln T / ln T)), where X
Optimal minimax strategy in a dice game
, 2009
"... Each of two players, by turns, rolls a dice several times accumulating the successive scores until he decides to stop, or he rolls an ace. When stopping, the accumulated turn score is added to the player account and the dice is given to his opponent. If he rolls an ace, the dice is given to the oppo ..."
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to the opponent without adding any point. In this paper we formulate this game in the framework of competitive Markov decision processes (also known as stochastic games), show that the game has a value, provide an algorithm to compute the optimal minimax strategy, and present results of this algorithm in three
Computing Minimax Strategy for Discretized SpatioTemporal ZeroSum Security Games?
"... Abstract. Among the many deployment areas of Stackelberg Security games, a major area involves games played out in space and time, which includes applications in multiple mobile defender resources protecting multiple mobile targets. Previous algorithms for such spatiotemporal security games fail t ..."
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to scaleup and little is known of the computational complexity properties of these problems. This paper provides a novel oraclebased algorithmic framework for a systematic study of different problem variants of computing optimal (minimax) strategies in spatiotemporal security games. Our framework
Guaranteeing Cost Minimax Strategies for Uncertain DiscreteTime Systems
"... Abstract: The paper gives a general definition of guaranteeing cost strategy for uncertain dynamical systems. The strategy is constructed by a parametrized Riccatiinequality for a fairly general system with linear nominal part and with uncertainty of linear fractional form. The strategy is determin ..."
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is determined by an LMI system and by the fullblock multiplier technique, too. The methods are compared. Also a fictitious system without uncertainty is shown, for which the minimax strategy is also the solution of the examined problem. Key–Words: systems and control, optimal control, dynamical systems
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).
Mixed Strategy Play and the Minimax Hypothesis
 JOURNAL OF ECONOMIC THEORY
, 1996
"... This paper reports on a set of experiments designed to discriminate among the possible sources of the failure of the unique mixed strategy minimax equilibrium of the O'Neill (1987) game. First, the experimental design allows one to identify the causes of the serial correlation in subjects&ap ..."
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Cited by 31 (4 self)
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This paper reports on a set of experiments designed to discriminate among the possible sources of the failure of the unique mixed strategy minimax equilibrium of the O'Neill (1987) game. First, the experimental design allows one to identify the causes of the serial correlation in subjects
Minimax Play at Wimbledon
, 1999
"... In many strategic situations it is important that one’s actions not be predictable by one’s opponent, or by one’s opponents. Indeed, the origins of modern game theory lie in the attempt to understand such situations. The theory of mixedstrategy play, including von Neumann’s Minimax Theorem and the ..."
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Cited by 54 (1 self)
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In many strategic situations it is important that one’s actions not be predictable by one’s opponent, or by one’s opponents. Indeed, the origins of modern game theory lie in the attempt to understand such situations. The theory of mixedstrategy play, including von Neumann’s Minimax Theorem
Professionals Play Minimax
 REVIEW OF ECONOMIC STUDIES
, 2003
"... The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a oneshot twoperson zerosum game. The results of the tests are remarkably consistent with equilibrium play i ..."
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Cited by 53 (1 self)
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The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a oneshot twoperson zerosum game. The results of the tests are remarkably consistent with equilibrium play
Minimax: Portfolio Choice Based on Pessimistic Decision Making
"... We propose a fund allocation strategy for a highly riskaverse investor based on pessimistic decision making to construct portfolios of four major asset classes. Using US data (indexes of stocks, bonds, real estate, and commodities) from January 1990 to December 2010, we find that the proposed Minim ..."
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Minimax strategy performs well outofsample with respect to standard risk measures. Its performance is better than common alternative trading strategies such as fixed weights, minimum variance, or meanvariance methods. Portfolio weights are stable across time, resulting in lower turnover than any mean
Results 1  10
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