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Jeff S Shamma - One of the best experts on this subject based on the ideXlab platform.
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an lp approach for solving two player zero sum repeated bayesian games
IEEE Transactions on Automatic Control, 2019Co-Authors: Cedric Langbort, Jeff S ShammaAbstract:This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the Initial Probability of the type of every player is publicly known. The types of players are independently chosen according to the Initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players’ security strategies. Moreover, this paper shows that a player's sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player's own type, the regret over the other player's type, and the stage. Explicit linear programs, whose size is linear in the size of the game tree, are provided to compute the Initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player's sufficient statistics consists of the belief of the player's own type and the antidiscounted regret with respect to the other player's type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy, and shows that the bound converges to 0 exponentially fast.
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an lp approach for solving two player zero sum repeated bayesian games
2017Co-Authors: Cedric Langbort, Jeff S ShammaAbstract:This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the Initial Probability of the type of every player is publicly known. The types of players are independently chosen according to the Initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players' security strategies. Moreover, based on the existing results in [1], this paper shows that a player's sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player's own type, the regret with respect to the other player's type, and the stage. Explicit linear programs are provided to compute the Initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player's sufficient statistics consists of the belief of the player's own type and the anti-discounted regret with respect to the other player's type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy.
Cedric Langbort - One of the best experts on this subject based on the ideXlab platform.
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an lp approach for solving two player zero sum repeated bayesian games
IEEE Transactions on Automatic Control, 2019Co-Authors: Cedric Langbort, Jeff S ShammaAbstract:This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the Initial Probability of the type of every player is publicly known. The types of players are independently chosen according to the Initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players’ security strategies. Moreover, this paper shows that a player's sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player's own type, the regret over the other player's type, and the stage. Explicit linear programs, whose size is linear in the size of the game tree, are provided to compute the Initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player's sufficient statistics consists of the belief of the player's own type and the antidiscounted regret with respect to the other player's type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy, and shows that the bound converges to 0 exponentially fast.
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an lp approach for solving two player zero sum repeated bayesian games
2017Co-Authors: Cedric Langbort, Jeff S ShammaAbstract:This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the Initial Probability of the type of every player is publicly known. The types of players are independently chosen according to the Initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players' security strategies. Moreover, based on the existing results in [1], this paper shows that a player's sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player's own type, the regret with respect to the other player's type, and the stage. Explicit linear programs are provided to compute the Initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player's sufficient statistics consists of the belief of the player's own type and the anti-discounted regret with respect to the other player's type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy.
Hiroo Kanamori - One of the best experts on this subject based on the ideXlab platform.
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uncertainty estimations for seismic source inversions
Geophysical Journal International, 2012Co-Authors: Zacharie Duputel, Yukitoshi Fukahata, Luis Rivera, Hiroo KanamoriAbstract:Source inversion is a widely used practice in seismology. Magnitudes, moment tensors, slip distributions are now routinely calculated and disseminated whenever an earthquake occurs. The accuracy of such models depends on many aspects like the event magnitude, the data coverage and the data quality (instrument response, isolation, timing, etc.). Here, like in any observational problem, the error estimation should be part of the solution. It is however very rare to find a source inversion algorithm which includes realistic error analyses, and the solutions are often given without any estimates of uncertainties. Our goal here is to stress the importance of such estimation and to explore different techniques aimed at achieving such analyses. In this perspective, we use the W phase source inversion algorithm recently developed to provide fast CMT estimations for large earthquakes. We focus in particular on the linear-inverse problem of estimating the moment tensor components at a given source location. We assume that the Initial Probability densities can be modelled by Gaussian distributions. Formally, we can separate two sources of error which generally contribute to the model parameter uncertainties. The first source of uncertainty is the error introduced by the more or less imperfect data. This is carried by the covariance matrix for the data (C_d). The second source of uncertainty, often overlooked, is associated with modelling error or mismodelling. This is represented by the covariance matrix on the theory, C_T. Among the different sources of mismodelling, we focus here on the modelling error associated with the mislocation of the centroid position. Both C_d and C_T describe Probability densities in the data space and it is well known that it is in fact C_D = C_d + C_T that should be included into the error propagation process. In source inversion problems, like in many other fields of geophysics, the data covariance (C_D) is often considered as diagonal or even proportional to the identity matrix. In this work, we demonstrate the importance of using a more realistic form for C_D. If we incorporate accurate covariance components during the inversion process, it refines the posterior error estimates but also improves the solution itself. We discuss these issues using several synthetic tests and by applying the W phase source inversion algorithm to several large earthquakes such as the recent 2011 Tohoku-oki earthquake.
Edmund Neugebauer - One of the best experts on this subject based on the ideXlab platform.
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evaluation of criteria for temporary external fixation in risk adapted damage control orthopedic surgery of femur shaft fractures in multiple trauma patients evidence based medicine versus reality in the trauma registry of the german trauma society
Journal of Trauma-injury Infection and Critical Care, 2005Co-Authors: Dieter Rixen, G Grass, Stefan Sauerland, Rolf Lefering, Marcus Raum, N Yucel, Bertil Bouillon, Edmund NeugebauerAbstract:Background: Femur-shaft fracture treatment (FSFT) follows controversial management concepts after multiple trauma: primary-definitive osteosynthesis, secondary-definitive osteosynthesis after temporary external fixation (EF) in all patients, or individualized primary- or secondary-definitive osteosynthesis (risk-adapted damage control orthopedics). This study compares the concepts by analyzing literature evidence and a prospective multicenter database. Methods: A systematic literature analysis was performed. The German Trauma Society trauma registry was used to assess variables predictive of treatment concept. Results: Contradictory results in 63 controlled trials failed to support a generalized management strategy. In all, 1,465 FSFTs in 8,057 trauma registry patients (age 39 ± 19.5 years; Injury Severity Score [ISS] 23.5 ± 14.9; 17.3% mortality) were treated Initially (<24 hour) by EF, nail, or plate in 47.0%, 41.1%, and 11.9%, respectively. Despite large interhospital variability, EF was more likely with increasing severity of ISS, Glasgow Coma Score, thorax trauma, base excess, coagulation abnormalities, and Initial Probability of death. Conclusions: Clinical reality reflects the controversies of scientific evidence for FSFT after multiple trauma in Germany. Although decision making is currently based on unvalidated criteria, anatomic and physiologic injury severity appears to influence the choice of management concept.
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evaluation of criteria for temporary external fixation in risk adapted damage control orthopedic surgery of femur shaft fractures in multiple trauma patients evidence based medicine versus reality in the trauma registry of the german trauma society
Journal of Trauma-injury Infection and Critical Care, 2005Co-Authors: Dieter Rixen, G Grass, Stefan Sauerland, Rolf Lefering, Marcus Raum, N Yucel, Bertil Bouillon, Edmund NeugebauerAbstract:Background: Femur-shaft fracture treatment (FSFT) follows controversial management concepts after multiple trauma: primary-definitive osteosynthesis, secondary-definitive osteosynthesis after temporary external fixation (EF) in all patients, or individualized primary- or secondary-definitive osteosynthesis (risk-adapted damage control orthopedics). This study compares the concepts by analyzing literature evidence and a prospective multicenter database. Methods: A systematic literature analysis was performed. The German Trauma Society trauma registry was used to assess variables predictive of treatment concept. Results: Contradictory results in 63 controlled trials failed to support a generalized management strategy. In all, 1,465 FSFTs in 8,057 trauma registry patients (age 39 ± 19.5 years; Injury Severity Score [ISS] 23.5 ± 14.9; 17.3% mortality) were treated Initially (<24 hour) by EF, nail, or plate in 47.0%, 41.1%, and 11.9%, respectively. Despite large interhospital variability, EF was more likely with increasing severity of ISS, Glasgow Coma Score, thorax trauma, base excess, coagulation abnormalities, and Initial Probability of death. Conclusions: Clinical reality reflects the controversies of scientific evidence for FSFT after multiple trauma in Germany. Although decision making is currently based on unvalidated criteria, anatomic and physiologic injury severity appears to influence the choice of management concept.
Werner Romisch - One of the best experts on this subject based on the ideXlab platform.
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scenario reduction in stochastic programming
Mathematical Programming, 2003Co-Authors: Jitka Dupacova, Nicole Growekuska, Werner RomischAbstract:Given a convex stochastic programming problem with a discrete Initial Probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a Probability measure based on this set that is the closest to the Initial distribution in terms of a natural (or canonical) Probability metric. Arguments from stability analysis indicate that Fortet-Mourier type Probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50% reduction of the scenario tree the optimal reduced tree still has about 90% relative accuracy.
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scenario reduction algorithms in stochastic programming
Computational Optimization and Applications, 2003Co-Authors: Holger Heitsch, Werner RomischAbstract:We consider convex stochastic programs with an (approximate) Initial Probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier Probability metric. The problem of optimal scenario reduction consists in determining a Probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a Probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced Probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.
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scenario reduction in stochastic programming an approach using Probability metrics
Mathematical Programming, 2000Co-Authors: Jitka Dupacova, Nicole Growekuska, Werner RomischAbstract:Given a convex stochastic programming problem with a discrete Initial Probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a Probability measure based on this set that is the closest to the Initial distribution in terms of a natural (or canonical) Probability metric. Arguments from stability analysis indicate that Fortet-Mourier type Probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50% reduction of the scenario tree the optimal reduced tree still has about 90% relative accuracy.