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Variance Reduction for Matrix Games [article]

Yair Carmon, Yujia Jin, Aaron Sidford, Kevin Tian
2019 arXiv   pre-print
Our results hold for x,y in the simplex (matrix games, linear programming) and for x in an ℓ_2 ball and y in the simplex (perceptron / SVM, minimum enclosing ball).  ...  We present a randomized primal-dual algorithm that solves the problem min_xmax_y y^ A x to additive error ϵ in time nnz(A) + √(nnz(A)n)/ϵ, for matrix A with larger dimension n and nnz(A) nonzero entries  ...  Balamurugan and Bach [3] apply standard variance reduction [19] to bilinear 2 -2 games by sampling elements proportional to squared matrix entries.  ... 
arXiv:1907.02056v2 fatcat:v4wkyamjebbjfkg62iz3dmqfzi

Submodular game for distributed application allocation in shared sensor networks

Chengjie Wu, You Xu, Yixin Chen, Chenyang Lu
2012 2012 Proceedings IEEE INFOCOM  
This paper presents a distributed game-theoretic approach to application allocation in shared sensor networks.  ...  We first transform the optimal application allocation problem to a submodular game and then develop a decentralized algorithm that only employs localized interactions among neighboring nodes.  ...  There is an inherent disadvantage of using variance reduction for our problem.  ... 
doi:10.1109/infcom.2012.6195490 dblp:conf/infocom/WuXCL12 fatcat:3wz6suff45buxjoaqzwv6s3pke

Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression [article]

Ian Covert, Su-In Lee
2021 arXiv   pre-print
We also find that the original version incurs a negligible increase in bias in exchange for significantly lower variance, and we propose a variance reduction technique that further accelerates the convergence  ...  Finally, we develop a version of KernelSHAP for stochastic cooperative games that yields fast new estimators for two global explanation methods.  ...  virtually no bias in exchange for a significant reduction in variance.  ... 
arXiv:2012.01536v3 fatcat:fvvx7qna35chjewuutb27npbmu

Difficulty of cooperation in iterated multi-Prisoner's Dilemma situation-Experimental evidence-

Kazuhito Ogawa, Tetsuya Kawamura, Tatsuya Kikutani, Sobei H. Oda
2006 Proceedings of the 9th Joint Conference on Information Sciences (JCIS)  
Second, AB contains the matrix that facilitates cooperation. For decision makers in AB, second feature is more powerful than first feature.  ...  The definition of the channel reduction is that in a game, a player chooses only a particular channel although he or she has more channels to choose.  ...  Third, the ChaRCIS is effective for the increase in the mutual cooperation. This may be helpful for the resolution of the diplomatic problems.  ... 
doi:10.2991/jcis.2006.322 dblp:conf/jcis/OgawaKKO06 fatcat:zcpscbqzhvgrfksg6qjxlr3icy

Extra-gradient with player sampling for faster convergence in n-player games

Samy Jelassi, Carles Domingo-Enrich, Damien Scieur, Arthur Mensch, Joan Bruna
2020 International Conference on Machine Learning  
We propose an additional variance reduction mechanism to obtain speed-ups in smooth convex games.  ...  This approach provably exhibits a better rate of convergence than full extra-gradient for non-smooth convex games with noisy gradient oracle.  ...  Variance reduction for player noise. To obtain faster rates in convex games with smooth losses, we propose to compute a variance-reduced estimate of the gradient oracle (5).  ... 
dblp:conf/icml/JelassiDSMB20 fatcat:l26fdywfofhgtoc6pnfkrhufhy

Compressing and Comparing the Generative Spaces of Procedural Content Generators [article]

Oliver Withington, Laurissa Tokarchuk
2022 arXiv   pre-print
The past decade has seen a rapid increase in the level of research interest in procedural content generation (PCG) for digital games, and there are now numerous research avenues focused on new approaches  ...  In this work we assess the efficacy of a selection of algorithms across sets of levels for 2D tile-based games by investigating how much their respective generative space compressions correlate with level  ...  The compressed 2D matrix representing all levels to analyse is now ready to have a dimensionality reduction algorithm applied.  ... 
arXiv:2205.15133v1 fatcat:s6bgioxjurc6dhcpwv7k7jra64

Learning a Value Analysis Tool for Agent Evaluation

Martha White, Michael H. Bowling
2009 International Joint Conference on Artificial Intelligence  
We show that we can reduce variance over state-of-the-art estimators for a specific population of limit poker players as well as construct the first variance reducing estimators for no-limit poker and  ...  Recently, an advantage sum technique has been proposed for constructing unbiased, low variance estimates of agent performance.  ...  Acknowledgments We would like to thank the University of Alberta Poker Research Group for help throughout for ideas and implementation issues.  ... 
dblp:conf/ijcai/WhiteB09 fatcat:ryqdljzxqnfjhpbtm3lu5molyq

Reinforcement Learning with Perturbed Rewards

Jingkang Wang, Yang Liu, Bo Li
For instance, the state-of-the-art PPO algorithm is able to obtain 84.6% and 80.8% improvements on average score for five Atari games, with error rates as 10% and 30% respectively.  ...  In this paper, we consider noisy RL problems with perturbed rewards, which can be approximated with a confusion matrix.  ...  To verify this idea, we repeated the experiments of Cartpole but included variance reduction step for estimated surrogate rewards.  ... 
doi:10.1609/aaai.v34i04.6086 fatcat:rkqpjretqvfcffij3xw2uqfpim

Detection of Appliance Utilization Patterns via Dimensionality Reduction

Fernanda Villar, Luiz Carlos Pereira da Silva, Pedro Henrique Juliano Nardelli, Hader Hazini
2019 2019 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America)  
information loses, (ii) the k-means method to clustering appliances into different groups and (iii) the elbow method was used to define the best number of clusters for each house with explained variance  ...  of at least 93% and reaching more than 99% for the best k.  ...  The PCA method performed dimensionality reduction keeping high values of variance explained for the cases under consideration.  ... 
doi:10.1109/isgt-la.2019.8895285 fatcat:mael52qijjfq5ebjywtftrf364

Smoothed Complexity of 2-player Nash Equilibria [article]

Shant Boodaghians and Joshua Brakensiek and Samuel B. Hopkins and Aviad Rubinstein
2020 arXiv   pre-print
The key ingredient in our reduction is the use of a random zero-sum game as a gadget to produce two-player games which remain hard even after smoothing.  ...  Our results therefore separate smoothed complexity and hardness of approximation for Nash equilibria in two-player games.  ...  Acknowledgements We thank anonymous reviewers for helpful suggestions which improved this manuscript.  ... 
arXiv:2007.10857v1 fatcat:i7tgbussgrcwxk3rva6vzwhrwm

Linear Game Theory : Reduction of complexity by decomposing large games into partial games [article]

Tatsuya Iwase, Takahiro Shiga
2016 arXiv   pre-print
Previous studies in algorithmic game theory propose succinct games that enable small descriptions of payoff matrices and reduction of complexities.  ...  This study proposes a method to identify an interaction graph between players and subsequently decompose games into smaller components by cutting out weak interactions for the purpose of reducing complexity  ...  Purpose of the study The purpose of this work is to decompose large complex games into sets of small games for reduction of computational complexity.  ... 
arXiv:1609.00481v2 fatcat:gclqmm34drhaxoqwhyidhl5pni

Analysis of panel data

2004 Computers and Mathematics with Applications  
Appendix 3B, Characteristic vectors and the inverse of the variance-covariance matrix of a three-component model. 4. Dynamic models with variable intercepts. 4.1. Introduction. 4.2.  ...  Derivation of the asymptotic covariance matrix of the feasible MDE.  ...  Variance of the estimates. 8.7. Information identity. 9. Drawing from densities. 9.1. Introduction. 9.2. Random draws. 9.3. Variance reduction. 10. Simulation-assisted estimation. 10.1.  ... 
doi:10.1016/s0898-1221(04)90099-5 fatcat:u24m4nd4bnedzjkdp3cln3psqe

Extragradient with player sampling for faster Nash equilibrium finding [article]

Carles Domingo Enrich
2020 arXiv   pre-print
We propose an additional variance reduction mechanism to obtain speed-ups in smooth convex games.  ...  This approach provably exhibits a better rate of convergence than full extra-gradient for non-smooth convex games with noisy gradient oracle.  ...  skew smooth game with increasing noise (sampling with variance reduction).  ... 
arXiv:1905.12363v5 fatcat:m552o5anereafej6vyh47kmxym

Page 855 of Mathematical Reviews Vol. 13, Issue 9 [page]

1952 Mathematical Reviews  
This paper gives a method for certain classes of games in exten- sive form which replaces the given game by an equivalent game with the smallest number of pure strategies.  ...  His Theorem 3 parallels the standard analysis of variance scheme for testing these hypotheses.  ... 

Matrix inversion by a Monte Carlo method

George E. Forsythe, Richard A. Leibler
1950 Mathematics of Computation  
However, conventional error estimates in terms of variances no longer apply and, in at least certain matrix inversions where an = 00, the accumulated payment after AT games cannot be normed so as to be  ...  Harris for this reference. n[\ -/»¿(.B-1)«], corresponding to the variance of the binomial distribution. George E. Forsythe Richard A.  ... 
doi:10.1090/s0025-5718-1950-0038138-x fatcat:ldplxnsgkbgwtdpyrii22l7hmy
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