A Minimax Game for Generative and Discriminative Sample Models for Recommendation

2019 ◽  
pp. 420-431 ◽  
Author(s):  
Zongwei Wang ◽  
Min Gao ◽  
Xinyi Wang ◽  
Junliang Yu ◽  
Junhao Wen ◽  
...  
Keyword(s):  
Minimax Game

Graphical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

2021 ◽  
pp. 2150011
Author(s):  
Wei Dong ◽  
Jianan Wang ◽  
Chunyan Wang ◽  
Zhenqiang Qi ◽  
Zhengtao Ding
Keyword(s):  
Reinforcement Learning ◽  
Spanning Tree ◽  
Learning Algorithm ◽  
Control Policy ◽  
Game Problem ◽  
Algebraic Riccati Equation ◽  
Multi Agent Systems ◽  
Rank Condition ◽  
Minimax Game ◽  
Tree Condition

In this paper, the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems (MASs) with spanning tree condition based on game theory and reinforcement learning. First, the graphical minimax game algebraic Riccati equation (ARE) is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors. The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically. Then, a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics. A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.

Minimax Game Tree Searching

2008 ◽  
pp. 2079-2087
Author(s):  
Claude G. Diderich ◽  
Marc Gengler
Keyword(s):  
Game Tree ◽  
Minimax Game ◽  
Tree Searching

A Multi-Player Minimax Game for Generative Adversarial Networks

2020 ◽  
Author(s):  
Ying Jin ◽  
Yunbo Wang ◽  
Mingsheng Long ◽  
Jianmin Wang ◽  
Philip S. Yu ◽  
...  
Keyword(s):  
Generative Adversarial Networks ◽  
Adversarial Networks ◽  
Minimax Game

Design of Globally Robust Control for Biologically-Inspired Noisy Recurrent Neural Networks

2011 ◽  
pp. 116-135
Author(s):  
Ziqian Liu
Keyword(s):  
Neural Networks ◽  
Robust Control ◽  
Recurrent Neural Networks ◽  
Disturbance Attenuation ◽  
Biologically Inspired ◽  
Inverse Optimality ◽  
Modeling Errors ◽  
Minimax Game ◽  
Biological Motor ◽  
Lyapunov Technique

This chapter presents a theoretical design of how a global robust control is achieved in a class of noisy recurrent neural networks which is a promising method for modeling the behavior of biological motor-sensor systems. The approach is developed by using differential minimax game, inverse optimality, Lyapunov technique, and the Hamilton-Jacobi-Isaacs equation. In order to implement the theory of differential games into neural networks, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The proposed design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, as well as global asymptotic stability provided no disturbance. Finally, numerical examples are used to demonstrate the effectiveness of the proposed design.

scholarly journals Image-to-Image Translation Using Identical-Pair Adversarial Networks

2019 ◽  
Vol 9 (13) ◽  
pp. 2668 ◽  
Author(s):  
Thai Leang Sung ◽  
Hyo Jong Lee
Keyword(s):  
Loss Function ◽  
Network Architectures ◽  
Perceptual Similarity ◽  
Image Transformation ◽  
Identical Pair ◽  
Similarity Network ◽  
Adversarial Networks ◽  
Image Translation ◽  
Minimax Game

We propose Identical-pair Adversarial Networks (iPANs) to solve image-to-image translation problems, such as aerial-to-map, edge-to-photo, de-raining, and night-to-daytime. Our iPANs rely mainly on the effectiveness of adversarial loss function and its network architectures. Our iPANs consist of two main networks, an image transformation network T and a discriminative network D. We use U-NET for the transformation network T and a perceptual similarity network, which has two streams of VGG16 that share the same weights for network D. Our proposed adversarial losses play a minimax game against each other based on a real identical-pair and a fake identical-pair distinguished by the discriminative network D; e.g. a discriminative network D considers two inputs as a real pair only when they are identical, otherwise a fake pair. Meanwhile, the transformation network T tries to persuade the discriminator network D that the fake pair is a real pair. We experimented on several problems of image-to-image translation and achieved results that are comparable to those of some existing approaches, such as pix2pix, and PAN.

scholarly journals A Stochastic Maximin Fixed-Point Equation Related to Game Tree Evaluation

2007 ◽  
Vol 44 (3) ◽  
pp. 586-606
Author(s):  
Gerold Alsmeyer ◽  
Matthias Meiners
Keyword(s):  
Fixed Point ◽  
Distribution Function ◽  
Unique Fixed Point ◽  
Game Tree ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Particular Solution ◽  
Minimax Game ◽  
Class Of Functions ◽  
Tree Evaluation

After suitable normalization the asymptotic root value W of a minimax game tree of order b ≥ 2 with independent and identically distributed input values having a continuous, strictly increasing distribution function on a subinterval of R appears to be a particular solution of the stochastic maximin fixed-point equation W ξ max1≤i≤bmin1≤j≤bWi,j, where Wi,j are independent copies of W and denotes equality in law. Moreover, ξ= g'(α) > 1, where g(x) := (1 − (1 − x)b)b and α denotes the unique fixed point of g in (0, 1). This equation, which takes the form F(t) = g(F(t/ξ)) in terms of the distribution function F of W, is studied in the present paper for a reasonably extended class of functions g so as to encompass more general stochastic maximin equations as well. A complete description of the set of solutions F is provided followed by a discussion of additional properties such as continuity, differentiability, or existence of moments. Based on these results, it is further shown that the particular solution mentioned above stands out among all other ones in that its distribution function is the restriction of an entire function to the real line. This extends recent work of Ali Khan, Devroye and Neininger (2005). A connection with another class of stochastic fixed-point equations for weighted minima and maxima is also discussed.

Control of Recurrent Neural Networks Using Differential Minimax Game: The Stochastic Case

2010 ◽  
Author(s):  
Ziqian Liu ◽  
Nirwan Ansari
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
New Approach ◽  
Numerical Example ◽  
Inverse Optimality ◽  
Stochastic Case ◽  
Stochastic Input ◽  
Minimax Game ◽  
Unknown Covariance ◽  
Lyapunov Technique

As a continuation of our study, this paper extends our research results of optimality-oriented stabilization from deterministic recurrent neural networks to stochastic recurrent neural networks, and presents a new approach to achieve optimally stochastic input-to-state stabilization in probability for stochastic recurrent neural networks driven by noise of unknown covariance. This approach is developed by using stochastic differential minimax game, Hamilton-Jacobi-Isaacs (HJI) equation, inverse optimality, and Lyapunov technique. A numerical example is given to demonstrate the effectiveness of the proposed approach.

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