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Lazy-CFR: fast and near-optimal regret minimization for extensive games with imperfect information

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arXiv 2018年

作者： Zhou, Yichi Ren, Tongzheng Yan, Dong Li, Jialian Zhu, Jun Dept. of Comp. Sci. & Tech. BNRist Center State Key Lab for Intell. Tech. & Sys. THBI Lab Tsinghua University Beijing100084 China

Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art results in practice. However, the performance of CFR is not fully understood, since empirical results on the regret are much better than the known upper bound in (Zinkevich et al., 2008). Moreover, CFR has to traverse the whole game tree in each round, which is time-consuming in large scale games. In this paper, we present a novel tech.ique, lazy update, which can avoid traversing the whole game tree in each round. We propose a novel analysis on the regret of CFR with lazy update, which can also be applied to the vanilla CFR, resulting in a much tighter regret bound than that in (Zinkevich et al., 2008). Inspired by lazy update, we further present a novel CFR variant, named Lazy-CFR. Compared to traversing O(|I|) information sets in the vanilla CFR, Lazy-CFR needs only to traverse O(p|I|) information sets per round while keeping the regret bound almost the same, where I is the class of all information sets. As a result, Lazy-CFR shows better convergence results compared with the vanilla CFR. Experimental results consistently show that Lazy-CFR outperforms the vanilla CFR significantly. Copyright © 2018, The Authors. All rights reserved.

关键词： Forestry

Semi-crowdsourced clustering with deep generative models

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arXiv 2018年

作者： Luo, Yucen Tian, Tian Shi, Jiaxin Zhu, Jun Zhang, Bo Dept. of Comp. Sci. & Tech. Institute for AI THBI Lab BNRist Center State Key Lab for Intell. Tech. & Sys. Tsinghua University Beijing China

We consider the semi-supervised clustering problem where crowdsourcing provides noisy information about the pairwise comparisons on a small subset of data, i.e., whether a sample pair is in the same cluster. We propose a new approach that includes a deep generative model (DGM) to characterize low-level features of the data, and a statistical relational model for noisy pairwise annotations on its subset. The two parts share the latent variables. To make the model automatically trade-off between its complexity and fitting data, we also develop its fully Bayesian variant. The challenge of inference is addressed by fast (natural-gradient) stochastic variational inference algorithms, where we effectively combine variational message passing for the relational part and amortized learning of the DGM under a unified framework. Empirical results on synthetic and real-world datasets show that our model outperforms previous crowdsourced clustering methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Crowdsourcing

Semi-crowdsourced clustering with deep generative models 18

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Semi-crowdsourced clustering with deep generative models

Proceedings of the 32nd International Conference on Neural Information Processing systems

作者： Yucen Luo Tian Tian Jiaxin Shi Jun Zhu Bo Zhang Dept. of Comp. Sci. & Tech. Institute for AI THBI Lab BNRist Center State Key Lab for Intell. Tech. & Sys. Tsinghua University Beijing China

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Deep structured generative models

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arXiv 2018年

作者： Xu, Kun Liang, Haoyu Su, Hang Zhang, Bo Zhu, Jun Dept. of Comp. Sci. and Tech BNRist Center State Key Lab for Intell. Tech. and Sys THBI Lab Tsinghua University Beijing100084 China

Deep generative models have shown promising results in generating realistic images, but it is still non-trivial to generate images with complicated structures. The main reason is that most of the current generative models fail to explore the structures in the images including spatial layout and semantic relations between objects. To address this issue, we propose a novel deep structured generative model which boosts generative adversarial networks (GANs) with the aid of structure information. In particular, the layout or structure of the scene is encoded by a stochastic and-or graph (sAOG), in which the terminal nodes represent single objects and edges represent relations between objects. With the sAOG appropriately harnessed, our model can successfully capture the intrinsic structure in the scenes and generate images of complicated scenes accordingly. Furthermore, a detection network is introduced to infer scene structures from a image. Experimental results demonstrate the effectiveness of our proposed method on both modeling the intrinsic structures, and generating realistic images. Copyright © 2018, The Authors. All rights reserved.

关键词： Generative adversarial networks

Graphical generative adversarial networks

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arXiv 2018年

作者： Li, Chongxuan Welling, Max Zhu, Jun Zhang, Bo Department of Computer Science & Technology Institute for Artificial Intelligence BNRist Center THBI Lab State Key Lab for Intell. Tech. & Sys. Tsinghua University

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We introduce a structured recognition model to infer the posterior distribution of latent variables given observations. We generalize the Expectation Propagation (EP) algorithm to learn the generative model and recognition model jointly. Finally, we present two important instances of Graphical-GAN, i.e. Gaussian Mixture GAN (GMGAN) and state Space GAN (SSGAN), which can successfully learn the discrete and temporal structures on visual datasets, respectively. Copyright © 2018, The Authors. All rights reserved.

关键词： Generative adversarial networks

Learning implicit generative models by teaching explicit ones

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arXiv 2018年

作者： Du, Chao Xu, Kun Li, Chongxuan Zhang, Bo Zhu, Jun Dept. of Comp. Sci. and Tech BNRist Center State Key Lab for Intell. Tech. and Sys THBI Lab Tsinghua University Beijing100084 China

Implicit generative models are difficult to train as no explicit density functions are defined. Generative adversarial nets (GANs) present a minimax framework to train such models, which however can suffer from mode collapse due to the nature of the JS-divergence. This paper presents a learning by teaching (LBT) approach to learning implicit models, which intrinsically avoids the mode collapse problem by optimizing a KLdivergence rather than the JS-divergence in GANs. In LBT, an auxiliary explicit model is introduced to fit the distribution defined by the implicit model while the later one teaches the explicit model to match the data distribution. LBT is formulated as a bilevel optimization problem, whose optimal generator matches the true data distribution. LBT can be naturally integrated with GANs to derive a hybrid LBT-GAN that enjoys complimentary benefits. Finally, we present a stochastic gradient ascent algorithm with unrolling to solve the challenging learning problems. Experimental results demonstrate the effectiveness of our method. Copyright © 2018, The Authors. All rights reserved.

关键词： Generative adversarial networks

Towards training probabilistic topic models on neuromorphic multi-chip systems

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arXiv 2018年

作者： Xiao, Zihao Chen, Jianfei Zhu, Jun Dept. of Comp. Sci. and Tech. TNList Lab State Key Lab for Intell. Tech. and Sys. Center for Bio-Inspired Computing Research Tsinghua University Beijing100084 China

Probabilistic topic models are popular unsupervised learning methods, including probabilistic latent semantic indexing (pLSI) and latent Dirichlet allocation (LDA). By now, their training is implemented on general purpose computers (GPCs), which are flexible in programming but energyconsuming. Towards low-energy implementations, this paper investigates their training on an emerging hardware tech.ology called the neuromorphic multi-chip systems (NMSs). NMSs are very effective for a family of algorithms called spiking neural networks (SNNs). We present three SNNs to train topic models. The first SNN is a batch algorithm combining the conventional collapsed Gibbs sampling (CGS) algorithm and an inference SNN to train LDA. The other two SNNs are online algorithms targeting at both energy- and storage-limited environments. The two online algorithms are equivalent with training LDA by using maximum-a-posterior estimation and maximizing the semi-collapsed likelihood, respectively. They use novel, tailored ordinary differential equations for stochastic optimization. We simulate the new algorithms and show that they are comparable with the GPC algorithms, while being suitable for NMS implementation. We also propose an extension to train pLSI and a method to prune the network to obey the limited fan-in of some NMSs. Copyright © 2018, The Authors. All rights reserved.

关键词： Statistics

A spectral approach to gradient estimation for implicit distributions

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arXiv 2018年

作者： Shi, Jiaxin Sun, Shengyang Zhu, Jun Dept. of Comp. Sci. and Tech. BNRist Center State Key Lab for Intell. Tech. and Sys. THBI Lab Tsinghua University Dept. of Comp. Sci. University of Toronto

Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's identity and a spectral decomposition of kernel operators, where the eigenfunctions are approximated by the Nyström method. Unlike the previous works that only provide estimates at the sample points, our approach directly estimates the gradient function, thus allows for a simple and principled out-ofsample extension. We provide theoretical results on the error bound of the estimator and discuss the bias-variance tradeoff in practice. The effectiveness of our method is demonstrated by applications to gradient-free Hamiltonian Monte Carlo and variational inference with implicit distributions. Finally, we discuss the intuition behind the estimator by drawing connections between the Nyström method and kernel PCA, which indicates that the estimator can automatically adapt to the geometry of the underlying distribution. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Bandit learning with implicit feedback 18

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Bandit learning with implicit feedback

Proceedings of the 32nd International Conference on Neural Information Processing systems

作者： Yi Qi Qingyun Wu Hongning Wang Jie Tang Maosong Sun State Key Lab of Intell. Tech. & Sys. Institution for Artificial Intelligence Dept. of Comp. Sci. & Tech. Tsinghua University Beijing China Department of Computer Science University of Virginia

Implicit feedback, such as user clicks, although abundant in online information service systems, does not provide substantial evidence on users' evaluation of system's output. Without proper modeling, such incomplete supervision inevitably misleads model estimation, especially in a bandit learning setting where the feedback is acquired on the fly. In this work, we perform contextual bandit learning with implicit feedback by modeling the feedback as a composition of user result examination and relevance judgment. Since users' examination behavior is unobserved, we introduce latent variables to model it. We perform Thompson sampling on top of variational Bayesian inference for arm selection and model update. Our upper regret bound analysis of the proposed algorithm proves its feasibility of learning from implicit feedback in a bandit setting; and extensive empirical evaluations on click logs collected from a major MOOC platform further demonstrate its learning effectiveness in practice.

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