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Qi Cai

Publications and source records attributed to Qi Cai.

46 records · Page 3Linked to original sources
arXiv2019

Neural Policy Gradient Methods: Global Optimality and Rates of Convergence

Policy gradient methods with actor-critic schemes demonstrate tremendous empirical successes, especially when the actors and critics are parameterized by neural networks. However, it remains less clear whether such "neural" policy gradient methods converge to globally optimal policies and whether they even converge at all. We answer both the questions affirmatively in the overparameterized regime. In detail, we prove that neural natural policy gradient converges to a globally optimal policy at a sublinear rate. Also, we show that neural vanilla policy gradient converges sublinearly to a stationary point. Meanwhile, by relating the suboptimality of the stationary points to the representation power of neural actor and critic classes, we prove the global optimality of all stationary points under mild regularity conditions. Particularly, we show that a key to the global optimality and convergence is the "compatibility" between the actor and critic, which is ensured by sharing neural architectures and random initializations across the actor and critic. To the best of our knowledge, our analysis establishes the first global optimality and convergence guarantees for neural policy gradient methods.

cs.LG↗
arXiv2019

Multi-Source Domain Adaptation and Semi-Supervised Domain Adaptation with Focus on Visual Domain Adaptation Challenge 2019

This notebook paper presents an overview and comparative analysis of our systems designed for the following two tasks in Visual Domain Adaptation Challenge (VisDA-2019): multi-source domain adaptation and semi-supervised domain adaptation. Multi-Source Domain Adaptation: We investigate both pixel-level and feature-level adaptation for multi-source domain adaptation task, i.e., directly hallucinating labeled target sample via CycleGAN and learning domain-invariant feature representations through self-learning. Moreover, the mechanism of fusing features from different backbones is further studied to facilitate the learning of domain-invariant classifiers. Source code and pre-trained models are available at \url{https://github.com/Panda-Peter/visda2019-multisource}. Semi-Supervised Domain Adaptation: For this task, we adopt a standard self-learning framework to construct a classifier based on the labeled source and target data, and generate the pseudo labels for unlabeled target data. These target data with pseudo labels are then exploited to re-training the classifier in a following iteration. Furthermore, a prototype-based classification module is additionally utilized to strengthen the predictions. Source code and pre-trained models are available at \url{https://github.com/Panda-Peter/visda2019-semisupervised}.

cs.CV↗
arXiv2019

vireoJD-MM at Activity Detection in Extended Videos

This notebook paper presents an overview and comparative analysis of our system designed for activity detection in extended videos (ActEV-PC) in ActivityNet Challenge 2019. Specifically, we exploit person/vehicle detections in spatial level and action localization in temporal level for action detection in surveillance videos. The mechanism of different tubelet generation and model decomposition methods are studied as well. The detection results are finally predicted by late fusing the results from each component.

cs.CV↗
arXiv2019

General Method for Prime-point Cyclic Convolution over the Real Field

A general and fast method is conceived for computing the cyclic convolution of n points, where n is a prime number. This method fully exploits the internal structure of the cyclic matrix, and hence leads to significant reduction of the multiplication complexity in terms of CPU time by 50%, as compared with Winograd's algorithm. In this paper, we only consider the real and complex fields due to their most important applications, but in general, the idea behind this method can be extended to any finite field of interest. Clearly, it is well-known that the discrete Fourier transform (DFT) can be expressed in terms of cyclic convolution, so it can be utilized to compute the DFT when the block length is a prime.

cs.AI↗
arXiv2019

The Hall--Paige conjecture, and synchronization for affine and diagonal groups

The Hall--Paige conjecture asserts that a finite group has a complete mapping if and only if its Sylow subgroups are not cyclic. The conjecture is now proved, and one aim of this paper is to document the final step in the proof (for the sporadic simple group $\mathrm{J}_4$). We apply this result to prove that primitive permutation groups of simple diagonal type with three or more simple factors in the socle are non-synchronizing. We also give the simpler proof that, for groups of affine type, or simple diagonal type with two socle factors, synchronization and separation are equivalent. Synchronization and separation are conditions on permutation groups which are stronger than primitivity but weaker than $2$-homogeneity, the second of these being stronger than the first. Empirically it has been found that groups which are synchronizing but not separating are rather rare. It follows from our results that such groups must be primitive of almost simple type.

math.GR↗
arXiv2019

On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator

We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a unique saddle point, which simultaneously recovers the globally optimal policy and reward function. We hope our results may serve as a small step towards understanding and taming the instability in imitation learning as well as in more general non-convex-concave alternating minimax optimization that arises from reinforcement learning and generative adversarial learning.

cs.LG↗
arXiv2018

Equivalent Constraints for Two-View Geometry: Pose Solution/Pure Rotation Identification and 3D Reconstruction

Two-view relative pose estimation and structure reconstruction is a classical problem in computer vision. The typical methods usually employ the singular value decomposition of the essential matrix to get multiple solutions of the relative pose, from which the right solution is picked out by reconstructing the three-dimension (3D) feature points and imposing the constraint of positive depth. This paper revisits the two-view geometry problem and discovers that the two-view imaging geometry is equivalently governed by a Pair of new Pose-Only (PPO) constraints: the same-side constraint and the intersection constraint. From the perspective of solving equation, the complete pose solutions of the essential matrix are explicitly derived and we rigorously prove that the orientation part of the pose can still be recovered in the case of pure rotation. The PPO constraints are simplified and formulated in the form of inequalities to directly identify the right pose solution with no need of 3D reconstruction and the 3D reconstruction can be analytically achieved from the identified right pose. Furthermore, the intersection inequality also enables a robust criterion for pure rotation identification. Experiment results validate the correctness of analyses and the robustness of the derived pose solution/pure rotation identification and analytical 3D reconstruction.

cs.CV↗
arXiv2018

Fast RodFIter for Attitude Reconstruction from Inertial Measurements

Attitude computation is of vital importance for a variety of applications. Based on the functional iteration of the Rodrigues vector integration equation, the RodFIter method can be advantageously applied to analytically reconstruct the attitude from discrete gyroscope measurements over the time interval of interest. It is promising to produce ultra-accurate attitude reconstruction. However, the RodFIter method imposes high computational load and does not lend itself to onboard implementation. In this paper, a fast approach to significantly reduce RodFIter's computation complexity is presented while maintaining almost the same accuracy of attitude reconstruction. It reformulates the Rodrigues vector iterative integration in terms of the Chebyshev polynomial iteration. Due to the excellent property of Chebyshev polynomials, the fast RodFIter is achieved by means of appropriate truncation of Chebyshev polynomials, with provably guaranteed convergence. Moreover, simulation results validate the speed and accuracy of the proposed method.

cs.RO↗
arXiv2018

Memory Matching Networks for One-Shot Image Recognition

In this paper, we introduce the new ideas of augmenting Convolutional Neural Networks (CNNs) with Memory and learning to learn the network parameters for the unlabelled images on the fly in one-shot learning. Specifically, we present Memory Matching Networks (MM-Net) --- a novel deep architecture that explores the training procedure, following the philosophy that training and test conditions must match. Technically, MM-Net writes the features of a set of labelled images (support set) into memory and reads from memory when performing inference to holistically leverage the knowledge in the set. Meanwhile, a Contextual Learner employs the memory slots in a sequential manner to predict the parameters of CNNs for unlabelled images. The whole architecture is trained by once showing only a few examples per class and switching the learning from minibatch to minibatch, which is tailored for one-shot learning when presented with a few examples of new categories at test time. Unlike the conventional one-shot learning approaches, our MM-Net could output one unified model irrespective of the number of shots and categories. Extensive experiments are conducted on two public datasets, i.e., Omniglot and \emph{mini}ImageNet, and superior results are reported when compared to state-of-the-art approaches. More remarkably, our MM-Net improves one-shot accuracy on Omniglot from 98.95% to 99.28% and from 49.21% to 53.37% on \emph{mini}ImageNet.

cs.CV↗