Xiaojing Zhang

Xiaojing Zhang, Alexander Liniger, Francesco Borrelli

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled objects that can be represented in an n-dimensional space as the finite union of convex sets. Furthermore, we connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be used in generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find "least-intrusive" trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on a quadcopter navigation and automated parking problem, and our numerical experiments suggest that the proposed methods enable real-time optimization-based trajectory planning problems in tight environments. Source code of our implementation is provided at https://github.com/XiaojingGeorgeZhang/OBCA.

Bochen Lyu, Xiaojing Zhang, Fangyi Zheng et al.

This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has been a promising approach for studying the discrete optimization methods. Despite the crucial role of momentum in gradient-based optimization methods, the gap between the original discrete dynamics and the continuous time approximations due to the discretization error has not been comprehensively bridged yet. In this work, we study the HB momentum method in continuous time while putting more focus on the discretization error to provide additional theoretical tools to this area. In particular, we design a first-order piece-wise continuous differential equation, where we add a number of counter terms to account for the discretization error explicitly. As a result, we provide a continuous time model for the HB momentum method that allows the control of discretization error to arbitrary order of the step size. As an application, we leverage it to find a new implicit regularization of the directional smoothness and investigate the implicit bias of HB for diagonal linear networks, indicating how our results can be used in deep learning. Our theoretical findings are further supported by numerical experiments.

Bin Zhang, Yang Wu, Xiaojing Zhang et al.

In the current salient object detection network, the most popular method is using U-shape structure. However, the massive number of parameters leads to more consumption of computing and storage resources which are not feasible to deploy on the limited memory device. Some others shallow layer network will not maintain the same accuracy compared with U-shape structure and the deep network structure with more parameters will not converge to a global minimum loss with great speed. To overcome all of these disadvantages, we proposed a new deep convolution network architecture with three contributions: (1) using smaller convolution neural networks (CNNs) to compress the model in our improved salient object features compression and reinforcement extraction module (ISFCREM) to reduce parameters of the model. (2) introducing channel attention mechanism in ISFCREM to weigh different channels for improving the ability of feature representation. (3) applying a new optimizer to accumulate the long-term gradient information during training to adaptively tune the learning rate. The results demonstrate that the proposed method can compress the model to 1/3 of the original size nearly without losing the accuracy and converging faster and more smoothly on six widely used datasets of salient object detection compared with the others models. Our code is published in https://gitee.com/binzhangbinzhangbin/code-a-novel-attention-based-network-for-fast-salient-object-detection.git

Mazharul Islam, Shuangrong Liu, Lin Wang et al.

Floating centroid method (FCM) offers an efficient way to solve a fixed-centroid problem for the neural network classifiers. However, evolutionary computation as its optimization method restrains the FCM to achieve satisfactory performance for different neural network structures, because of the high computational complexity and inefficiency. Traditional gradient-based methods have been extensively adopted to optimize the neural network classifiers. In this study, a gradient-based floating centroid (GDFC) method is introduced to address the fixed centroid problem for the neural network classifiers optimized by gradient-based methods. Furthermore, a new loss function for optimizing GDFC is introduced. The experimental results display that GDFC obtains promising classification performance than the comparison methods on the benchmark datasets.