Zhuang Yang

Jianhao Xu, Zhuang Yang

The existing optimizers for deep neural networks (DNNs) typically rely on either the $\ell_2$ norm or the $\ell_\infty$ norm, resulting in optimizers that do not adapt well to substantial changes in curvature across parameter dimensions. Generally, the training process of DNNs often exhibits strong curvature anisotropy in the early period, whereas in the later period, the training process of DNNs tends to move toward flatter regions with weaker anisotropy. Particularly, optimizers based on the \(\ell_2\)-norm are usually dominated by high-curvature directions, restricting updates of optimizers along with lower curvature direction and thus leading to a slower convergence rate. While optimizers based on the \(\ell_\infty\)-norm are prone to oscillations in flatter regions, due to the coordinate-wise updates of the same magnitude. To address these two extreme cases generated by $\ell_2$ and $\ell_\infty$ norms, we propose a novel $\ell_p$-norm scheme with a dynamical value of $p$ and incorporate it into stochastic gradient descent (SGD) and SGD with momentum (SGDM), leading to two novel optimizers with better generalization performance: ${\ell_p}$-SGD (LPSGD) and ${\ell_p}$-SGDM (LPSGDM). Particularly, the resulting optimizers suppress the dominance of high-curvature directions in the early period by utilizing a large $p$ ($p>2$), followed by a gradual decrease of $p$ toward 2 to enable more stable and refined updates, where the latter process is motivated by the cosine annealing strategy. We establish theoretical guarantees of the resulting algorithms and analyze that both LPSGD and LPSGDM achieve an \(O(T^{-1/2})\) convergence rate for the nonconvex setting. Extensive experiments are conducted on benchmark datasets, including CIFAR-10, CIFAR-100, and ImageNet-1K, with multiple DNNs such as VGG-11, ResNet-18, and ResNet-50.

Huiyun Jiang, Zhuang Yang

Recent studies have shown the great potential of diffusion models in improving reinforcement learning (RL) by modeling complex policies, expressing a high degree of multi-modality, and efficiently handling high-dimensional continuous control tasks. However, there is currently limited research on how to optimize diffusion-based polices (e.g., Diffusion Policy) fast and stably. In this paper, we propose an Adam-based Diffusion Policy Optimization (ADPO), a fast algorithmic framework containing best practices for fine-tuning diffusion-based polices in robotic control tasks using the adaptive gradient descent method in RL. Adaptive gradient method is less studied in training RL, let alone diffusion-based policies. We confirm that ADPO outperforms other diffusion-based RL methods in terms of overall effectiveness for fine-tuning on standard robotic tasks. Concretely, we conduct extensive experiments on standard robotic control tasks to test ADPO, where, particularly, six popular diffusion-based RL methods are provided as benchmark methods. Experimental results show that ADPO acquires better or comparable performance than the baseline methods. Finally, we systematically analyze the sensitivity of multiple hyperparameters in standard robotics tasks, providing guidance for subsequent practical applications. Our video demonstrations are released in https://github.com/Timeless-lab/ADPO.git.

Zhuang Yang

Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one or more additional hyper-parameters manually whose bottlenecks include huge computational expenditure, time and power in practice. This work, in a natural and direct manner, clarifies how LR should be updated automatically only according to the intrinsic variation of stochastic gradients. An explainable LR regime by leveraging stochastic second-order algorithms is developed, behaving a similar pattern to heuristic algorithms but implemented simply without any parameter tuning requirement, where it is of an automatic procedure that LR should increase (decrease) as the norm of stochastic gradients decreases (increases). The resulting LR regime shows its efficiency, robustness, and scalability in different classical stochastic algorithms, containing SGD, SGDM, and SIGNSGD, on machine learning tasks.

Haobin Zhang, Zhuang Yang

Stochastic optimization algorithms, particularly stochastic policy gradient (SPG), report significant success in reinforcement learning (RL). Nevertheless, up to now, that how to speedily acquire an optimal solution for RL is still a challenge. To tackle this issue, this work develops a fast SPG algorithm from the perspective of utilizing a momentum, coined SPG-NM. Specifically, in SPG-NM, a novel type of the negative momentum (NM) technique is applied into the classical SPG algorithm. Different from the existing NM techniques, we have adopted a few hyper-parameters in our SPG-NM algorithm. Moreover, the computational complexity is nearly same as the modern SPG-type algorithms, e.g., accelerated policy gradient (APG), which equips SPG with Nesterov's accelerated gradient (NAG). We evaluate the resulting algorithm on two classical tasks, bandit setting and Markov decision process (MDP). Numerical results in different tasks demonstrate faster convergence rate of the resulting algorithm by comparing state-of-the-art algorithms, which confirm the positive impact of NM in accelerating SPG for RL. Also, numerical experiments under different settings confirm the robustness of our SPG-NM algorithm for some certain crucial hyper-parameters, which ride the user feel free in practice.

Zhuang Yang, Zengping Chen, Cheng Wang

StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating stochastic gradient estimates. The performance of SARAH significantly depends on the choice of step size sequence. However, SARAH and its variants often employ a best-tuned step size by mentor, which is time consuming in practice. Motivated by this gap, we proposed a variant of the Barzilai-Borwein (BB) method, referred to as the Random Barzilai-Borwein (RBB) method, to calculate step size for SARAH in the mini-batch setting, thereby leading to a new SARAH method: MB-SARAH-RBB. We prove that MB-SARAH-RBB converges linearly in expectation for strongly convex objective functions. We analyze the complexity of MB-SARAH-RBB and show that it is better than the original method. Numerical experiments on standard data sets indicate that MB-SARAH-RBB outperforms or matches state-of-the-art algorithms.

Shanxin Zhang, Cheng Wang, Zhuang Yang et al.

The timely provision of traffic sign information to drivers is essential for the drivers to respond, to ensure safe driving, and to avoid traffic accidents in a timely manner. We proposed a timely visual recognizability quantitative evaluation method for traffic signs in large-scale transportation environments. To achieve this goal, we first address the concept of a visibility field to reflect the visible distribution of three-dimensional (3D) space and construct a traffic sign Visibility Evaluation Model (VEM) to measure the traffic sign visibility for a given viewpoint. Then, based on the VEM, we proposed the concept of the Visual Recognizability Field (VRF) to reflect the visual recognizability distribution in 3D space and established a Visual Recognizability Evaluation Model (VREM) to measure a traffic sign visual recognizability for a given viewpoint. Next, we proposed a Traffic Sign Timely Visual Recognizability Evaluation Model (TSTVREM) by combining VREM, the actual maximum continuous visual recognizable distance, and traffic big data to measure a traffic sign visual recognizability in different lanes. Finally, we presented an automatic algorithm to implement the TSTVREM model through traffic sign and road marking detection and classification, traffic sign environment point cloud segmentation, viewpoints calculation, and TSTVREM model realization. The performance of our method for traffic sign timely visual recognizability evaluation is tested on three road point clouds acquired by a mobile laser scanning system (RIEGL VMX-450) according to Road Traffic Signs and Markings (GB 5768-1999 in China), showing that our method is feasible and efficient.