Zengde Deng

Jinxin Wang, Jiang Hu, Shixiang Chen et al.

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization problems, albeit frequently encountered in applications, are quite challenging due to their non-smoothness and non-convexity. To tackle them, we propose an iterative method called the decentralized Riemannian subgradient method (DRSM). The global convergence and an iteration complexity of $\mathcal{O}(\varepsilon^{-2} \log^2(\varepsilon^{-1}))$ for forcing a natural stationarity measure below $\varepsilon$ are established via the powerful tool of proximal smoothness from variational analysis, which could be of independent interest. Besides, we show the local linear convergence of the DRSM using geometrically diminishing stepsizes when the problem at hand further possesses a sharpness property. Numerical experiments are conducted to corroborate our theoretical findings.

Yue Xu, Hao Chen, Zengde Deng et al.

Graph Convolutional Networks (GCNs) and their variants have achieved significant performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which can arise severe computational burden to hinder their application to large-scale recommendation tasks. To this end, this paper proposes the flattened GCN~(FlatGCN) model, which is able to achieve superior performance with remarkably less complexity compared with existing models. Our main contribution is three-fold. First, we propose a simplified but powerful GCN architecture which aggregates the neighborhood information using one flattened GCN layer, instead of recursively. The aggregation step in FlatGCN is parameter-free such that it can be pre-computed with parallel computation to save memory and computational cost. Second, we propose an informative neighbor-infomax sampling method to select the most valuable neighbors by measuring the correlation among neighboring nodes based on a principled metric. Third, we propose a layer ensemble technique which improves the expressiveness of the learned representations by assembling the layer-wise neighborhood representations at the final layer. Extensive experiments on three datasets verify that our proposed model outperforms existing GCN models considerably and yields up to a few orders of magnitude speedup in training efficiency.

Qixin Zhang, Zengde Deng, Zaiyi Chen et al.

In this paper, we revisit the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, which finds wide real-world applications in the domain of machine learning, economics, and operations research. At first, we present the Meta-MFW algorithm achieving a $1/e$-regret of $O(\sqrt{T})$ at the cost of $T^{3/2}$ stochastic gradient evaluations per round. As far as we know, Meta-MFW is the first algorithm to obtain $1/e$-regret of $O(\sqrt{T})$ for the online non-monotone continuous DR-submodular maximization problem over a down-closed convex set. Furthermore, in sharp contrast with ODC algorithm \citep{thang2021online}, Meta-MFW relies on the simple online linear oracle without discretization, lifting, or rounding operations. Considering the practical restrictions, we then propose the Mono-MFW algorithm, which reduces the per-function stochastic gradient evaluations from $T^{3/2}$ to 1 and achieves a $1/e$-regret bound of $O(T^{4/5})$. Next, we extend Mono-MFW to the bandit setting and propose the Bandit-MFW algorithm which attains a $1/e$-regret bound of $O(T^{8/9})$. To the best of our knowledge, Mono-MFW and Bandit-MFW are the first sublinear-regret algorithms to explore the one-shot and bandit setting for online non-monotone continuous DR-submodular maximization problem over a down-closed convex set, respectively. Finally, we conduct numerical experiments on both synthetic and real-world datasets to verify the effectiveness of our methods.

Qixin Zhang, Zengde Deng, Xiangru Jian et al.

Maximizing a monotone submodular function is a fundamental task in machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of per-function gradient evaluations and per-round communication complexity from $T^{3/2}$ to $1$. The first one, One-shot Decentralized Meta-Frank-Wolfe (Mono-DMFW), achieves a $(1-1/e)$-regret bound of $O(T^{4/5})$. As far as we know, this is the first one-shot and projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function \citep{zhang2022boosting}, we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a $(1-1/e)$-regret of $O(\sqrt{T})$. To the best of our knowledge, this is the first result to obtain the optimal $O(\sqrt{T})$ against a $(1-1/e)$-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.

Yuwei Chen, Zengde Deng, Yinzhi Zhou et al.

This paper studies the online stochastic resource allocation problem (RAP) with chance constraints. The online RAP is a 0-1 integer linear programming problem where the resource consumption coefficients are revealed column by column along with the corresponding revenue coefficients. When a column is revealed, the corresponding decision variables are determined instantaneously without future information. Moreover, in online applications, the resource consumption coefficients are often obtained by prediction. To model their uncertainties, we take the chance constraints into the consideration. To the best of our knowledge, this is the first time chance constraints are introduced in the online RAP problem. Assuming that the uncertain variables have known Gaussian distributions, the stochastic RAP can be transformed into a deterministic but nonlinear problem with integer second-order cone constraints. Next, we linearize this nonlinear problem and analyze the performance of vanilla online primal-dual algorithm for solving the linearized stochastic RAP. Under mild technical assumptions, the optimality gap and constraint violation are both on the order of $\sqrt{n}$. Then, to further improve the performance of the algorithm, several modified online primal-dual algorithms with heuristic corrections are proposed. Finally, extensive numerical experiments on both synthetic and real data demonstrate the applicability and effectiveness of our methods.

Jiawei Liu, Junqiao Li, Jiangfan Deng et al.

The "one-shot" technique represents a distinct and sophisticated aesthetic in filmmaking. However, its practical realization is often hindered by prohibitive costs and complex real-world constraints. Although emerging video generation models offer a virtual alternative, existing approaches typically rely on naive clip concatenation, which frequently fails to maintain visual smoothness and temporal coherence. In this paper, we introduce DreaMontage, a comprehensive framework designed for arbitrary frame-guided generation, capable of synthesizing seamless, expressive, and long-duration one-shot videos from diverse user-provided inputs. To achieve this, we address the challenge through three primary dimensions. (i) We integrate a lightweight intermediate-conditioning mechanism into the DiT architecture. By employing an Adaptive Tuning strategy that effectively leverages base training data, we unlock robust arbitrary-frame control capabilities. (ii) To enhance visual fidelity and cinematic expressiveness, we curate a high-quality dataset and implement a Visual Expression SFT stage. In addressing critical issues such as subject motion rationality and transition smoothness, we apply a Tailored DPO scheme, which significantly improves the success rate and usability of the generated content. (iii) To facilitate the production of extended sequences, we design a Segment-wise Auto-Regressive (SAR) inference strategy that operates in a memory-efficient manner. Extensive experiments demonstrate that our approach achieves visually striking and seamlessly coherent one-shot effects while maintaining computational efficiency, empowering users to transform fragmented visual materials into vivid, cohesive one-shot cinematic experiences.

Qixin Zhang, Zongqi Wan, Zengde Deng et al.

Projected Gradient Ascent (PGA) is the most commonly used optimization scheme in machine learning and operations research areas. Nevertheless, numerous studies and examples have shown that the PGA methods may fail to achieve the tight approximation ratio for continuous DR-submodular maximization problems. To address this challenge, we present a boosting technique in this paper, which can efficiently improve the approximation guarantee of the standard PGA to \emph{optimal} with only small modifications on the objective function. The fundamental idea of our boosting technique is to exploit non-oblivious search to derive a novel auxiliary function $F$, whose stationary points are excellent approximations to the global maximum of the original DR-submodular objective $f$. Specifically, when $f$ is monotone and $γ$-weakly DR-submodular, we propose an auxiliary function $F$ whose stationary points can provide a better $(1-e^{-γ})$-approximation than the $(γ^2/(1+γ^2))$-approximation guaranteed by the stationary points of $f$ itself. Similarly, for the non-monotone case, we devise another auxiliary function $F$ whose stationary points can achieve an optimal $\frac{1-\min_{\boldsymbol{x}\in\mathcal{C}}\|\boldsymbol{x}\|_{\infty}}{4}$-approximation guarantee where $\mathcal{C}$ is a convex constraint set. In contrast, the stationary points of the original non-monotone DR-submodular function can be arbitrarily bad~\citep{chen2023continuous}. Furthermore, we demonstrate the scalability of our boosting technique on four problems. In all of these four problems, our resulting variants of boosting PGA algorithm beat the previous standard PGA in several aspects such as approximation ratio and efficiency. Finally, we corroborate our theoretical findings with numerical experiments, which demonstrate the effectiveness of our boosting PGA methods.

Hao Chen, Zhong Huang, Yue Xu et al.

The recently proposed Graph Convolutional Networks (GCNs) have achieved significantly superior performance on various graph-related tasks, such as node classification and recommendation. However, currently researches on GCN models usually recursively aggregate the information from all the neighbors or randomly sampled neighbor subsets, without explicitly identifying whether the aggregated neighbors provide useful information during the graph convolution. In this paper, we theoretically analyze the affection of the neighbor quality over GCN models' performance and propose the Neighbor Enhanced Graph Convolutional Network (NEGCN) framework to boost the performance of existing GCN models. Our contribution is three-fold. First, we at the first time propose the concept of neighbor quality for both node classification and recommendation tasks in a general theoretical framework. Specifically, for node classification, we propose three propositions to theoretically analyze how the neighbor quality affects the node classification performance of GCN models. Second, based on the three proposed propositions, we introduce the graph refinement process including specially designed neighbor evaluation methods to increase the neighbor quality so as to boost both the node classification and recommendation tasks. Third, we conduct extensive node classification and recommendation experiments on several benchmark datasets. The experimental results verify that our proposed NEGCN framework can significantly enhance the performance for various typical GCN models on both node classification and recommendation tasks.

Qixin Zhang, Zengde Deng, Zaiyi Chen et al.

In this paper, we revisit Stochastic Continuous Submodular Maximization in both offline and online settings, which can benefit wide applications in machine learning and operations research areas. We present a boosting framework covering gradient ascent and online gradient ascent. The fundamental ingredient of our methods is a novel non-oblivious function $F$ derived from a factor-revealing optimization problem, whose any stationary point provides a $(1-e^{-γ})$-approximation to the global maximum of the $γ$-weakly DR-submodular objective function $f\in C^{1,1}_L(\mathcal{X})$. Under the offline scenario, we propose a boosting gradient ascent method achieving $(1-e^{-γ}-ε^{2})$-approximation after $O(1/ε^2)$ iterations, which improves the $(\frac{γ^2}{1+γ^2})$ approximation ratio of the classical gradient ascent algorithm. In the online setting, for the first time we consider the adversarial delays for stochastic gradient feedback, under which we propose a boosting online gradient algorithm with the same non-oblivious function $F$. Meanwhile, we verify that this boosting online algorithm achieves a regret of $O(\sqrt{D})$ against a $(1-e^{-γ})$-approximation to the best feasible solution in hindsight, where $D$ is the sum of delays of gradient feedback. To the best of our knowledge, this is the first result to obtain $O(\sqrt{T})$ regret against a $(1-e^{-γ})$-approximation with $O(1)$ gradient inquiry at each time step, when no delay exists, i.e., $D=T$. Finally, numerical experiments demonstrate the effectiveness of our boosting methods.

Hao Chen, Zengde Deng, Yue Xu et al.

Graph Convolutional Networks (GCNs) are powerful models for node representation learning tasks. However, the node representation in existing GCN models is usually generated by performing recursive neighborhood aggregation across multiple graph convolutional layers with certain sampling methods, which may lead to redundant feature mixing, needless information loss, and extensive computations. Therefore, in this paper, we propose a novel architecture named Non-Recursive Graph Convolutional Network (NRGCN) to improve both the training efficiency and the learning performance of GCNs in the context of node classification. Specifically, NRGCN proposes to represent different hops of neighbors for each node based on inner-layer aggregation and layer-independent sampling. In this way, each node can be directly represented by concatenating the information extracted independently from each hop of its neighbors thereby avoiding the recursive neighborhood expansion across layers. Moreover, the layer-independent sampling and aggregation can be precomputed before the model training, thus the training process can be accelerated considerably. Extensive experiments on benchmark datasets verify that our NRGCN outperforms the state-of-the-art GCN models, in terms of the node classification performance and reliability.

Yue Xu, Hao Chen, Zengde Deng et al.

Graph Convolutional Networks (GCNs) and their variants have received significant attention and achieved start-of-the-art performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which arises severe computational burden. Moreover, they favor multi-layer architectures in conjunction with complicated modeling techniques. Though effective, the excessive amount of model parameters largely hinder their applications in real-world recommender systems. To this end, in this paper, we propose the single-layer GCN model which is able to achieve superior performance along with remarkably less complexity compared with existing models. Our main contribution is three-fold. First, we propose a principled similarity metric named distribution-aware similarity (DA similarity), which can guide the neighbor sampling process and evaluate the quality of the input graph explicitly. We also prove that DA similarity has a positive correlation with the final performance, through both theoretical analysis and empirical simulations. Second, we propose a simplified GCN architecture which employs a single GCN layer to aggregate information from the neighbors filtered by DA similarity and then generates the node representations. Moreover, the aggregation step is a parameter-free operation, such that it can be done in a pre-processing manner to further reduce red the training and inference costs. Third, we conduct extensive experiments on four datasets. The results verify that the proposed model outperforms existing GCN models considerably and yields up to a few orders of magnitude speedup in training, in terms of the recommendation performance.

Shixiang Chen, Zengde Deng, Shiqian Ma et al.

We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms for tackling this problem. Specifically, our contribution is threefold. First, we present a manifold proximal point algorithm (ManPPA) for the problem and show that it converges at a sublinear rate. Furthermore, we show that ManPPA can achieve a quadratic convergence rate when applied to the ODL and RSR problems. Second, we propose a stochastic variant of ManPPA called StManPPA, which is well suited for large-scale computation, and establish its sublinear convergence rate. Both ManPPA and StManPPA have provably faster convergence rates than existing subgradient-type methods. Third, using ManPPA as a building block, we propose a new approach to solving a matrix analog of the problem, in which the sphere is replaced by the Stiefel manifold. The results from our extensive numerical experiments on the ODL and RSR problems demonstrate the efficiency and efficacy of our proposed methods.

Xiao Li, Shixiang Chen, Zengde Deng et al.

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely unexplored. We present a family of Riemannian subgradient-type methods -- namely Riemannain subgradient, incremental subgradient, and stochastic subgradient methods -- to solve these problems and show that they all have an iteration complexity of ${\cal O}(\varepsilon^{-4})$ for driving a natural stationarity measure below $\varepsilon$. In addition, we establish the local linear convergence of the Riemannian subgradient and incremental subgradient methods when the problem at hand further satisfies a sharpness property and the algorithms are properly initialized and use geometrically diminishing stepsizes. To the best of our knowledge, these are the first convergence guarantees for using Riemannian subgradient-type methods to optimize a class of nonconvex nonsmooth functions over the Stiefel manifold. The fundamental ingredient in the proof of the aforementioned convergence results is a new Riemannian subgradient inequality for restrictions of weakly convex functions on the Stiefel manifold, which could be of independent interest. We also show that our convergence results can be extended to handle a class of compact embedded submanifolds of the Euclidean space. Finally, we discuss the sharpness properties of various formulations of the robust subspace recovery and orthogonal dictionary learning problems and demonstrate the convergence performance of the algorithms on both problems via numerical simulations.

Hao Chen, Yue Xu, Feiran Huang et al.

Recent advances in Graph Convolutional Networks (GCNs) have led to state-of-the-art performance on various graph-related tasks. However, most existing GCN models do not explicitly identify whether all the aggregated neighbors are valuable to the learning tasks, which may harm the learning performance. In this paper, we consider the problem of node classification and propose the Label-Aware Graph Convolutional Network (LAGCN) framework which can directly identify valuable neighbors to enhance the performance of existing GCN models. Our contribution is three-fold. First, we propose a label-aware edge classifier that can filter distracting neighbors and add valuable neighbors for each node to refine the original graph into a label-aware~(LA) graph. Existing GCN models can directly learn from the LA graph to improve the performance without changing their model architectures. Second, we introduce the concept of positive ratio to evaluate the density of valuable neighbors in the LA graph. Theoretical analysis reveals that using the edge classifier to increase the positive ratio can improve the learning performance of existing GCN models. Third, we conduct extensive node classification experiments on benchmark datasets. The results verify that LAGCN can improve the performance of existing GCN models considerably, in terms of node classification.

Yue Xu, Zengde Deng, Mengdi Wang et al.

The recent success of single-agent reinforcement learning (RL) in Internet of things (IoT) systems motivates the study of multi-agent reinforcement learning (MARL), which is more challenging but more useful in large-scale IoT. In this paper, we consider a voting-based MARL problem, in which the agents vote to make group decisions and the goal is to maximize the globally averaged returns. To this end, we formulate the MARL problem based on the linear programming form of the policy optimization problem and propose a distributed primal-dual algorithm to obtain the optimal solution. We also propose a voting mechanism through which the distributed learning achieves the same sublinear convergence rate as centralized learning. In other words, the distributed decision making does not slow down the process of achieving global consensus on optimality. Lastly, we verify the convergence of our proposed algorithm with numerical simulations and conduct case studies in practical multi-agent IoT systems.

Zengde Deng, Anthony Man-Cho So

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem with linear equality constraints. By fully exploiting second-order sparsity of the problem, we are able to greatly reduce the computational cost and obtain highly efficient implementations. Furthermore, numerical results on both synthetic data and real data show that our algorithm is superior to existing first-order methods in terms of both running time and solution accuracy.