arXiv subjects

Qing Ling

Publications and source records attributed to Qing Ling.

At least 55 records · Page 3Linked to original sources

arXiv2018

Solving Non-smooth Constrained Programs with Lower Complexity than $\mathcal{O}(1/\varepsilon)$: A Primal-Dual Homotopy Smoothing Approach

We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a non-smooth problem is $\mathcal{O}(\varepsilon^{-1})$. In this paper, we show that by leveraging a local error bound condition on the dual function, the proposed algorithm can achieve a better primal convergence time of $\mathcal{O}\left(\varepsilon^{-2/(2+β)}\log_2(\varepsilon^{-1})\right)$, where $β\in(0,1]$ is a local error bound parameter. As an example application of the general algorithm, we show that the distributed geometric median problem, which can be formulated as a constrained convex program, has its dual function non-smooth but satisfying the aforementioned local error bound condition with $β=1/2$, therefore enjoying a convergence time of $\mathcal{O}\left(\varepsilon^{-4/5}\log_2(\varepsilon^{-1})\right)$. This result improves upon the $\mathcal{O}(\varepsilon^{-1})$ convergence time bound achieved by existing distributed optimization algorithms. Simulation experiments also demonstrate the performance of our proposed algorithm.

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arXiv2018

DADA: Deep Adversarial Data Augmentation for Extremely Low Data Regime Classification

Deep learning has revolutionized the performance of classification, but meanwhile demands sufficient labeled data for training. Given insufficient data, while many techniques have been developed to help combat overfitting, the challenge remains if one tries to train deep networks, especially in the ill-posed extremely low data regimes: only a small set of labeled data are available, and nothing -- including unlabeled data -- else. Such regimes arise from practical situations where not only data labeling but also data collection itself is expensive. We propose a deep adversarial data augmentation (DADA) technique to address the problem, in which we elaborately formulate data augmentation as a problem of training a class-conditional and supervised generative adversarial network (GAN). Specifically, a new discriminator loss is proposed to fit the goal of data augmentation, through which both real and augmented samples are enforced to contribute to and be consistent in finding the decision boundaries. Tailored training techniques are developed accordingly. To quantitatively validate its effectiveness, we first perform extensive simulations to show that DADA substantially outperforms both traditional data augmentation and a few GAN-based options. We then extend experiments to three real-world small labeled datasets where existing data augmentation and/or transfer learning strategies are either less effective or infeasible. All results endorse the superior capability of DADA in enhancing the generalization ability of deep networks trained in practical extremely low data regimes. Source code is available at https://github.com/SchafferZhang/DADA.

cs.CV↗

arXiv2018

Decentralized RLS with Data-Adaptive Censoring for Regressions over Large-Scale Networks

The deluge of networked data motivates the development of algorithms for computation- and communication-efficient information processing. In this context, three data-adaptive censoring strategies are introduced to considerably reduce the computation and communication overhead of decentralized recursive least-squares (D-RLS) solvers. The first relies on alternating minimization and the stochastic Newton iteration to minimize a network-wide cost, which discards observations with small innovations. In the resultant algorithm, each node performs local data-adaptive censoring to reduce computations, while exchanging its local estimate with neighbors so as to consent on a network-wide solution. The communication cost is further reduced by the second strategy, which prevents a node from transmitting its local estimate to neighbors when the innovation it induces to incoming data is minimal. In the third strategy, not only transmitting, but also receiving estimates from neighbors is prohibited when data-adaptive censoring is in effect. For all strategies, a simple criterion is provided for selecting the threshold of innovation to reach a prescribed average data reduction. The novel censoring-based (C)D-RLS algorithms are proved convergent to the optimal argument in the mean-square deviation sense. Numerical experiments validate the effectiveness of the proposed algorithms in reducing computation and communication overhead.

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arXiv2017

Learn-and-Adapt Stochastic Dual Gradients for Network Resource Allocation

Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of Lagrange multipliers in network resource allocation, a novel learn-and-adapt stochastic dual gradient (LA-SDG) method is developed in this paper to learn the sample-optimal Lagrange multiplier from historical data, and accordingly adapt the upcoming resource allocation strategy. Remarkably, LA-SDG only requires just an extra sample (gradient) evaluation relative to the celebrated stochastic dual gradient (SDG) method. LA-SDG can be interpreted as a foresighted learning scheme with an eye on the future, or, a modified heavy-ball iteration from an optimization viewpoint. It is established - both theoretically and empirically - that LA-SDG markedly improves the cost-delay tradeoff over state-of-the-art allocation schemes.

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arXiv2017

Decentralized Consensus Optimization with Asynchrony and Delays

We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network in which the agents communicate with their neighbors and perform local computation. In the proposed algorithm, each agent can compute and communicate independently at different times, for different durations, with the information it has even if the latest information from its neighbors is not yet available. Such an asynchronous algorithm reduces the time that agents would otherwise waste idle because of communication delays or because their neighbors are slower. It also eliminates the need for a global clock for synchronization. Mathematically, the algorithm involves both primal and dual variables, uses fixed step-size parameters, and provably converges to the exact solution under a bounded delay assumption and a random agent assumption. When running synchronously, the algorithm performs just as well as existing competitive synchronous algorithms such as PG-EXTRA, which diverges without synchronization. Numerical experiments confirm the theoretical findings and illustrate the performance of the proposed algorithm.

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arXiv2017

An Online Convex Optimization Approach to Dynamic Network Resource Allocation

Existing approaches to online convex optimization (OCO) make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret that measures the difference of losses between the online solution and the best yet fixed overall solution in hindsight. The present paper deals with online convex optimization involving adversarial loss functions and adversarial constraints, where the constraints are revealed after making decisions, and can be tolerable to instantaneous violations but must be satisfied in the long term. Performance of an online algorithm in this setting is assessed by: i) the difference of its losses relative to the best dynamic solution with one-slot-ahead information of the loss function and the constraint (that is here termed dynamic regret); and, ii) the accumulated amount of constraint violations (that is here termed dynamic fit). In this context, a modified online saddle-point (MOSP) scheme is developed, and proved to simultaneously yield sub-linear dynamic regret and fit, provided that the accumulated variations of per-slot minimizers and constraints are sub-linearly growing with time. MOSP is also applied to the dynamic network resource allocation task, and it is compared with the well-known stochastic dual gradient method. Under various scenarios, numerical experiments demonstrate the performance gain of MOSP relative to the state-of-the-art.

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arXiv2017

Robust Group LASSO Over Decentralized Networks

This paper considers the recovery of group sparse signals over a multi-agent network, where the measurements are subject to sparse errors. We first investigate the robust group LASSO model and its centralized algorithm based on the alternating direction method of multipliers (ADMM), which requires a central fusion center to compute a global row-support detector. To implement it in a decentralized network environment, we then adopt dynamic average consensus strategies that enable dynamic tracking of the global row-support detector. Numerical experiments demonstrate the effectiveness of the proposed algorithms.

cs.DC↗

arXiv2016

Stacked Approximated Regression Machine: A Simple Deep Learning Approach

With the agreement of my coauthors, I Zhangyang Wang would like to withdraw the manuscript "Stacked Approximated Regression Machine: A Simple Deep Learning Approach". Some experimental procedures were not included in the manuscript, which makes a part of important claims not meaningful. In the relevant research, I was solely responsible for carrying out the experiments; the other coauthors joined in the discussions leading to the main algorithm. Please see the updated text for more details.

cs.LG↗

arXiv2016

Make Workers Work Harder: Decoupled Asynchronous Proximal Stochastic Gradient Descent

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD), to minimize an objective function that is the composite of the average of multiple empirical losses and a regularization term. Unlike the traditional asynchronous proximal stochastic gradient descent (TAP-SGD) in which the master carries much of the computation load, the proposed algorithm off-loads the majority of computation tasks from the master to workers, and leaves the master to conduct simple addition operations. This strategy yields an easy-to-parallelize algorithm, whose performance is justified by theoretical convergence analyses. To be specific, DAP-SGD achieves an $O(\log T/T)$ rate when the step-size is diminishing and an ergodic $O(1/\sqrt{T})$ rate when the step-size is constant, where $T$ is the number of total iterations.

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arXiv2016

$\mathbf{D^3}$: Deep Dual-Domain Based Fast Restoration of JPEG-Compressed Images

In this paper, we design a Deep Dual-Domain ($\mathbf{D^3}$) based fast restoration model to remove artifacts of JPEG compressed images. It leverages the large learning capacity of deep networks, as well as the problem-specific expertise that was hardly incorporated in the past design of deep architectures. For the latter, we take into consideration both the prior knowledge of the JPEG compression scheme, and the successful practice of the sparsity-based dual-domain approach. We further design the One-Step Sparse Inference (1-SI) module, as an efficient and light-weighted feed-forward approximation of sparse coding. Extensive experiments verify the superiority of the proposed $D^3$ model over several state-of-the-art methods. Specifically, our best model is capable of outperforming the latest deep model for around 1 dB in PSNR, and is 30 times faster.

cs.CV↗

arXiv2016

Learning A Deep $\ell_\infty$ Encoder for Hashing

We investigate the $\ell_\infty$-constrained representation which demonstrates robustness to quantization errors, utilizing the tool of deep learning. Based on the Alternating Direction Method of Multipliers (ADMM), we formulate the original convex minimization problem as a feed-forward neural network, named \textit{Deep $\ell_\infty$ Encoder}, by introducing the novel Bounded Linear Unit (BLU) neuron and modeling the Lagrange multipliers as network biases. Such a structural prior acts as an effective network regularization, and facilitates the model initialization. We then investigate the effective use of the proposed model in the application of hashing, by coupling the proposed encoders under a supervised pairwise loss, to develop a \textit{Deep Siamese $\ell_\infty$ Network}, which can be optimized from end to end. Extensive experiments demonstrate the impressive performances of the proposed model. We also provide an in-depth analysis of its behaviors against the competitors.

cs.LG↗

arXiv2016

A Decentralized Second-Order Method for Dynamic Optimization

This paper considers decentralized dynamic optimization problems where nodes of a network try to minimize a sequence of time-varying objective functions in a real-time scheme. At each time slot, nodes have access to different summands of an instantaneous global objective function and they are allowed to exchange information only with their neighbors. This paper develops the application of the Exact Second-Order Method (ESOM) to solve the dynamic optimization problem in a decentralized manner. The proposed dynamic ESOM algorithm operates by primal descending and dual ascending on a quadratic approximation of an augmented Lagrangian of the instantaneous consensus optimization problem. The convergence analysis of dynamic ESOM indicates that a Lyapunov function of the sequence of primal and dual errors converges linearly to an error bound when the local functions are strongly convex and have Lipschitz continuous gradients. Numerical results demonstrate the claim that the sequence of iterates generated by the proposed method is able to track the sequence of optimal arguments.

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arXiv2016

A Decentralized Second-Order Method with Exact Linear Convergence Rate for Consensus Optimization

This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is considered as a powerful tool that relies on proximal primal descent and dual ascent updates on a suitably defined augmented Lagrangian. The structure of the augmented Lagrangian makes this problem non-decomposable, which precludes distributed implementations. This problem is regularly addressed by the use of the alternating direction method of multipliers. The exact second order method (ESOM) is introduced here as an alternative that relies on: (i) The use of a separable quadratic approximation of the augmented Lagrangian. (ii) A truncated Taylor's series to estimate the solution of the first order condition imposed on the minimization of the quadratic approximation of the augmented Lagrangian. The sequences of primal and dual variables generated by ESOM are shown to converge linearly to their optimal arguments when the aggregate cost function is strongly convex and its gradients are Lipschitz continuous. Numerical results demonstrate advantages of ESOM relative to decentralized alternatives in solving least squares and logistic regression problems.

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arXiv2015

Learning Deep $\ell_0$ Encoders

Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two typical forms, the $\ell_0$ regularized problem and the $M$-sparse problem, are investigated. Based on solid iterative algorithms, we model them as feed-forward neural networks, through introducing novel neurons and pooling functions. Enforcing such structural priors acts as an effective network regularization. The deep encoders also enjoy faster inference, larger learning capacity, and better scalability compared to conventional sparse coding solutions. Furthermore, under task-driven losses, the models can be conveniently optimized from end to end. Numerical results demonstrate the impressive performances of the proposed encoders.

cs.LG↗

arXiv2015

Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

This paper considers an optimization problem that components of the objective function are available at different nodes of a network and nodes are allowed to only exchange information with their neighbors. The decentralized alternating method of multipliers (DADMM) is a well-established iterative method for solving this category of problems; however, implementation of DADMM requires solving an optimization subproblem at each iteration for each node. This procedure is often computationally costly for the nodes. We introduce a decentralized quadratic approximation of ADMM (DQM) that reduces computational complexity of DADMM by minimizing a quadratic approximation of the objective function. Notwithstanding that DQM successively minimizes approximations of the cost, it converges to the optimal arguments at a linear rate which is identical to the convergence rate of DADMM. Further, we show that as time passes the coefficient of linear convergence for DQM approaches the one for DADMM. Numerical results demonstrate the effectiveness of DQM.

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arXiv2015

Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso

This paper considers the problem of recovering a group sparse signal matrix $\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corrupted measurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots, \mathbf{A}_{(L)}\mathbf{y}_{L}] + \mathbf{S}$, where $\mathbf{A}_{(i)}$'s are known sensing matrices and $\mathbf{S}$ is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover $\mathbf{Y}$ and $\mathbf{S}$ through simultaneously minimizing the $\ell_{2,1}$-norm of $\mathbf{Y}$ and the $\ell_1$-norm of $\mathbf{S}$ under the measurement constraints. We prove that $\mathbf{Y}$ and $\mathbf{S}$ can be exactly recovered from the RGL model with a high probability for a very general class of $\mathbf{A}_{(i)}$'s.

cs.IT↗

arXiv2015

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

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arXiv2015

On the Convergence of Decentralized Gradient Descent

Consider the consensus problem of minimizing $f(x)=\sum_{i=1}^n f_i(x)$ where each $f_i$ is only known to one individual agent $i$ out of a connected network of $n$ agents. All the agents shall collaboratively solve this problem and obtain the solution subject to data exchanges restricted to between neighboring agents. Such algorithms avoid the need of a fusion center, offer better network load balance, and improve data privacy. We study the decentralized gradient descent method in which each agent $i$ updates its variable $x_{(i)}$, which is a local approximate to the unknown variable $x$, by combining the average of its neighbors' with the negative gradient step $-α\nabla f_i(x_{(i)})$. The iteration is $$x_{(i)}(k+1) \gets \sum_{\text{neighbor} j \text{of} i} w_{ij} x_{(j)}(k) - α\nabla f_i(x_{(i)}(k)),\quad\text{for each agent} i,$$ where the averaging coefficients form a symmetric doubly stochastic matrix $W=[w_{ij}] \in \mathbb{R}^{n \times n}$. We analyze the convergence of this iteration and derive its converge rate, assuming that each $f_i$ is proper closed convex and lower bounded, $\nabla f_i$ is Lipschitz continuous with constant $L_{f_i}$, and stepsize $α$ is fixed. Provided that $α< O(1/L_h)$ where $L_h=\max_i\{L_{f_i}\}$, the objective error at the averaged solution, $f(\frac{1}{n}\sum_i x_{(i)}(k))-f^*$, reduces at a speed of $O(1/k)$ until it reaches $O(α)$. If $f_i$ are further (restricted) strongly convex, then both $\frac{1}{n}\sum_i x_{(i)}(k)$ and each $x_{(i)}(k)$ converge to the global minimizer $x^*$ at a linear rate until reaching an $O(α)$-neighborhood of $x^*$. We also develop an iteration for decentralized basis pursuit and establish its linear convergence to an $O(α)$-neighborhood of the true unknown sparse signal.

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