arXiv subjects

Tianyou Chai

Publications and source records attributed to Tianyou Chai.

31 records · Page 2Linked to original sources

arXiv2022

Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization

This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and constraint functions. At each round, each agent selects a decision from the decision set, and then only a portion of the loss function and a coordinate block of the constraint function at this round are privately revealed to this agent. The goal of the network is to minimize the network-wide loss accumulated over time. Two distributed online algorithms with full-information and bandit feedback are proposed. Both dynamic and static network regret bounds are analyzed for the proposed algorithms, and network cumulative constraint violation is used to measure constraint violation, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. In particular, we show that the proposed algorithms achieve $\mathcal{O}(T^{\max\{κ,1-κ\}})$ static network regret and $\mathcal{O}(T^{1-κ/2})$ network cumulative constraint violation, where $T$ is the time horizon and $κ\in(0,1)$ is a user-defined trade-off parameter. Moreover, if the loss functions are strongly convex, then the static network regret bound can be reduced to $\mathcal{O}(T^κ)$. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

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arXiv2022

Communication Compression for Distributed Nonconvex Optimization

This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents iteratively communicate with neighbors, we propose three distributed primal--dual algorithms with compressed communication. The first two algorithms are applicable to a general class of compressors with bounded relative compression error and the third algorithm is suitable for two general classes of compressors with bounded absolute compression error. We show that the proposed distributed algorithms with compressed communication have comparable convergence properties as state-of-the-art algorithms with exact communication. Specifically, we show that they can find first-order stationary points with sublinear convergence rate $\mathcal{O}(1/T)$ when each local cost function is smooth, where $T$ is the total number of iterations, and find global optima with linear convergence rate under an additional condition that the global cost function satisfies the Polyak--Łojasiewicz condition. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.

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arXiv2022

Safety-based Speed Control of a Wheelchair using Robust Adaptive Model Predictive Control

Electric-powered wheelchair plays an important role in providing accessibility for people with mobility impairment. Ensuring the safety of wheelchair operation in different application scenarios and for diverse users is crucial when the designing controller for tracking tasks. In this work, we propose a safety-based speed tracking control algorithm for wheelchair systems with external disturbances and uncertain parameters at the dynamic level. The set-membership approach is applied to estimate the sets of uncertain parameters online and a designed model predictive control scheme with online model and control parameter adaptation is presented to guarantee safety-related constraints during the tracking process. The proposed controller can drive the wheelchair speed to a desired reference within safety constraints. For the inadmissible reference that violates the constraints, the proposed controller can steer the system to the neighbourhood of the closest admissible reference. The effectiveness of the proposed control scheme is validated based on the high-fidelity speed tracking results of two tasks that involve feasible and infeasible references.

eess.SY↗

arXiv2022

A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine learning techniques with data parallelism, such as deep learning and federated learning. We propose a distributed primal--dual stochastic gradient descent (SGD) algorithm, suitable for arbitrarily connected communication networks and any smooth (possibly nonconvex) cost functions. We show that the proposed algorithm achieves the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ for general nonconvex cost functions and the linear speedup convergence rate $\mathcal{O}(1/(nT))$ when the global cost function satisfies the Polyak--Łojasiewicz (P--Ł) condition, where $T$ is the total number of iterations. We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum. We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

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arXiv2021

Spatial-Angular Attention Network for Light Field Reconstruction

Typical learning-based light field reconstruction methods demand in constructing a large receptive field by deepening the network to capture correspondences between input views. In this paper, we propose a spatial-angular attention network to perceive correspondences in the light field non-locally, and reconstruction high angular resolution light field in an end-to-end manner. Motivated by the non-local attention mechanism, a spatial-angular attention module specifically for the high-dimensional light field data is introduced to compute the responses from all the positions in the epipolar plane for each pixel in the light field, and generate an attention map that captures correspondences along the angular dimension. We then propose a multi-scale reconstruction structure to efficiently implement the non-local attention in the low spatial scale, while also preserving the high frequency components in the high spatial scales. Extensive experiments demonstrate the superior performance of the proposed spatial-angular attention network for reconstructing sparsely-sampled light fields with non-Lambertian effects.

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arXiv2021

Linear Convergence of First- and Zeroth-Order Primal-Dual Algorithms for Distributed Nonconvex Optimization

This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual algorithm. We show that it converges sublinearly to a stationary point if each local cost function is smooth and linearly to a global optimum under an additional condition that the global cost function satisfies the Polyak-Łojasiewicz condition. This condition is weaker than strong convexity, which is a standard condition for proving linear convergence of distributed optimization algorithms, and the global minimizer is not necessarily unique. Motivated by the situations where the gradients are unavailable, we then propose a distributed zeroth-order algorithm, derived from the considered first-order algorithm by using a deterministic gradient estimator, and show that it has the same convergence properties as the considered first-order algorithm under the same conditions. The theoretical results are illustrated by numerical simulations.

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arXiv2021

Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraints

This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to measure constraint violations, which excludes the situation that strictly feasible constraints can compensate the effects of violated constraints. A novel algorithm is first proposed and it achieves an $\mathcal{O}(T^{\max\{c,1-c\}})$ bound for static regret and an $\mathcal{O}(T^{(1-c)/2})$ bound for cumulative constraint violation, where $c\in(0,1)$ is a user-defined trade-off parameter, and thus has improved performance compared with existing results. Both static regret and cumulative constraint violation bounds are reduced to $\mathcal{O}(\log(T))$ when the loss functions are strongly convex, which also improves existing results. %In order to bound the regret with respect to any comparator sequence, In order to achieve the optimal regret with respect to any comparator sequence, another algorithm is then proposed and it achieves the optimal $\mathcal{O}(\sqrt{T(1+P_T)})$ regret and an $\mathcal{O}(\sqrt{T})$ cumulative constraint violation, where $P_T$ is the path-length of the comparator sequence. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

cs.LG↗

arXiv2021

Revisiting Light Field Rendering with Deep Anti-Aliasing Neural Network

The light field (LF) reconstruction is mainly confronted with two challenges, large disparity and the non-Lambertian effect. Typical approaches either address the large disparity challenge using depth estimation followed by view synthesis or eschew explicit depth information to enable non-Lambertian rendering, but rarely solve both challenges in a unified framework. In this paper, we revisit the classic LF rendering framework to address both challenges by incorporating it with advanced deep learning techniques. First, we analytically show that the essential issue behind the large disparity and non-Lambertian challenges is the aliasing problem. Classic LF rendering approaches typically mitigate the aliasing with a reconstruction filter in the Fourier domain, which is, however, intractable to implement within a deep learning pipeline. Instead, we introduce an alternative framework to perform anti-aliasing reconstruction in the image domain and analytically show comparable efficacy on the aliasing issue. To explore the full potential, we then embed the anti-aliasing framework into a deep neural network through the design of an integrated architecture and trainable parameters. The network is trained through end-to-end optimization using a peculiar training set, including regular LFs and unstructured LFs. The proposed deep learning pipeline shows a substantial superiority in solving both the large disparity and the non-Lambertian challenges compared with other state-of-the-art approaches. In addition to the view interpolation for an LF, we also show that the proposed pipeline also benefits light field view extrapolation.

cs.CV↗

arXiv2021

Light Field Reconstruction Using Convolutional Network on EPI and Extended Applications

In this paper, a novel convolutional neural network (CNN)-based framework is developed for light field reconstruction from a sparse set of views. We indicate that the reconstruction can be efficiently modeled as angular restoration on an epipolar plane image (EPI). The main problem in direct reconstruction on the EPI involves an information asymmetry between the spatial and angular dimensions, where the detailed portion in the angular dimensions is damaged by undersampling. Directly upsampling or super-resolving the light field in the angular dimensions causes ghosting effects. To suppress these ghosting effects, we contribute a novel "blur-restoration-deblur" framework. First, the "blur" step is applied to extract the low-frequency components of the light field in the spatial dimensions by convolving each EPI slice with a selected blur kernel. Then, the "restoration" step is implemented by a CNN, which is trained to restore the angular details of the EPI. Finally, we use a non-blind "deblur" operation to recover the spatial high frequencies suppressed by the EPI blur. We evaluate our approach on several datasets, including synthetic scenes, real-world scenes and challenging microscope light field data. We demonstrate the high performance and robustness of the proposed framework compared with state-of-the-art algorithms. We further show extended applications, including depth enhancement and interpolation for unstructured input. More importantly, a novel rendering approach is presented by combining the proposed framework and depth information to handle large disparities.

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arXiv2020

Incremental Data-driven Optimization of Complex Systems in Nonstationary Environments

Existing work on data-driven optimization focuses on problems in static environments, but little attention has been paid to problems in dynamic environments. This paper proposes a data-driven optimization algorithm to deal with the challenges presented by the dynamic environments. First, a data stream ensemble learning method is adopted to train the surrogates so that each base learner of the ensemble learns the time-varying objective function in the previous environments. After that, a multi-task evolutionary algorithm is employed to simultaneously optimize the problems in the past environments assisted by the ensemble surrogate. This way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the real fitness function is not available for verifying the surrogates in offline data-driven optimization, a support vector domain description that was designed for outlier detection is introduced to select a reliable solution. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art data-driven optimization algorithms.

cs.NE↗

arXiv2019

Distributed Bandit Online Convex Optimization with Time-Varying Coupled Inequality Constraints

This paper considers the problem of distributed bandit online convex optimization with time-varying coupled inequality constraints. This problem can be defined as a repeated game between a group of learners and an adversary. The learners attempt to minimize a sequence of global loss functions and at the same time satisfy a sequence of coupled constraint functions. The global loss and the coupled constraint functions are the sum of local convex loss and constraint functions, respectively, which are adaptively generated by the adversary. The local loss and constraint functions are revealed in a bandit manner, i.e., only the values of loss and constraint functions at sampled points are revealed to the learners, and the revealed function values are held privately by each learner. We consider two scenarios, one- and two-point bandit feedback, and propose two corresponding distributed bandit online algorithms used by the learners. We show that sublinear expected regret and constraint violation are achieved by these two algorithms, if the accumulated variation of the comparator sequence also grows sublinearly. In particular, we show that $\mathcal{O}(T^{θ_1})$ expected static regret and $\mathcal{O}(T^{7/4-θ_1})$ constraint violation are achieved in the one-point bandit feedback setting, and $\mathcal{O}(T^{\max\{κ,1-κ\}})$ expected static regret and $\mathcal{O}(T^{1-κ/2})$ constraint violation in the two-point bandit feedback setting, where $θ_1\in(3/4,5/6]$ and $κ\in(0,1)$ are user-defined trade-off parameters. Finally, these theoretical results are illustrated by numerical simulations of a simple power grid example.

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arXiv2019

Exponential Convergence for Distributed Smooth Optimization Under the Restricted Secant Inequality Condition

This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for proving exponential/linear convergence of first-order methods is the strong convexity of the cost functions, which does not hold for many practical applications. In this paper, we first show that the continuous-time distributed primal-dual gradient algorithm converges to one global minimizer exponentially under the assumption that the global cost function satisfies the restricted secant inequality condition. This condition is weaker than the strong convexity condition since it does not require convexity and the global minimizers are not necessary to be unique. We then show that the discrete-time distributed primal-dual algorithm constructed by using the Euler's approximation method converges to one global minimizer linearly under the same condition. The theoretical results are illustrated by numerical simulations.

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arXiv2019

LapEPI-Net: A Laplacian Pyramid EPI structure for Learning-based Dense Light Field Reconstruction

For dense sampled light field (LF) reconstruction problem, existing approaches focus on a depth-free framework to achieve non-Lambertian performance. However, they trap in the trade-off "either aliasing or blurring" problem, i.e., pre-filtering the aliasing components (caused by the angular sparsity of the input LF) always leads to a blurry result. In this paper, we intend to solve this challenge by introducing an elaborately designed epipolar plane image (EPI) structure within a learning-based framework. Specifically, we start by analytically showing that decreasing the spatial scale of an EPI shows higher efficiency in addressing the aliasing problem than simply adopting pre-filtering. Accordingly, we design a Laplacian Pyramid EPI (LapEPI) structure that contains both low spatial scale EPI (for aliasing) and high-frequency residuals (for blurring) to solve the trade-off problem. We then propose a novel network architecture for the LapEPI structure, termed as LapEPI-net. To ensure the non-Lambertian performance, we adopt a transfer-learning strategy by first pre-training the network with natural images then fine-tuning it with unstructured LFs. Extensive experiments demonstrate the high performance and robustness of the proposed approach for tackling the aliasing-or-blurring problem as well as the non-Lambertian reconstruction.

cs.CV↗