Search

This paper considers the distributed bandit convex optimization problem with time-varying inequality constraints over a network of agents, where the goal is to minimize network regret and cumulative constraint violation. Existing distributed online algorithms require that each agent broadcasts its decision to its neighbors at each iteration. To better utilize the limited communication resources, we propose a distributed event-triggered online primal--dual algorithm with two-point bandit feedback. Under several classes of appropriately chosen decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. These bounds are comparable to the results achieved by distributed event-triggered online algorithms with full-information feedback. Finally, a numerical example is provided to verify the theoretical results., Comment: 34 pages, 4 figures. arXiv admin note: text overlap with arXiv:2311.01957

Fused Magnesium Furnace (FMF) is a crucial industrial equipment in the production of magnesia, and anomaly detection plays a pivotal role in ensuring its efficient, stable, and secure operation. Existing anomaly detection methods primarily focus on analyzing dominant anomalies using the process variables (such as arc current) or constructing neural networks based on abnormal visual features, while overlooking the intrinsic correlation of cross-modal information. This paper proposes a cross-modal Transformer (dubbed FmFormer), designed to facilitate anomaly detection in fused magnesium smelting processes by exploring the correlation between visual features (video) and process variables (current). Our approach introduces a novel tokenization paradigm to effectively bridge the substantial dimensionality gap between the 3D video modality and the 1D current modality in a multiscale manner, enabling a hierarchical reconstruction of pixel-level anomaly detection. Subsequently, the FmFormer leverages self-attention to learn internal features within each modality and bidirectional cross-attention to capture correlations across modalities. To validate the effectiveness of the proposed method, we also present a pioneering cross-modal benchmark of the fused magnesium smelting process, featuring synchronously acquired video and current data for over 2.2 million samples. Leveraging cross-modal learning, the proposed FmFormer achieves state-of-the-art performance in detecting anomalies, particularly under extreme interferences such as current fluctuations and visual occlusion caused by heavy water mist. The presented methodology and benchmark may be applicable to other industrial applications with some amendments. The benchmark will be released at https://github.com/GaochangWu/FMF-Benchmark., Comment: 14 pages, 6 figures, 5 tables. Submitted to IEEE

Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher flexibility in the machine links. This flexibility is often position dependent and compromises precision of the end effector of the machine. To address the need for improved contouring accuracy in industrial machines with position-dependent structural flexibility, this paper introduces a novel contouring error-bounded control algorithm for biaxial switched linear systems. The proposed algorithm utilizes model predictive control to guarantee the satisfaction of state, input, and contouring error constraints for any admissible mode switching. In this paper, the switching signal remains unknown to the controller, although information about the minimum time the system is expected to stay in a specific mode is considered to be available. The proposed algorithm has the property of recursive feasibility and ensures the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated by applying it to a high-fidelity simulation of a dual-drive industrial laser machine. The results show that the contouring error is successfully bounded within the given tolerance.

Unsupervised Domain Adaptive Semantic Segmentation (UDA-SS) aims to transfer the supervision from a labeled source domain to an unlabeled target domain. The majority of existing UDA-SS works typically consider images whilst recent attempts have extended further to tackle videos by modeling the temporal dimension. Although the two lines of research share the major challenges -- overcoming the underlying domain distribution shift, their studies are largely independent, resulting in fragmented insights, a lack of holistic understanding, and missed opportunities for cross-pollination of ideas. This fragmentation prevents the unification of methods, leading to redundant efforts and suboptimal knowledge transfer across image and video domains. Under this observation, we advocate unifying the study of UDA-SS across video and image scenarios, enabling a more comprehensive understanding, synergistic advancements, and efficient knowledge sharing. To that end, we explore the unified UDA-SS from a general data augmentation perspective, serving as a unifying conceptual framework, enabling improved generalization, and potential for cross-pollination of ideas, ultimately contributing to the overall progress and practical impact of this field of research. Specifically, we propose a Quad-directional Mixup (QuadMix) method, characterized by tackling distinct point attributes and feature inconsistencies through four-directional paths for intra- and inter-domain mixing in a feature space. To deal with temporal shifts with videos, we incorporate optical flow-guided feature aggregation across spatial and temporal dimensions for fine-grained domain alignment. Extensive experiments show that our method outperforms the state-of-the-art works by large margins on four challenging UDA-SS benchmarks. Our source code and models will be released at \url{https://github.com/ZHE-SAPI/UDASS}., Comment: 18 pages,10 figures, 11 tables

This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal-dual algorithm over a time-varying directed graph. With several classes of appropriately chose decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. Finally, a numerical simulation example is provided to verify the theoretical results., Comment: 12 pages, 3 figures

This paper considers distributed online convex optimization with adversarial constraints. In this setting, a network of agents makes decisions at each round, and then only a portion of the loss function and a coordinate block of the constraint function are privately revealed to each agent. The loss and constraint functions are convex and can vary arbitrarily across rounds. The agents collaborate to minimize network regret and cumulative constraint violation. A novel distributed online algorithm is proposed and it achieves an $\mathcal{O}(T^{\max\{c,1-c\}})$ network regret bound and an $\mathcal{O}(T^{1-c/2})$ network cumulative constraint violation bound, where $T$ is the number of rounds and $c\in(0,1)$ is a user-defined trade-off parameter. When Slater's condition holds (i.e, there is a point that strictly satisfies the inequality constraints), the network cumulative constraint violation bound is reduced to $\mathcal{O}(T^{1-c})$. Moreover, if the loss functions are strongly convex, then the network regret bound is reduced to $\mathcal{O}(\log(T))$, and the network cumulative constraint violation bound is reduced to $\mathcal{O}(\sqrt{\log(T)T})$ and $\mathcal{O}(\log(T))$ without and with Slater's condition, respectively. To the best of our knowledge, this paper is the first to achieve reduced (network) cumulative constraint violation bounds for (distributed) online convex optimization with adversarial constraints under Slater's condition. Finally, the theoretical results are verified through numerical simulations.

In this paper, we formulate inverse reinforcement learning (IRL) as an expert-learner interaction whereby the optimal performance intent of an expert or target agent is unknown to a learner agent. The learner observes the states and controls of the expert and hence seeks to reconstruct the expert's cost function intent and thus mimics the expert's optimal response. Next, we add non-cooperative disturbances that seek to disrupt the learning and stability of the learner agent. This leads to the formulation of a new interaction we call zero-sum game IRL. We develop a framework to solve the zero-sum game IRL problem that is a modified extension of RL policy iteration (PI) to allow unknown expert performance intentions to be computed and non-cooperative disturbances to be rejected. The framework has two parts: a value function and control action update based on an extension of PI, and a cost function update based on standard inverse optimal control. Then, we eventually develop an off-policy IRL algorithm that does not require knowledge of the expert and learner agent dynamics and performs single-loop learning. Rigorous proofs and analyses are given. Finally, simulation experiments are presented to show the effectiveness of the new approach., Comment: 9 pages, 3 figures

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.

In this paper, we present a Geometry-aware Neural Interpolation (Geo-NI) framework for light field rendering. Previous learning-based approaches either rely on the capability of neural networks to perform direct interpolation, which we dubbed Neural Interpolation (NI), or explore scene geometry for novel view synthesis, also known as Depth Image-Based Rendering (DIBR). Instead, we incorporate the ideas behind these two kinds of approaches by launching the NI with a novel DIBR pipeline. Specifically, the proposed Geo-NI first performs NI using input light field sheared by a set of depth hypotheses. Then the DIBR is implemented by assigning the sheared light fields with a novel reconstruction cost volume according to the reconstruction quality under different depth hypotheses. The reconstruction cost is interpreted as a blending weight to render the final output light field by blending the reconstructed light fields along the dimension of depth hypothesis. By combining the superiorities of NI and DIBR, the proposed Geo-NI is able to render views with large disparity with the help of scene geometry while also reconstruct non-Lambertian effect when depth is prone to be ambiguous. Extensive experiments on various datasets demonstrate the superior performance of the proposed geometry-aware light field rendering framework., Comment: 13 pages, 8 figures, 4 tables

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--{\L}ojasiewicz condition. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.

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.

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 $\mathcal{O}(T^{\max\{\kappa,1-\kappa\}})$ static network regret and $\mathcal{O}(T^{1-\kappa/2})$ network cumulative constraint violation, where $T$ is the time horizon and $\kappa\in(0,1)$ 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 $\mathcal{O}(T^{\kappa})$. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

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., Comment: 15 pages, 12 figures. Accepted by IEEE TPAMI

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., Comment: Published in IEEE TPAMI, 2019

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.

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., Comment: 15 pages, 13 figures and 5 tables, Accepted by IEEE Transactions on Image Processing (IEEE TIP)

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--{\L}ojasiewicz (P--{\L}) 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., Comment: arXiv admin note: text overlap with arXiv:1912.12110

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-{\L}ojasiewicz 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.

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 $\mathcal{O}(T^{\theta_1})$ expected static regret and $\mathcal{O}(T^{7/4-\theta_1})$ constraint violation are achieved in the one-point bandit feedback setting, and $\mathcal{O}(T^{\max\{\kappa,1-\kappa\}})$ expected static regret and $\mathcal{O}(T^{1-\kappa/2})$ constraint violation in the two-point bandit feedback setting, where $\theta_1\in(3/4,5/6]$ and $\kappa\in(0,1)$ are user-defined trade-off parameters. Finally, these theoretical results are illustrated by numerical simulations of a simple power grid example.

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.

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., Comment: 10 pages, 8 figures, 4 tables