Existing Online Algorithms Research Articles

A Space-Efficient One-Pass Online SVM Algorithm

In this paper we consider the problem of training a Support Vector Machine (SVM) online using a stream of data in random order. We provide a fast online training algorithm for general SVM on very large datasets. Based on the geometric interpretation of SVM known as the polytope distance, our algorithm uses a gradient descent procedure to solve the problem. With high probability our algorithm outputs an [Formula: see text]-approximation result in constant time and space, which is independent of the size of the dataset, where [Formula: see text]-approximation means that the separating margin of the classifier is almost optimal (with error [Formula: see text]), and the number of misclassified training points is very small (with error [Formula: see text]). Experimental results show that our algorithm outperforms most of existing online algorithms, especially in the space requirement aspect, while maintaining high accuracy.

Online Integrated Production and Distribution Scheduling: Review and Extensions

As a growing number of manufacturers adopt the make-to-order business mode and a growing number of retailers sell online, we are seeing numerous decision problems that can be modeled as what are known in the literature as integrated production and distribution scheduling (IPDS) problems. In such problems, order processing and delivery must be scheduled jointly in order to achieve an optimal balance between total operational costs and overall customer service. Offline IPDS problems, in which the information about every order is known in advance with certainty, are extensively studied. However, research on online IPDS problems, in which orders arrive randomly with their information unknown until they arrive, is relatively recent but is growing rapidly. In this paper, we first describe several real-world applications to illustrate the importance of studying online IPDS problems from a practical point of view. We then review the existing literature on online IPDS problems with a focus on existing online algorithms for these problems and their theoretical performance. We also derive some new results to fill several gaps left in the literature and discuss possible topics for future research. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0305 .

AMM: An Adaptive Online Map Matching Algorithm

Online map matching is essential for some location-based services, such as car navigation. However, due to GPS measurement errors and/or the lack of sufficient information, the performance of most existing online algorithms will degrade in the increasingly complex traffic environment. In this paper, we propose an adaptive online map matching algorithm called AMM. The basic idea is that AMM should be able to calibrate GPS observation data for various measurement errors and under complex urban conditions. First, we establish a collaborative evaluation model between GPS points and candidate points to effectively filter low-quality GPS measurement points, dynamically set the weights of different features and comprehensively select the best candidate points. Second, we propose a retrospective correction mechanism to correct the previous matching results when more information is available, which will help improve the accuracy of future GPS points. Furthermore, we define parameter self-tuning rules for AMM to enhance its portability by avoiding time-consuming parameter tuning steps. We conduct extensive experiments to evaluate the performance of AMM on real vehicle trajectory datasets. The experiment results show that AMM outperforms its counterparts by up to 32% in terms of accuracy and its performance in different traffic conditions is more stable.

Online learning for the Dirichlet process mixture model via weakly conjugate approximation

The Dirichlet process (DP) mixture model is widely used for clustering and density estimation. The use of the DP mixture model has become computationally feasible because of the development of various Markov chain Monte Carlo algorithms. However, when analyzing large data, DP mixture models are impractical owing to their high computational costs. An online learning algorithm that processes data sequentially as they arrive is an attractive way to analyze large data. Existing online learning algorithms based on variational inference are very fast; however, their performance is unsatisfactory owing to the crude approximation of the posterior distribution. We propose a novel mini-batch online learning algorithm based on assumed density filtering, which takes full advantage of available computing resources to improve performance and achieves better performances relative to existing online algorithms based on variational inference.

Measurement-based prediction-correction online distributed optimal power flow algorithm for multi-phase active distribution networks

Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy resource (DER) integrations. However, existing online algorithms have the following limitations: 1) Correction-only algorithms ignore the time-varying characteristics of the optimization problem; 2) Prediction-correction algorithms cannot handle nonlinear OPF problems; 3) Most algorithms only consider the application of single-phase cases. This paper addresses the above limitations by proposing a novel measurement-based prediction-correction online distributed OPF algorithm for multi-phase ADNs. This algorithm is based on an improved multi-phase linearized alternating current (AC) power flow model that takes advantage of the voltage measurements to improve the approximation accuracy. In each sampling period, the proposed algorithm first performs a limited number of correction steps, iterating the incremental variable based on the current outputs of DERs and the voltage measurements to track the optimal solution. The DERs then execute the resultant incremental output powers. After forecasting the time-varying parameters, the proposed algorithm performs a few prediction steps to seek a better starting point for the correction steps before the next sampling. Numerical test results of the modified IEEE 37-bus and 123-bus distribution systems demonstrated that the proposed algorithm can track the optimal solution of the time-varying nonlinear OPF problem more accurately than existing online algorithms, even in extra-high penetration scenarios (≥200%).

Online Linear Programming: Dual Convergence, New Algorithms, and Regret Bounds

We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are independently and identically drawn from an unknown distribution and revealed sequentially over time. Virtually all existing online algorithms were based on learning the dual optimal solutions/prices of the linear programs (LPs), and their analyses were focused on the aggregate objective value and solving the packing LP, where all coefficients in the constraint matrix and objective are nonnegative. However, two major open questions were as follows. (i) Does the set of LP optimal dual prices learned in the existing algorithms converge to those of the “offline” LP? (ii) Could the results be extended to general LP problems where the coefficients can be either positive or negative? We resolve these two questions by establishing convergence results for the dual prices under moderate regularity conditions for general LP problems. Specifically, we identify an equivalent form of the dual problem that relates the dual LP with a sample average approximation to a stochastic program. Furthermore, we propose a new type of OLP algorithm, action-history-dependent learning algorithm, which improves the previous algorithm performances by taking into account the past input data and the past decisions/actions. We derive an [Formula: see text] regret bound (under a locally strong convexity and smoothness condition) for the proposed algorithm, against the [Formula: see text] bound for typical dual-price learning algorithms, where n is the number of decision variables. Numerical experiments demonstrate the effectiveness of the proposed algorithm and the action-history-dependent design.

Improving the Performance of Online Bitrate Adaptation with Multi-Step Prediction Over Cellular Networks

Video streaming over mobile is flourishing, and most commercial players use adaptive bitrate (ABR) streaming to deliver video in varying network conditions. Using network capacity and buffer occupancy as system states, ABR algorithms adjust bitrate based on the instantaneous system states, which is able to adapt to network changes in real-time and ensure high quality of experience (QoE). However, they are incapable of providing good QoE over mobile. Due to the high dynamic characteristics of cellular network, the system states change rapidly over time. The instantaneous state-based adaptation can induce significant video quality fluctuation which greatly degrades QoE. In this paper, we propose an online ABR algorithm called MSPC to provide good QoE in cellular network. To balance the conflict between rapid adaptation and smooth bitrate, MSPC utilizes the multi-step prediction of future system states to select bitrates instead of the instantaneous current states. At the same time, it controls the buffer occupancy to eliminate the impact of prediction error on performance. We implement MSPC on a reference video player with performance evaluated based on realistic cellular traces. Experimental results show that MSPC reduces the bitrate change of existing online algorithms by 62.4 percent on average while maintaining high bitrates and achieving zero rebuffering over 97.83 percent of all tested sessions.

Online detection of failures generated by storage simulator

Modern large-scale data-farms consist of hundreds of thousands of storage devices that span distributed infrastructure. Devices used in modern data centers (such as controllers, links, SSD- and HDD-disks) can fail due to hardware as well as software problems. Such failures or anomalies can be detected by monitoring the activity of components using machine learning techniques. In order to use these techniques, researchers need plenty of historical data of devices in normal and failure mode for training algorithms. In this work, we challenge two problems: 1) lack of storage data in the methods above by creating a simulator and 2) applying existing online algorithms that can faster detect a failure occurred in one of the components.We created a Go-based (golang) package for simulating the behavior of modern storage infrastructure. The software is based on the discrete-event modeling paradigm and captures the structure and dynamics of high-level storage system building blocks. The package's exible structure allows us to create a model of a real-world storage system with a configurable number of components. The primary area of interest is exploring the storage machine's behavior under stress testing or exploitation in the medium-or long-term for observing failures of its components.To discover failures in the time series distribution generated by the simulator, we modified a change point detection algorithm that works in online mode. The goal of the change-point detection is to discover differences in time series distribution. This work describes an approach for failure detection in time series data based on direct density ratio estimation via binary classifiers.

On formulation of online algorithm and framework of near-optimally tractable eviction for nonuniform caches

Distributed data sharing in Internet, social, and cloud computing paradigms incurs nonuniform costs such as consumed downstream bandwidth, downloading delays, and cloud-data-out monetary charges. To alleviate such costs, caches have been widely deployed and researched to find efficient online-cache-eviction algorithms. However, existing online algorithms have no offline foundation, thus they are far from a global optimum. This paper proposes a framework for developing an online cache eviction algorithm, which is grounded in a near-optimally and tractably offline algorithm namely Shortest Maximum Forward Distance (SMFD). On the formulation of the framework, the near-optimality and tractability properties of existing offline algorithms were evaluated through the formal evaluation of the optimality and computational tractability based upon variable object costs. Subsequently, the lowest-complexity suboptimal schemes were empirically investigated to seek a near-optimal offline one, which appears to be SMFD. Also, the results originally show that SMFD and its variant can practically achieve multiple conventionally upper bounds of limitless cache sizes in a stable and simultaneous manner. SMFD was then transformed into novel online SMFD by quantifying the offline property, maximum forward distance, of SMFD with cache-scope time-to-live approximation. To guarantee the effectiveness of online SMFD over evolving request streams, a safety bound guideline and a cache-scope time-to-live distribution model are also proposed. Finally, experience on the framework was gained via experiments based on deep-neural-network models.

Multi-User Cooperative Mobile Video Streaming: Performance Analysis and Online Mechanism Design

Adaptive bitrate streaming enables video users to adapt their playing bitrates to the real-time network conditions, hence achieving the desirable quality-of-experience (QoE). In a multi-user wireless scenario, however, existing single-user based bitrate adaptation methods may fail to provide the desirable QoE, due to lack of consideration of multi-user interactions (such as the multi-user interferences and network congestion). In this work, we propose a novel user cooperation framework based on user-provided networking for multi-user mobile video streaming over wireless cellular networks. The framework enables nearby mobile video users to crowdsource their cellular links and resources for cooperative video streaming. We first analyze the social welfare performance bound of the proposed cooperative streaming system by introducing a virtual time-slotted system. Then, we design a low complexity Lyapunov-based online algorithm, which can be implemented in an online and distributed manner without the complete future and global network information. Numerical results show that the proposed online algorithm achieves an average 97% of the theoretical maximum social welfare. We further conduct experiments with real data traces, to compare our proposed online algorithm with the existing online algorithms in the literature. Experiment results show that our algorithm outperforms the existing algorithms in terms of both the achievable bitrate (with an average gain of 20% - 30%) and social welfare (with an average gain of 10% - 50%).

Large-Scale Online Feature Selection for Ultra-High Dimensional Sparse Data

Feature selection (FS) is an important technique in machine learning and data mining, especially for large-scale high-dimensional data. Most existing studies have been restricted to batch learning, which is often inefficient and poorly scalable when handling big data in real world. As real data may arrive sequentially and continuously, batch learning has to retrain the model for the new coming data, which is very computationally intensive. Online feature selection (OFS) is a promising new paradigm that is more efficient and scalable than batch learning algorithms. However, existing online algorithms usually fall short in their inferior efficacy. In this article, we present a novel second-order OFS algorithm that is simple yet effective, very fast and extremely scalable to deal with large-scale ultra-high dimensional sparse data streams. The basic idea is to exploit the second-order information to choose the subset of important features with high confidence weights. Unlike existing OFS methods that often suffer from extra high computational cost, we devise a novel algorithm with a MaxHeap-based approach, which is not only more effective than the existing first-order algorithms, but also significantly more efficient and scalable. Our extensive experiments validated that the proposed technique achieves highly competitive accuracy as compared with state-of-the-art batch FS methods, meanwhile it consumes significantly less computational cost that is orders of magnitude lower. Impressively, on a billion-scale synthetic dataset (1-billion dimensions, 1-billion non-zero features, and 1-million samples), the proposed algorithm takes less than 3 minutes to run on a single PC.

Event-Trigger Based Robust-Optimal Control for Energy Harvesting Transmitter

This paper studies an online algorithm for an energy harvesting transmitter, where the transmission (completion) time is considered as the system performance. Unlike the existing online algorithms which more or less require the knowledge on the future behavior of the energy-harvesting rate, we consider a practical but significantly more challenging scenario where the energy-harvesting rate is assumed to be totally unknown. Our design is formulated as a robust-optimal control problem which aims to optimize the worst-case performance. The transmit power is designed only based on the current battery energy level and the data queue length directly monitored by the transmitter itself. Specifically, we apply an event-trigger approach in which the transmitter continuously monitors the battery energy and triggers an event when a significant change occurs. Once an event is triggered, the transmit power is updated according to the solution to the robust-optimal control problem, which is given in a simple analytic form. We present numerical results on the transmission time achieved by the proposed design and demonstrate its robust-optimality.

Real-Time Energy Management in Microgrids

Energy management in microgrids is typically formulated as an offline optimization problem for day-ahead scheduling by previous studies. Most of these offline approaches assume perfect forecasting of the renewables, the demands, and the market, which is difficult to achieve in practice. Existing online algorithms, on the other hand, oversimplify the microgrid model by only considering the aggregate supply-demand balance while omitting the underlying power distribution network and the associated power flow and system operational constraints. Consequently, such approaches may result in control decisions that violate the real-world constraints. This paper focuses on developing an online energy management strategy (EMS) for real-time operation of microgrids that takes into account the power flow and system operational constraints on a distribution network. We model the online energy management as a stochastic optimal power flow problem and propose an online EMS based on Lyapunov optimization. The proposed online EMS is subsequently applied to a real-microgrid system. The simulation results demonstrate that the performance of the proposed EMS exceeds a greedy algorithm and is close to an optimal offline algorithm. Lastly, the effect of the underlying network structure on energy management is observed and analyzed.

A theoretical approach to optimal association control in vehicular Wi-Fi networks

Abstract The recent ubiquitous deployment of Wi-Fi access points (APs) has offered vehicles to use the high-speed and low-cost Internet service via the roadside APs. However, the high mobility of vehicles and the limited coverage of APs render some challenges. First, it results in frequent handoffs, thus leading to long delay and low service availability. Second, the available AP sets and their channel quality change dynamically, making the AP selection problem even harder. Therefore, there is a strong need to develop an efficient association control mechanism that provides efficient vehicular Wi-Fi access. In this paper, we present a theoretical framework to formulate the optimal association problem through non-linear integer programming, whose objective function is to maximize the throughput or to minimize the handoff overhead. We show that this problem holds the totally unimodular (TU) property and is thus solvable in polynomial time. Then, we study the optimality of association control by comparing existing online algorithms through real trace-based simulations. The results show that there exists a large performance gap between the performance of existing online algorithms and the optimal one. We also observe that the association control algorithm can be further improved if it has access to future knowledge. Particularly, the offline optimal with future AP information improves the performance of the local optimal by up to 10%.

Error tolerance based support vector machine for regression

Most existing online algorithms in support vector machines (SVM) can only grow support vectors. This paper proposes an online error tolerance based support vector machine (ET-SVM) which not only grows but also prunes support vectors. Similar to least square support vector machines (LS-SVM), ET-SVM converts the original quadratic program (QP) in standard SVM into a group of easily solved linear equations. Different from LS-SVM, ET-SVM remains support vectors sparse and realizes a compact structure. Thus, ET-SVM can significantly reduce computational time while ensuring satisfactory learning accuracy. Simulation results verify the effectiveness of the newly proposed algorithm.

Online rescheduling of multiple picking agents for warehouse management

In this paper, we present a solution for a dynamic rescheduling problem involving new orders arriving randomly while static orders have been given in advance in warehouse environments. We propose two variations of an incremental static scheduling scheme: one based on the steepest descent insertion, called OR1, and the other, on multistage rescheduling, called OR2. Both techniques are enhanced by a local search procedure specifically designed for the problem at hand. We also implemented several existing online algorithms to our problem for evaluative purposes. Extensive statistical experiments based on real picking data indicate that the proposed methodologies are competitive with existing online schedulers and show that load-balancing algorithms, such as OR1, yield the best results on the average and that OR2 is effective in reducing the picking time when dynamism is low to moderate.

Implementing Online Natural Gradient Learning: Problems and Solutions

The online natural gradient learning is an efficient algorithm to resolve the slow learning speed and poor performance of the standard gradient descent method. However, there are several problems to implement this algorithm. In this paper, we proposed a new algorithm to solve these problems and then compared the new algorithm with other known algorithms for online learning, including Almeida-Langlois-Amaral-Plakhov algorithm (ALAP), Vario-eta, local adaptive learning rate and learning with momentum etc., using sample data sets from Proben1 and normalized handwritten digits, automatically scanned from envelopes by the U.S. Postal Services. The strong and weak points of these algorithms were analyzed and tested empirically. We found out that using the online training error as the criterion to determine whether the learning rate should be changed or not is not appropriate and our new algorithm has better performance than other existing online algorithms.