Showing papers on "Approximation algorithm published in 2019"

Dendritic Neuron Model With Effective Learning Algorithms for Classification, Approximation, and Prediction

Abstract: An artificial neural network (ANN) that mimics the information processing mechanisms and procedures of neurons in human brains has achieved a great success in many fields, e.g., classification, prediction, and control. However, traditional ANNs suffer from many problems, such as the hard understanding problem, the slow and difficult training problems, and the difficulty to scale them up. These problems motivate us to develop a new dendritic neuron model (DNM) by considering the nonlinearity of synapses, not only for a better understanding of a biological neuronal system, but also for providing a more useful method for solving practical problems. To achieve its better performance for solving problems, six learning algorithms including biogeography-based optimization, particle swarm optimization, genetic algorithm, ant colony optimization, evolutionary strategy, and population-based incremental learning are for the first time used to train it. The best combination of its user-defined parameters has been systemically investigated by using the Taguchi’s experimental design method. The experiments on 14 different problems involving classification, approximation, and prediction are conducted by using a multilayer perceptron and the proposed DNM. The results suggest that the proposed learning algorithms are effective and promising for training DNM and thus make DNM more powerful in solving classification, approximation, and prediction problems.

Provably Efficient Reinforcement Learning with Linear Function Approximation

Abstract: Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational and statistical efficiency, especially given the need to manage the exploration/exploitation tradeoff. As a result, a core RL question remains open: how can we design provably efficient RL algorithms that incorporate function approximation? This question persists even in a basic setting with linear dynamics and linear rewards, for which only linear function approximation is needed. This paper presents the first provable RL algorithm with both polynomial runtime and polynomial sample complexity in this linear setting, without requiring a "simulator" or additional assumptions. Concretely, we prove that an optimistic modification of Least-Squares Value Iteration (LSVI)---a classical algorithm frequently studied in the linear setting---achieves $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret, where $d$ is the ambient dimension of feature space, $H$ is the length of each episode, and $T$ is the total number of steps. Importantly, such regret is independent of the number of states and actions.

IGD Indicator-Based Evolutionary Algorithm for Many-Objective Optimization Problems

Abstract: Inverted generational distance (IGD) has been widely considered as a reliable performance indicator to concurrently quantify the convergence and diversity of multiobjective and many-objective evolutionary algorithms. In this paper, an IGD indicator-based evolutionary algorithm for solving many-objective optimization problems (MaOPs) has been proposed. Specifically, the IGD indicator is employed in each generation to select the solutions with favorable convergence and diversity. In addition, a computationally efficient dominance comparison method is designed to assign the rank values of solutions along with three newly proposed proximity distance assignments. Based on these two designs, the solutions are selected from a global view by linear assignment mechanism to concern the convergence and diversity simultaneously. In order to facilitate the accuracy of the sampled reference points for the calculation of IGD indicator, we also propose an efficient decomposition-based nadir point estimation method for constructing the Utopian Pareto front (PF) which is regarded as the best approximate PF for real-world MaOPs at the early stage of the evolution. To evaluate the performance, a series of experiments is performed on the proposed algorithm against a group of selected state-of-the-art many-objective optimization algorithms over optimization problems with 8-, 15-, and 20-objective. Experimental results measured by the chosen performance metrics indicate that the proposed algorithm is very competitive in addressing MaOPs.

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Abstract: High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work, we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (1) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (2) a merged formulation of the PDE and the 2BSDE problem, (3) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (4) a stochastic gradient descent-type optimization procedure. Numerical results obtained using TensorFlow in Python illustrate the efficiency and the accuracy of the method in the cases of a 100-dimensional Black–Scholes–Barenblatt equation, a 100-dimensional Hamilton–Jacobi–Bellman equation, and a nonlinear expectation of a 100-dimensional G-Brownian motion.

Coevolutionary Particle Swarm Optimization With Bottleneck Objective Learning Strategy for Many-Objective Optimization

Abstract: The application of multiobjective evolutionary algorithms to many-objective optimization problems often faces challenges in terms of diversity and convergence. On the one hand, with a limited population size, it is difficult for an algorithm to cover different parts of the whole Pareto front (PF) in a large objective space. The algorithm tends to concentrate only on limited areas. On the other hand, as the number of objectives increases, solutions easily have poor values on some objectives, which can be regarded as poor bottleneck objectives that restrict solutions’ convergence to the PF. Thus, we propose a coevolutionary particle swarm optimization with a bottleneck objective learning (BOL) strategy for many-objective optimization. In the proposed algorithm, multiple swarms coevolve in distributed fashion to maintain diversity for approximating different parts of the whole PF, and a novel BOL strategy is developed to improve convergence on all objectives. In addition, we develop a solution reproduction procedure with both an elitist learning strategy (ELS) and a juncture learning strategy (JLS) to improve the quality of archived solutions. The ELS helps the algorithm to jump out of local PFs, and the JLS helps to reach out to the missing areas of the PF that are easily missed by the swarms. The performance of the proposed algorithm is evaluated using two widely used test suites with different numbers of objectives. Experimental results show that the proposed algorithm compares favorably with six other state-of-the-art algorithms on many-objective optimization.

SimGNN: A Neural Network Approach to Fast Graph Similarity Computation

Abstract: Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity/distance computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other applications, but very costly to compute in practice. Inspired by the recent success of neural network approaches to several graph applications, such as node or graph classification, we propose a novel neural network based approach to address this classic yet challenging graph problem, aiming to alleviate the computational burden while preserving a good performance. The proposed approach, called SimGNN, combines two strategies. First, we design a learnable embedding function that maps every graph into an embedding vector, which provides a global summary of a graph. A novel attention mechanism is proposed to emphasize the important nodes with respect to a specific similarity metric. Second, we design a pairwise node comparison method to supplement the graph-level embeddings with fine-grained node-level information. Our model achieves better generalization on unseen graphs, and in the worst case runs in quadratic time with respect to the number of nodes in two graphs. Taking GED computation as an example, experimental results on three real graph datasets demonstrate the effectiveness and efficiency of our approach. Specifically, our model achieves smaller error rate and great time reduction compared against a series of baselines, including several approximation algorithms on GED computation, and many existing graph neural network based models. Our study suggests SimGNN provides a new direction for future research on graph similarity computation and graph similarity search.

Fast Deployment of UAV Networks for Optimal Wireless Coverage

Abstract: Unmanned Aerial Vehicle (UAV) networks have emerged as a promising technique to rapidly provide wireless coverage to a geographical area, where a flying UAV can be fast deployed to serve as cell site. Existing work on UAV-enabled wireless networks overlook the fast UAV deployment for wireless coverage, and such deployment problems have only been studied recently in sensor networks. Unlike sensors, UAVs should be deployed to the air and they are generally different in flying speed, operating altitude and wireless coverage radius. By considering such UAV heterogeneity to cover the whole target area, this paper studies two fast UAV deployment problems: one is to minimize the maximum deployment delay among all UAVs (min-max) for fairness consideration, and the other is to minimize the total deployment delay (min-sum) for efficiency consideration. We prove both min-max and min-sum problems are NP-complete in general. When dispatching UAVs from the same location, we present an optimal algorithm of low computational complexity $O(n^2)$ for the min-max problem. When UAVs are dispatched from different locations, we propose to preserve their location order during deployment and successfully design a fully polynomial time approximation scheme (FPTAS) of computation complexity $O(n^2 \log \frac{1}{\epsilon })$ to arbitrarily approach the global optimum with relative error $\epsilon$ . The min-sum problem is more challenging. When UAVs are dispatched from the same initial location, we present an approximation algorithm of linear time. As for the general case, we further reformulate it as a dynamic program and propose a pseudo polynomial-time algorithm to solve it optimally.

Towards Practical Differentially Private Convex Optimization

Abstract: Building useful predictive models often involves learning from sensitive data. Training models with differential privacy can guarantee the privacy of such sensitive data. For convex optimization tasks, several differentially private algorithms are known, but none has yet been deployed in practice. In this work, we make two major contributions towards practical differentially private convex optimization. First, we present Approximate Minima Perturbation, a novel algorithm that can leverage any off-the-shelf optimizer. We show that it can be employed without any hyperparameter tuning, thus making it an attractive technique for practical deployment. Second, we perform an extensive empirical evaluation of the state-of-the-art algorithms for differentially private convex optimization, on a range of publicly available benchmark datasets, and real-world datasets obtained through an industrial collaboration. We release open-source implementations of all the differentially private convex optimization algorithms considered, and benchmarks on as many as nine public datasets, four of which are high-dimensional.

A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems

Abstract: Separable nonlinear least-squares (SNLLS) problems arise frequently in many research fields, such as system identification and machine learning. The variable projection (VP) method is a very powerful tool for solving such problems. In this paper, we consider the regularization of ill-conditioned SNLLS problems based on the VP method. Selecting an appropriate regularization parameter is difficult because of the nonlinear optimization procedure. We propose to determine the regularization parameter using the weighted generalized cross-validation method at every iteration. This makes the original objective function changing during the optimization procedure. To circumvent this problem, we use an inequation to produce a consistent demand of decreasing at successive iterations. The approximation of the Jacobian of the regularized problem is also discussed. The proposed regularized VP algorithm is tested by the parameter estimation problem of several statistical models. Numerical results demonstrate the effectiveness of the proposed algorithm.

Offline Data-Driven Evolutionary Optimization Using Selective Surrogate Ensembles

Abstract: In solving many real-world optimization problems, neither mathematical functions nor numerical simulations are available for evaluating the quality of candidate solutions. Instead, surrogate models must be built based on historical data to approximate the objective functions and no new data will be available during the optimization process. Such problems are known as offline data-driven optimization problems. Since the surrogate models solely depend on the given historical data, the optimization algorithm is able to search only in a very limited decision space during offline data-driven optimization. This paper proposes a new offline data-driven evolutionary algorithm to make the full use of the offline data to guide the search. To this end, a surrogate management strategy based on ensemble learning techniques developed in machine learning is adopted, which builds a large number of surrogate models before optimization and adaptively selects a small yet diverse subset of them during the optimization to achieve the best local approximation accuracy and reduce the computational complexity. Our experimental results on the benchmark problems and a transonic airfoil design example show that the proposed algorithm is able to handle offline data-driven optimization problems with up to 100 decision variables.

Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO Systems

Abstract: We propose an iterative channel estimation algorithm based on the least square estimation (LSE) and sparse message passing (SMP) algorithm for the millimeter wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are approximately modeled as a Bernoulli–Gaussian distribution and the channel matrix is sparse with only a few nonzero entries. By leveraging the advantage of sparseness, we propose an algorithm that iteratively detects the exact locations and values of nonzero entries of the sparse channel matrix. At each iteration, the locations are detected by the SMP, and values are estimated with the LSE. We also analyze the Cramer–Rao Lower Bound (CLRB), and show that the proposed algorithm is a minimum variance unbiased estimator under the assumption that we have the partial priori knowledge of the channel. Furthermore, we employ the Gaussian approximation for message densities under density evolution to simplify the analysis of the algorithm, which provides a simple method to predict the performance of the proposed algorithm. Numerical experiments show that the proposed algorithm has much better performance than the existing sparse estimators, especially when the channel is sparse. In addition, our proposed algorithm converges to the CRLB of the genie-aided estimation of sparse channels with only five turbo iterations.

Service Placement and Request Scheduling for Data-intensive Applications in Edge Clouds

Abstract: Mobile edge computing allows wireless users to exploit the power of cloud computing without the large communication delay. To serve data-intensive applications (e.g., augmented reality, video analytics) from the edge, we need, in addition to CPU cycles and memory for computation, storage resource for storing server data and network bandwidth for receiving user-provided data. Moreover, the data placement needs to be adapted over time to serve time-varying demands, while considering system stability and operation cost. We address this problem by proposing a two-time-scale framework that jointly optimizes service (data & code) placement and request scheduling, under storage, communication, computation, and budget constraints. We fully characterize the complexity of our problem by analyzing the hardness of various cases. By casting our problem as a set function optimization, we develop a polynomial-time algorithm that achieves a constant-factor approximation under certain conditions. Extensive synthetic and trace-driven simulations show that the proposed algorithm achieves 90% of the optimal performance.

Near Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems

Abstract: We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every possible underlying distribution, obtains a $1-\epsilon$ fraction of the profit obtained by an algorithm that knows the entire request sequence ahead of time. The factor $\epsilon$ approaches $0$ when no single request consumes/contributes a significant fraction of the global consumption/contribution by all requests together. We show that the tradeoff we obtain here that determines how fast $\epsilon$ approaches $0$, is near optimal: we give a nearly matching lower bound showing that the tradeoff cannot be improved much beyond what we obtain. Going beyond the model of a static underlying distribution, we introduce the adversarial stochastic input model, where an adversary, possibly in an adaptive manner, controls the distributions from which the requests are drawn at each step. Placing no restriction on the adversary, we design an algorithm that obtains a $1-\epsilon$ fraction of the optimal profit obtainable w.r.t. the worst distribution in the adversarial sequence. In the offline setting we give a fast algorithm to solve very large LPs with both packing and covering constraints. We give algorithms to approximately solve (within a factor of $1+\epsilon$) the mixed packing-covering problem with $O(\frac{\gamma m \log (n/\delta)}{\epsilon^2})$ oracle calls where the constraint matrix of this LP has dimension $n\times m$, the success probability of the algorithm is $1-\delta$, and $\gamma$ quantifies how significant a single request is when compared to the sum total of all requests. We discuss implications of our results to several special cases including online combinatorial auctions, network routing and the adwords problem.

Model-Free Training of End-to-End Communication Systems

Abstract: The idea of end-to-end learning of communication systems through neural network (NN)-based autoencoders has the shortcoming that it requires a differentiable channel model. We present in this paper a novel learning algorithm which alleviates this problem. The algorithm enables training of communication systems with an unknown channel model or with non-differentiable components. It iterates between training of the receiver using the true gradient, and training of the transmitter using an approximation of the gradient. We show that this approach works as well as model-based training for a variety of channels and tasks. Moreover, we demonstrate the algorithm’s practical viability through hardware implementation on software defined radios (SDRs) where it achieves state-of-the-art performance over a coaxial cable and wireless channel.

Distributed Online One-Class Support Vector Machine for Anomaly Detection Over Networks

Abstract: Anomaly detection has attracted much attention in recent years since it plays a crucial role in many domains. Various anomaly detection approaches have been proposed, among which one-class support vector machine (OCSVM) is a popular one. In practice, data used for anomaly detection can be distributively collected via wireless sensor networks. Besides, as the data usually arrive at the nodes sequentially, online detection method that can process streaming data is preferred. In this paper, we formulate a distributed online OCSVM for anomaly detection over networks and get a decentralized cost function. To get the decentralized implementation without transmitting the original data, we use a random approximate function to replace the kernel function. Furthermore, to find an appropriate approximate dimension, we add a sparse constraint into the decentralized cost function to get another one. Then we minimize these two cost functions by stochastic gradient descent and derive two distributed algorithms. Some theoretical analysis and experiments are performed to show the effectiveness of the proposed algorithms. Experimental results on both synthetic and real datasets reveal that both of the proposed algorithms achieve low misdetection rates and high true positive rates. Compared with other state-of-the-art anomaly detection methods, the proposed distributed algorithms not only show good anomaly detection performance, but also require relatively short running time and low CPU memory consumption.

Efficient task-specific data valuation for nearest neighbor algorithms

Abstract: Given a data set D containing millions of data points and a data consumer who is willing to pay for $X to train a machine learning (ML) model over D, how should we distribute this $X to each data point to reflect its "value"? In this paper, we define the "relative value of data" via the Shapley value, as it uniquely possesses properties with appealing real-world interpretations, such as fairness, rationality and decentralizability. For general, bounded utility functions, the Shapley value is known to be challenging to compute: to get Shapley values for all N data points, it requires O(2N) model evaluations for exact computation and O(N log N) for (ϵ, δ)-approximation.In this paper, we focus on one popular family of ML models relying on K-nearest neighbors (KNN). The most surprising result is that for unweighted KNN classifiers and regressors, the Shapley value of all N data points can be computed, exactly, in O(N log N) time - an exponential improvement on computational complexity! Moreover, for (ϵ, δ)-approximation, we are able to develop an algorithm based on Locality Sensitive Hashing (LSH) with only sublinear complexity O(Nh(ϵ, K) log N) when ϵ is not too small and K is not too large. We empirically evaluate our algorithms on up to 10 million data points and even our exact algorithm is up to three orders of magnitude faster than the baseline approximation algorithm. The LSH-based approximation algorithm can accelerate the value calculation process even further.We then extend our algorithm to other scenarios such as (1) weighed KNN classifiers, (2) different data points are clustered by different data curators, and (3) there are data analysts providing computation who also requires proper valuation. Some of these extensions, although also being improved exponentially, are less practical for exact computation (e.g., O(NK) complexity for weigthed KNN). We thus propose an Monte Carlo approximation algorithm, which is O(N(log N)2/(log K)2) times more efficient than the baseline approximation algorithm.

Task Scheduling in Deadline-Aware Mobile Edge Computing Systems

Abstract: Mobile edge computing (MEC) is a new computing approach in which computation tasks carried by mobile devices (MDs) can be offloaded to MEC servers or computed locally. Since the MDs are always battery limited and computation tasks have strict deadlines, how to schedule the execution of each task energy effectively is important. Comparing with existing works, we consider a much more complexed scenario, in which multiple moving MDs sharing multiple heterogeneous MEC servers, and a problem named as minimum energy consumption problem in deadline-aware MEC system is formulated. Such problem is proved to be NP-hard, and two approximation algorithms are proposed focusing on single and multiple MD scenarios, respectively. The performances of these algorithms are varied by theoretical analysis and simulations.

Variational Bayesian Learning for Dirichlet Process Mixture of Inverted Dirichlet Distributions in Non-Gaussian Image Feature Modeling

Abstract: In this paper, we develop a novel variational Bayesian learning method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently proposed extended variational inference (EVI) framework is adopted to derive an analytically tractable solution. The convergency of the proposed algorithm is theoretically guaranteed by introducing single lower bound approximation to the original objective function in the EVI framework. In principle, the proposed model can be viewed as an infinite inverted Dirichlet mixture model that allows the automatic determination of the number of mixture components from data. Therefore, the problem of predetermining the optimal number of mixing components has been overcome. Moreover, the problems of overfitting and underfitting are avoided by the Bayesian estimation approach. Compared with several recently proposed DP-related methods and conventional applied methods, the good performance and effectiveness of the proposed method have been demonstrated with both synthesized data and real data evaluations.

EP-Based Joint Active User Detection and Channel Estimation for Massive Machine-Type Communications

Abstract: Massive machine-type communication (mMTC) is a newly introduced service category in 5G wireless communication systems to support a variety of Internet-of-Things (IoT) applications. In recovering sparsely represented multi-user vectors, compressed sensing-based multi-user detection (CS-MUD) can be used. CS-MUD is a feasible solution to the grant-free uplink non-orthogonal multiple access (NOMA) environments. In CS-MUD, active user detection (AUD) and channel estimation (CE) should be performed before data detection. In this paper, we propose the expectation propagation-based joint AUD and CE (EP-AUD/CE) technique for mMTC networks. The EP algorithm is a Bayesian framework that approximates a computationally intractable probability distribution to an easily tractable distribution. The proposed technique finds a close approximation of the posterior distribution of the sparse channel vector. Using the approximate distribution, AUD and CE are jointly performed. We show by numerical simulations that the proposed technique substantially enhances AUD and CE performances over competing algorithms.

Optimal Synchronization Control of Multiagent Systems With Input Saturation via Off-Policy Reinforcement Learning

Abstract: In this paper, we aim to investigate the optimal synchronization problem for a group of generic linear systems with input saturation. To seek the optimal controller, Hamilton–Jacobi–Bellman (HJB) equations involving nonquadratic input energy terms in coupled forms are established. The solutions to these coupled HJB equations are further proven to be optimal and the induced controllers constitute interactive Nash equilibrium. Due to the difficulty to analytically solve HJB equations, especially in coupled forms, and the possible lack of model information of the systems, we apply the data-based off-policy reinforcement learning algorithm to learn the optimal control policies. A byproduct of this off-policy algorithm is shown that it is insensitive to probing noise that is exerted to the system to maintain persistence of excitation condition. In order to implement this off-policy algorithm, we employ actor and critic neural networks to approximate the controllers and the cost functions. Furthermore, the estimated control policies obtained by this presented implementation are proven to converge to the optimal ones under certain conditions. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

Intuitionistic Fuzzy Rough Set-Based Granular Structures and Attribute Subset Selection

Abstract: Attribute subset selection is an important issue in data mining and information processing. However, most automatic methodologies consider only the relevance factor between samples while ignoring the diversity factor. This may not allow the utilization value of hidden information to be exploited. For this reason, we propose a hybrid model named intuitionistic fuzzy (IF) rough set to overcome this limitation. The model combines the technical advantages of rough set and IF set and can effectively consider the above-mentioned statistical factors. First, fuzzy information granules based on IF relations are defined and used to characterize the hierarchical structures of the lower and upper approximations of IF rough set within the framework of granular computing. Then, the computation of IF rough approximations and knowledge reduction in IF information systems are investigated. Third, based on the approximations of IF rough set, significance measures are developed to evaluate the approximation quality and classification ability of IF relations. Furthermore, a forward heuristic algorithm for finding one optimal reduct of IF information systems is developed using these measures. Finally, numerical experiments are conducted on public datasets to examine the effectiveness and efficiency of the proposed algorithm in terms of the number of selected attributes, computational time, and classification accuracy.

Iterative Multiple Hypothesis Tracking With Tracklet-Level Association

Abstract: This paper proposes a novel iterative maximum weighted independent set (MWIS) algorithm for multiple hypothesis tracking (MHT) in a tracking-by-detection framework. MHT converts the tracking problem into a series of MWIS problems across the tracking time. Previous works solve these NP-hard MWIS problems independently without the use of any prior information from each frame, and they ignore the relevance between adjacent frames. In this paper, we iteratively solve the MWIS problems by using the MWIS solution from the previous frame rather than solving the problem from scratch each time. First, we define five hypothesis categories and a hypothesis transfer model, which explicitly describes the hypothesis relationship between adjacent frames. We also propose a polynomial-time approximation algorithm for the MWIS problem in MHT. In addition to that, we present a confident short tracklet generation method and incorporate tracklet-level association into MHT, which further improves the computational efficiency. Our experiments on both MOT16 and MOT17 benchmarks show that our tracker outperforms all the previously published tracking algorithms on both MOT16 and MOT17 benchmarks. Finally, we demonstrate that the polynomial-time approximate tracker reaches nearly the same tracking performance.

Service Placement with Provable Guarantees in Heterogeneous Edge Computing Systems

Abstract: Mobile edge computing (MEC) is a promising technique for providing low-latency access to services at the network edge. The services are hosted at various types of edge nodes with both computation and communication capabilities. Due to the heterogeneity of edge node characteristics and user locations, the performance of MEC varies depending on where the service is hosted. In this paper, we consider such a heterogeneous MEC system, and focus on the problem of placing multiple services in the system to maximize the total reward. We show that the problem is NP-hard via reduction from the set cover problem, and propose a deterministic approximation algorithm to solve the problem, which has an approximation ratio that is not worse than$(1-e^{-1})/4$. The proposed algorithm is based on two subroutines that are suitable for small and arbitrarily sized services, respectively. The algorithm is designed using a novel way of partitioning each edge node into multiple slots, where each slot contains one service. The approximation guarantee is obtained via a specialization of the method of conditional expectations, which uses a randomized procedure as an intermediate step. In addition to theoretical guarantees, simulation results also show that the proposed algorithm outperforms other state-of-the-art approaches.

Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints

Abstract: An effective Emergency Medical Service (EMS) system can provide medical relief supplies for common emergencies (fire, accident, etc.) or large-scale disasters (earthquake, tsunami, bioterrorism attack, explosion, etc.) and decrease morbidity and mortality dramatically. This paper proposes a distributionally robust model for optimizing the location, number of ambulances and demand assignment in an EMS system by minimizing the expected total cost. The model guarantees that the probability of satisfying the maximum concurrent demand in the whole system is larger than a predetermined reliability level by introducing joint chance constraints and characterizes the expected total cost by moment uncertainty based on a data-driven approach. The model is approximated as a parametric second-order conic representable program. Furthermore, a special case of the model is considered and converted into a standard second-order cone program, which can be efficiently solved with a proposed outer approximation algorithm. Extensive numerical experiments are conducted to illustrate the benefit of the proposed approach. Moreover, a dataset from a real application is also used to demonstrate the application of the data-driven approach.

$p$ -Laplacian Regularization for Scene Recognition

Abstract: The explosive growth of multimedia data on the Internet makes it essential to develop innovative machine learning algorithms for practical applications especially where only a small number of labeled samples are available. Manifold regularized semi-supervised learning (MRSSL) thus received intensive attention recently because it successfully exploits the local structure of data distribution including both labeled and unlabeled samples to leverage the generalization ability of a learning model. Although there are many representative works in MRSSL, including Laplacian regularization (LapR) and Hessian regularization, how to explore and exploit the local geometry of data manifold is still a challenging problem. In this paper, we introduce a fully efficient approximation algorithm of graph ${p}$ -Laplacian, which significantly saving the computing cost. And then we propose ${p}$ -LapR (pLapR) to preserve the local geometry. Specifically, ${p}$ -Laplacian is a natural generalization of the standard graph Laplacian and provides convincing theoretical evidence to better preserve the local structure. We apply pLapR to support vector machines and kernel least squares and conduct the implementations for scene recognition. Extensive experiments on the Scene 67 dataset, Scene 15 dataset, and UC-Merced dataset validate the effectiveness of pLapR in comparison to the conventional manifold regularization methods.

Algebraic Methods in the Congested Clique

Abstract: In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an $$O(n^{1-2/\omega })$$ round matrix multiplication algorithm, where $$\omega < 2.3728639$$ is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.

Optimization of the Sherrington-Kirkpatrick Hamiltonian

Abstract: Let A be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing the quadratic form associated to A over binary vectors. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this optimization problem was characterized by Parisi via a celebrated variational principle, subsequently proved by Talagrand. We give an algorithm that, for any e > 0, outputs a feasible solution whose value is at least (1 – e) of the optimum, with probability converging to one as the dimension n of the matrix diverges. The algorithm's time complexity is of order n^2. It is a message-passing algorithm, but the specific structure of its update rules is new. As a side result, we prove that, at (low) non-zero temperature, the algorithm constructs approximate solutions of the Thouless-Anderson-Palmer equations.

Off-Policy Interleaved $Q$ -Learning: Optimal Control for Affine Nonlinear Discrete-Time Systems

Abstract: In this paper, a novel off-policy interleaved Q-learning algorithm is presented for solving optimal control problem of affine nonlinear discrete-time (DT) systems, using only the measured data along the system trajectories. Affine nonlinear feature of systems, unknown dynamics, and off-policy learning approach pose tremendous challenges on approximating optimal controllers. To this end, on-policy Q-learning method for optimal control of affine nonlinear DT systems is reviewed first, and its convergence is rigorously proven. The bias of solution to Q-function-based Bellman equation caused by adding probing noises to systems for satisfying persistent excitation is also analyzed when using on-policy Q-learning approach. Then, a behavior control policy is introduced followed by proposing an off-policy Q-learning algorithm. Meanwhile, the convergence of algorithm and no bias of solution to optimal control problem when adding probing noise to systems are investigated. Third, three neural networks run by the interleaved Q-learning approach in the actor-critic framework. Thus, a novel off-policy interleaved Q-learning algorithm is derived, and its convergence is proven. Simulation results are given to verify the effectiveness of the proposed method.

Communication-Censored ADMM for Decentralized Consensus Optimization

Abstract: In this paper, we devise a communication-efficient decentralized algorithm, named as communication-censored alternating direction method of multipliers (ADMM) (COCA), to solve a convex consensus optimization problem defined over a network. Similar to popular decentralized consensus optimization algorithms such as ADMM, at every iteration of COCA, a node exchanges its local variable with neighbors, and then updates its local variable according to the received neighboring variables and its local cost function. A different feature of COCA is that a node is not allowed to transmit its local variable to neighbors, if this variable is not sufficiently different to the previously transmitted one. The sufficiency of the difference is evaluated by a properly designed censoring function. Though this censoring strategy may slow down the optimization process, it effectively reduces the communication cost. We prove that when the censoring function is properly chosen, COCA converges to an optimal solution of the convex consensus optimization problem. Furthermore, if the local cost functions are strongly convex, COCA has a fast linear convergence rate. Numerical experiments demonstrate that, given a target solution accuracy, COCA is able to significantly reduce the overall communication cost compared to existing algorithms including ADMM, and hence fits for applications where network communication is a bottleneck.