Emerging technologies and applications including Internet of Things (IoT), social networking, and crowd-sourcing generate large amounts of data at the network edge. Machine learning models are often built from the collected data, to enable the detection, classification, and prediction of future events. Due to bandwidth, storage, and privacy concerns, it is often impractical to send all the data to a centralized location. In this paper, we consider the problem of learning model parameters from data distributed across multiple edge nodes, without sending raw data to a centralized place. Our focus is on a generic class of machine learning models that are trained using gradientdescent based approaches. We analyze the convergence bound of distributed gradient descent from a theoretical point of view, based on which we propose a control algorithm that determines the best trade-off between local update and global parameter aggregation to minimize the loss function under a given resource budget. The performance of the proposed algorithm is evaluated via extensive experiments with real datasets, both on a networked prototype system and in a larger-scale simulated environment. The experimentation results show that our proposed approach performs near to the optimum with various machine learning models and different data distributions.

Emerging technologies and applications including Internet of Things (IoT), social networking, and crowd-sourcing generate large amounts of data at the network edge. Machine learning models are often built from the collected data, to enable the detection, classification, and prediction of future events. Due to bandwidth, storage, and privacy concerns, it is often impractical to send all the data to a centralized location. In this paper, we consider the problem of learning model parameters from data distributed across multiple edge nodes, without sending raw data to a centralized place. Our focus is on a generic class of machine learning models that are trained using gradientdescent based approaches. We analyze the convergence rate of distributed gradient descent from a theoretical point of view, based on which we propose a control algorithm that determines the best trade-off between local update and global parameter aggregation to minimize the loss function under a given resource budget. The performance of the proposed algorithm is evaluated via extensive experiments with real datasets, both on a networked prototype system and in a larger-scale simulated environment. The experimentation results show that our proposed approach performs near to the optimum with various machine learning models and different data distributions.

We study the dynamic service migration problem in mobile edge-clouds that host cloud-based services at the network edge. This offers the benefits of reduction in network overhead and latency but requires service migrations as user locations change over time. It is challenging to make these decisions in an optimal manner because of the uncertainty in node mobility as well as possible non-linearity of the migration and transmission costs. In this paper, we formulate a sequential decision making problem for service migration using the framework of Markov Decision Process (MDP). Our formulation captures general cost models and provides a mathematical framework to design optimal service migration policies. In order to overcome the complexity associated with computing the optimal policy, we approximate the underlying state space by the distance between the user and service locations. We show that the resulting MDP is exact for uniform one-dimensional mobility while it provides a close approximation for uniform two-dimensional mobility with a constant additive error term. We also propose a new algorithm and a numerical technique for computing the optimal solution which is significantly faster in computation than traditional methods based on value or policy iteration. We illustrate the effectiveness of our approach by simulation using real-world mobility traces of taxis in San Francisco.

We investigate the problem of optimal request routing and content caching in a heterogeneous network supporting in-network content caching with the goal of minimizing average content access delay. Here, content can either be accessed directly from a back-end server (where content resides permanently) or be obtained from one of multiple in-network caches. To access a piece of content, a user must decide whether to route its request to a cache or to the back-end server. Additionally, caches must decide which content to cache. We investigate the problem complexity of two problem formulations, where the direct path to the back-end server is modeled as i) a congestionsensitive or ii) a congestion-insensitive path, reflecting whether or not the delay of the uncached path to the back-end server depends on the user request load, respectively. We show that the problem is NP-complete in both cases. We prove that under the congestion-insensitive model the problem can be solved optimally in polynomial time if each piece of content is requested by only one user, or when there are at most two caches in the network. We also identify a structural property of the user-cache graph that potentially makes the problem NP-complete. For the congestionsensitive model, we prove that the problem remains NP-complete even if there is only one cache in the network and each content is requested by only one user. We show that approximate solutions can be found for both models within a (1 − 1/e) factor of the optimal solution, and demonstrate a greedy algorithm that is found to be within 1% of optimal for small problem sizes. Through trace-driven simulations we evaluate the performance of our greedy algorithms, which show up to a 50% reduction in average delay over solutions based on LRU content caching.

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Seamless computing and data access is enabled by the emerging technology of mobile micro-clouds (MMCs). Different from traditional centralized clouds, an MMC is typically connected directly to a wireless base-station and provides services to a small group of users, which allows users to have instantaneous access to cloud services. Due to the limited coverage area of base-stations and the dynamic nature of mobile users, network background traffic, etc., the question of where to place the services to cope with these dynamics arises. In this paper, we focus on dynamic service placement for MMCs. We consider the case where there is an underlying mechanism to predict the future costs of service hosting and migration, and the prediction error is assumed to be bounded. Our goal is to find the optimal service placement sequence which minimizes the average cost over a given time. To solve this problem, we first propose a method which solves for the optimal placement sequence for a specific look-ahead time-window, based on the predicted costs in this time-window. We show that this problem is equivalent to a shortest-path problem and propose an algorithm with polynomial time-complexity to find its solution. Then, we propose a method to find the optimal look-ahead window size, which minimizes an upper bound of the average cost. Finally, we evaluate the effectiveness of the proposed approach by simulations with realworld user-mobility traces.

Mobile edge computing is an emerging technology to offer resource-intensive yet delay-sensitive applications from the edge of mobile networks, where a major challenge is to allocate limited edge resources to competing demands. While prior works often make a simplifying assumption that resources assigned to different users are non-sharable, this assumption does not hold for storage resources, where users interested in services (e.g., data analytics) based on the same set of data/code can share storage resource. Meanwhile, serving each user request also consumes non-sharable resources (e.g., CPU cycles, bandwidth). We study the optimal provisioning of edge services with non-trivial demands of both sharable (storage) and non-sharable (communication, computation) resources via joint service placement and request scheduling. In the homogeneous case, we show that while the problem is polynomial-time solvable without storage constraints, it is NP-hard even if each edge cloud has unlimited communication or computation resources. We further show that the hardness is caused by the service placement subproblem, while the request scheduling subproblem is polynomial-time solvable via maximum-flow algorithms. In the general case, both subproblems are NP-hard. We develop a constant-factor approximation algorithm for the homogeneous case and efficient heuristics for the general case. Our trace-driven simulations show that the proposed algorithms, especially the approximation algorithm, can achieve near-optimal performance, serving 2-3 times more requests than a baseline solution that optimizes service placement and request scheduling separately. Index Terms-mobile edge computing; service placement; request scheduling; complexity analysis; approximation algorithm.

… Area Backhaul network … Figure 1. Application scenario of mobile edge computing where edge servers (ES) are co-located with base stations (BS).