Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Distributed Online Modified Greedy Algorithm for Networked Storage Operation under Uncertainty

The integration of intermittent and stochastic renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of storage networks in stochastic environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems on continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or provably near-optimal performance for this problem. This paper provides an efficient algorithm to solve this problem with performance guarantees. We study the operation of storage networks, i.e., a storage system interconnected via a power network. An online algorithm, termed Online Modified Greedy algorithm, is developed for the corresponding constrained stochastic control problem. A sub-optimality bound for the algorithm is derived, and a semidefinite program is constructed to minimize the bound. In many cases, the bound approaches zero so that the algorithm is near-optimal. A task-based distributed implementation of the online algorithm relying only on local information and neighbor communication is then developed based on the alternating direction method of multipliers. Numerical examples verify the established theoretical performance bounds, and demonstrate the scalability of the algorithm.Comment: arXiv admin note: text overlap with arXiv:1405.778

Dynamic Collaborative Multi-Agent Reinforcement Learning Communication for Autonomous Drone Reforestation

We approach autonomous drone-based reforestation with a collaborative multi-agent reinforcement learning (MARL) setup. Agents can communicate as part of a dynamically changing network. We explore collaboration and communication on the back of a high-impact problem. Forests are the main resource to control rising CO2 conditions. Unfortunately, the global forest volume is decreasing at an unprecedented rate. Many areas are too large and hard to traverse to plant new trees. To efficiently cover as much area as possible, here we propose a Graph Neural Network (GNN) based communication mechanism that enables collaboration. Agents can share location information on areas needing reforestation, which increases viewed area and planted tree count. We compare our proposed communication mechanism with a multi-agent baseline without the ability to communicate. Results show how communication enables collaboration and increases collective performance, planting precision and the risk-taking propensity of individual agents.Comment: Deep Reinforcement Learning Workshop at the 36th Conference on Neural Information Processing Systems (NeurIPS 2022

Leveraging Resources on Anonymous Mobile Edge Nodes

Smart devices have become an essential component in the life of mankind. The quick rise of smartphones, IoTs, and wearable devices enabled applications that were not possible few years ago, e.g., health monitoring and online banking. Meanwhile, smart sensing laid the infrastructure for smart homes and smart cities. The intrusive nature of smart devices granted access to huge amounts of raw data. Researchers seized the moment with complex algorithms and data models to process the data over the cloud and extract as much information as possible. However, the pace and amount of data generation, in addition to, networking protocols transmitting data to cloud servers failed short in touching more than 20% of what was generated on the edge of the network. On the other hand, smart devices carry a large set of resources, e.g., CPU, memory, and camera, that sit idle most of the time. Studies showed that for plenty of the time resources are either idle, e.g., sleeping and eating, or underutilized, e.g. inertial sensors during phone calls. These findings articulate a problem in processing large data sets, while having idle resources in the close proximity. In this dissertation, we propose harvesting underutilized edge resources then use them in processing the huge data generated, and currently wasted, through applications running at the edge of the network. We propose flipping the concept of cloud computing, instead of sending massive amounts of data for processing over the cloud, we distribute lightweight applications to process data on users\u27 smart devices. We envision this approach to enhance the network\u27s bandwidth, grant access to larger datasets, provide low latency responses, and more importantly involve up-to-date user\u27s contextual information in processing. However, such benefits come with a set of challenges: How to locate suitable resources? How to match resources with data providers? How to inform resources what to do? and When? How to orchestrate applications\u27 execution on multiple devices? and How to communicate between devices on the edge? Communication between devices at the edge has different parameters in terms of device mobility, topology, and data rate. Standard protocols, e.g., Wi-Fi or Bluetooth, were not designed for edge computing, hence, does not offer a perfect match. Edge computing requires a lightweight protocol that provides quick device discovery, decent data rate, and multicasting to devices in the proximity. Bluetooth features wide acceptance within the IoT community, however, the low data rate and unicast communication limits its use on the edge. Despite being the most suitable communication protocol for edge computing and unlike other protocols, Bluetooth has a closed source code that blocks lower layer in front of all forms of research study, enhancement, and customization. Hence, we offer an open source version of Bluetooth and then customize it for edge computing applications. In this dissertation, we propose Leveraging Resources on Anonymous Mobile Edge Nodes (LAMEN), a three-tier framework where edge devices are clustered by proximities. On having an application to execute, LAMEN clusters discover and allocate resources, share application\u27s executable with resources, and estimate incentives for each participating resource. In a cluster, a single head node, i.e., mediator, is responsible for resource discovery and allocation. Mediators orchestrate cluster resources and present them as a virtually large homogeneous resource. For example, two devices each offering either a camera or a speaker are presented outside the cluster as a single device with both camera and speaker, this can be extended to any combination of resources. Then, mediator handles applications\u27 distribution within a cluster as needed. Also, we provide a communication protocol that is customizable to the edge environment and application\u27s need. Pushing lightweight applications that end devices can execute over their locally generated data have the following benefits: First, avoid sharing user data with cloud server, which is a privacy concern for many of them; Second, introduce mediators as a local cloud controller closer to the edge; Third, hide the user\u27s identity behind mediators; and Finally, enhance bandwidth utilization by keeping raw data at the edge and transmitting processed information. Our evaluation shows an optimized resource lookup and application assignment schemes. In addition to, scalability in handling networks with large number of devices. In order to overcome the communication challenges, we provide an open source communication protocol that we customize for edge computing applications, however, it can be used beyond the scope of LAMEN. Finally, we present three applications to show how LAMEN enables various application domains on the edge of the network. In summary, we propose a framework to orchestrate underutilized resources at the edge of the network towards processing data that are generated in their proximity. Using the approaches explained later in the dissertation, we show how LAMEN enhances the performance of applications and enables a new set of applications that were not feasible