Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201

Energy Efficient Protocols for Delay Tolerant Networks

The delay tolerant networks (DTNs) is characterized by frequent disconnections and long delays of links among devices due to mobility, sparse deployment of devices, attacks, and noise, etc. Considerable research efforts have been devoted recently to DTNs enabling communications between network entities with intermittent connectivity. Unfortunately, mobile devices have limited energy capacity, and the fundamental problem is that traditional power-saving mechanisms are designed assuming well connected networks. Due to much larger inter-contact durations than contact durations, devices spend most of their life time in the neighbor discovery, and centralized power-saving strategies are difficult. Consequently, mobile devices consume a significant amount of energy in the neighbor discovery, rather than in infrequent data transfers. Therefore, distributed energy efficient neighbor discovery protocols for DTNs are essential to minimize the degradation of network connectivity and maximize the benefits from mobility. In this thesis, we develop sleep scheduling protocols in the medium access control (MAC) layer that are adaptive and distributed under different clock synchronization conditions: synchronous, asynchronous, and semi-asynchronous. In addition, we propose a distributed clock synchronization protocol to mitigate the clock synchronization problem in DTNs. Our research accomplishments are briefly outlined as follows: Firstly, we design an adaptive exponential beacon (AEB) protocol. By exploiting the trend of contact availability, beacon periods are independently adjusted by each device and optimized using the distribution of contact durations. The AEB protocol significantly reduces energy consumption while maintaining comparable packet delivery delay and delivery ratio. Secondly, we design two asynchronous clock based sleep scheduling (ACDS) protocols. Based on the fact that global clock synchronization is difficult to achieve in general, predetermined patterns of sleep schedules are constructed using hierarchical arrangements of cyclic difference sets such that devices independently selecting different duty cycle lengths are still guaranteed to have overlapping awake intervals with other devices within the communication range. Thirdly, we design a distributed semi-asynchronous sleep scheduling (DSA) protocol. Although the synchronization error is unavoidable, some level of clock accuracy may be possible for many practical scenarios. The sleep schedules are constructed to guarantee contacts among devices having loosely synchronized clocks, and parameters are optimized using the distribution of synchronization error. We also define conditions for which the proposed semi-asynchronous protocol outperforms existing asynchronous sleep scheduling protocols. Lastly, we design a distributed clock synchronization (DCS) protocol. The proposed protocol considers asynchronous and long delayed connections when exchanging relative clock information among nodes. As a result, smaller synchronization error achieved by the proposed protocol allows more accurate timing information and renders neighbor discovery more energy efficient. The designed protocols improve the lifetime of mobile devices in DTNs by means of energy efficient neighbor discoveries that reduce the energy waste caused by idle listening problems

Dimmer: Self-Adaptive Network-Wide Flooding with Reinforcement Learning

The last decade saw an emergence of Synchronous Transmissions (ST) as an effective communication paradigm in low-power wireless networks. Numerous ST protocols provide high reliability and energy efficiency in normal wireless conditions, for a large variety of traffic requirements. Recently, with the EWSN dependability competitions, the community pushed ST to harsher and highly-interfered environments, improving upon classical ST protocols through the use of custom rules, hand-tailored parameters, and additional retransmissions. The results are sophisticated protocols, that require prior expert knowledge and extensive testing, often tuned for a specific deployment and envisioned scenario. In this paper, we explore how ST protocols can benefit from self-adaptivity; a self-adaptive ST protocol selects itself its best parameters to (1) tackle external environment dynamics and (2) adapt to its topology over time. We introduce Dimmer as a self-adaptive ST protocol. Dimmer builds on LWB and uses Reinforcement Learning to tune its parameters and match the current properties of the wireless medium. By learning how to behave from an unlabeled dataset, Dimmer adapts to different interference types and patterns, and is able to tackle previously unseen interference. With Dimmer, we explore how to efficiently design AI-based systems for constrained devices, and outline the benefits and downfalls of AI-based low-power networking. We evaluate our protocol on two deployments of resource-constrained nodes achieving 95.8% reliability against strong, unknown WiFi interference. Our results outperform baselines such as non-adaptive ST protocols (27%) and PID controllers, and show a performance close to hand-crafted and more sophisticated solutions, such as Crystal (99%)

Efficient Methods For Large-Scale Empirical Risk Minimization

Empirical risk minimization (ERM) problems express optimal classifiers as solutions of optimization problems in which the objective is the sum of a very large number of sample costs. An evident obstacle in using traditional descent algorithms for solving this class of problems is their prohibitive computational complexity when the number of component functions in the ERM problem is large. The main goal of this thesis is to study different approaches to solve these large-scale ERM problems. We begin by focusing on incremental and stochastic methods which split the training samples into smaller sets across time to lower the computation burden of traditional descent algorithms. We develop and analyze convergent stochastic variants of quasi-Newton methods which do not require computation of the objective Hessian and approximate the curvature using only gradient information. We show that the curvature approximation in stochastic quasi-Newton methods leads to faster convergence relative to first-order stochastic methods when the problem is ill-conditioned. We culminate with the introduction of an incremental method that exploits memory to achieve a superlinear convergence rate. This is the best known convergence rate for an incremental method. An alternative strategy for lowering the prohibitive cost of solving large-scale ERM problems is decentralized optimization whereby samples are separated not across time but across multiple nodes of a network. In this regime, the main contribution of this thesis is in incorporating second-order information of the aggregate risk corresponding to samples of all nodes in the network in a way that can be implemented in a distributed fashion. We also explore the separation of samples across both, time and space, to reduce the computational and communication cost for solving large-scale ERM problems. We study this path by introducing a decentralized stochastic method which incorporates the idea of stochastic averaging gradient leading to a low computational complexity method with a fast linear convergence rate. We then introduce a rethinking of ERM in which we consider not a partition of the training set as in the case of stochastic and distributed optimization, but a nested collection of subsets that we grow geometrically. The key insight is that the optimal argument associated with a training subset of a certain size is not that far from the optimal argument associated with a larger training subset. Based on this insight, we present adaptive sample size schemes which start with a small number of samples and solve the corresponding ERM problem to its statistical accuracy. The sample size is then grown geometrically and use the solution of the previous ERM as a warm start for the new ERM. Theoretical analyses show that the use of adaptive sample size methods reduces the overall computational cost of achieving the statistical accuracy of the whole dataset for a broad range of deterministic and stochastic first-order methods. We further show that if we couple the adaptive sample size scheme with Newton\u27s method, it is possible to consider subsequent doubling of the training set and perform a single Newton iteration in between. This is possible because of the interplay between the statistical accuracy and the quadratic convergence region of these problems and yields a method that is guaranteed to solve an ERM problem by performing just two passes over the dataset

Scalable Learning In Distributed Robot Teams

Mobile robots are already in use for mapping, agriculture, entertainment, and the delivery of goods and people. As robotic systems continue to become more affordable, large numbers of mobile robots may be deployed concurrently to accomplish tasks faster and more efficiently. Practical deployments of very large teams will require scalable algorithms to enable the distributed cooperation of autonomous agents. This thesis focuses on the three main algorithmic obstacles to the scalability of robot teams: coordination, control, and communication. To address these challenges, we design graph-based abstractions that allow us to apply Graph Neural Networks (GNNs).First, a team of robots must continually coordinate to divide up mission requirements among all agents. We focus on the case studies of exploration and coverage to develop a spatial GNN controller that can coordinate a team of dozens of agents as they visit thousands of landmarks. A routing problem of this size is intractable for existing optimization-based approaches. Second, a robot in a team must be able to execute the trajectory that will accomplish its given sub-task. In large teams with high densities of robots, planning and execution of safe, collision-free trajectories requires the joint optimization over all agent trajectories, which may be impractical in large teams. We present two approaches to scalable control: a) a controller for flocking that uses delayed communication formalized via a GNN; and b) an inverse optimal planning method that learns from real air traffic data. Third, robot teams may need to operate in harsh environments without existing communication infrastructure, requiring the formation of ad-hoc networks to exchange information. Many algorithms for control of multi-robot teams operate under the assumption that low-latency, global state information necessary to coordinate agent actions can readily be disseminated among the team. Our approach leverages GNNs to control the connectivity within the ad-hoc network and to provide the data distribution infrastructure necessary for countless multi-robot algorithms. Finally, this thesis develops a framework for distributed learning to be used when centralized information is unavailable during training. Our approach allows robots to train controllers independently and then share their experiences by composing multiple models represented in a Reproducing Kernel Hilbert Space

Distributed averaging over communication networks:Fragility, robustness and opportunities

Distributed averaging, a canonical operation among many natural interconnected systems, has found applications in a tremendous variety of applied fields, including statistical physics, signal processing, systems and control, communication and social science. As information exchange is a central part of distributed averaging systems, it is of practical as well as theoretical importance to understand various properties/limitations of those systems in the presence of communication constraints and devise new algorithms to alleviate those limitations. We study the fragility of a popular distributed averaging algorithm when the information exchange among the nodes is limited by communication delays, fading connections and additive noise. We show that the otherwise well studied and benign multi-agent system can generate a collective global complex behavior. We characterize this behavior, common to many natural and human-made interconnected systems, as a collective hyper-jump diffusion process and as a L\\u27{e}vy flights process in a special case. We further describe the mechanism for its emergence and predict its occurrence, under standard assumptions, by checking the Mean Square instability of a certain part of the system. We show that the strong connectivity property of the network topology guarantees that the complex behavior is global and manifested by all the agents in the network, even though the source of uncertainty is localized. We provide novel computational analysis of the MS stability index under spatially invariant structures and gain certain qualitative as well as quantitative insights of the system. We then focus on design of agents\u27 dynamics to increase the robustness of distributed averaging system to topology variations. We provide a general structure of distributed averaging systems where individual agents are modeled by LTI systems. We show the problem of designing agents\u27 dynamics for distributed averaging is equivalent to an $\mathcal{H}_{\infty}$ minimization problem. In this way, we could use tools from robust control theory to build the distributed averaging system where the design is fully distributed and scalable with the size of the network. It is also shown that the agents could be used in different fixed networks and networks with speical time varying interconnections. We develop new iterative distributed averaging algorithms which allow agents to compute the average quantity in the presence of additive noise and random changing interconnections. The algorithm relaxes several previous restrictive assumptions on distributed averaging under uncertainties, such as diminishing step size rule, doubly stochastic weights, symmetric link switching styles, etc, and introduces novel mechanism of network feedback to mitigate effects of communication uncertainties on information aggregation. Based on the robust distributed averaging algorithm, we propose continuous as well as discrete time computation models to solve the distributed optimization problem where the objective function is formed by the summation of convex functions of the same variable. The algorithm shows faster convergence speed than existing ones and exhibits robustness to additive noise, which is the main source of limitation on algorithms based on convex mixing. It is shown that agents with simple dynamics and gradient sensing abilities could collectively solve complicated convex optimization problems. Finally, we generalize this algorithm to build a general framework forconstrained convex optimization problems. This framework is shown to be particularly effective to derive solutions for distributed decision making problems and lead to a systems perspective for convex optimization