Stochastic Optimization For Multi-Agent Statistical Learning And Control

The goal of this thesis is to develop a mathematical framework for optimal, accurate, and affordable complexity statistical learning among networks of autonomous agents. We begin by noting the connection between statistical inference and stochastic programming, and consider extensions of this setup to settings in which a network of agents each observes a local data stream and would like to make decisions that are good with respect to information aggregated across the entire network. There is an open-ended degree of freedom in this problem formulation, however: the selection of the estimator function class which defines the feasible set of the stochastic program. Our central contribution is the design of stochastic optimization tools in reproducing kernel Hilbert spaces that yield optimal, accurate, and affordable complexity statistical learning for a multi-agent network. To obtain this result, we first explore the relative merits and drawbacks of different function class selections. In Part I, we consider multi-agent expected risk minimization this problem setting for the case that each agent seems to learn a common globally optimal generalized linear models (GLMs) by developing a stochastic variant of Arrow-Hurwicz primal-dual method. We establish convergence to the primal-dual optimal pair when either consensus or ``proximity constraints encode the fact that we want all agents\u27 to agree, or nearby agents to make decisions that are close to one another. Empirically, we observe that these convergence results are substantiated but that convergence may not translate into statistical accuracy. More broadly, optimality within a given estimator function class is not the same as one that makes minimal inference errors. The optimality-accuracy tradeoff of GLMs motivates subsequent efforts to learn more sophisticated estimators based upon learned feature encodings of the data that is fed into the statistical model. The specific tool we turn to in Part II is dictionary learning, where we optimize both over regression weights and an encoding of the data, which yields a non-convex problem. We investigate the use of stochastic methods for online task-driven dictionary learning, and obtain promising performance for the task of a ground robot learning to anticipate control uncertainty based on its past experience. Heartened by this implementation, we then consider extensions of this framework for a multi-agent network to each learn globally optimal task-driven dictionaries based on stochastic primal-dual methods. However, it is here the non-convexity of the optimization problem causes problems: stringent conditions on stochastic errors and the duality gap limit the applicability of the convergence guarantees, and impractically small learning rates are required for convergence in practice. Thus, we seek to learn nonlinear statistical models while preserving convexity, which is possible through kernel methods ( Part III). However, the increased descriptive power of nonparametric estimation comes at the cost of infinite complexity. Thus, we develop a stochastic approximation algorithm in reproducing kernel Hilbert spaces (RKHS) that ameliorates this complexity issue while preserving optimality: we combine the functional generalization of stochastic gradient method (FSGD) with greedily constructed low-dimensional subspace projections based on matching pursuit. We establish that the proposed method yields a controllable trade-off between optimality and memory, and yields highly accurate parsimonious statistical models in practice. % Then, we develop a multi-agent extension of this method by proposing a new node-separable penalty function and applying FSGD together with low-dimensional subspace projections. This extension allows a network of autonomous agents to learn a memory-efficient approximation to the globally optimal regression function based only on their local data stream and message passing with neighbors. In practice, we observe agents are able to stably learn highly accurate and memory-efficient nonlinear statistical models from streaming data. From here, we shift focus to a more challenging class of problems, motivated by the fact that true learning is not just revising predictions based upon data but augmenting behavior over time based on temporal incentives. This goal may be described by Markov Decision Processes (MDPs): at each point, an agent is in some state of the world, takes an action and then receives a reward while randomly transitioning to a new state. The goal of the agent is to select the action sequence to maximize its long-term sum of rewards, but determining how to select this action sequence when both the state and action spaces are infinite has eluded researchers for decades. As a precursor to this feat, we consider the problem of policy evaluation in infinite MDPs, in which we seek to determine the long-term sum of rewards when starting in a given state when actions are chosen according to a fixed distribution called a policy. We reformulate this problem as a RKHS-valued compositional stochastic program and we develop a functional extension of stochastic quasi-gradient algorithm operating in tandem with the greedy subspace projections mentioned above. We prove convergence with probability 1 to the Bellman fixed point restricted to this function class, and we observe a state of the art trade off in memory versus Bellman error for the proposed method on the Mountain Car driving task, which bodes well for incorporating policy evaluation into more sophisticated, provably stable reinforcement learning techniques, and in time, developing optimal collaborative multi-agent learning-based control systems

Neural Radiance Fields: Past, Present, and Future

The various aspects like modeling and interpreting 3D environments and surroundings have enticed humans to progress their research in 3D Computer Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in Computer Graphics, Robotics, Computer Vision, and the possible scope of High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D models have gained traction from res with more than 1000 preprints related to NeRFs published. This paper serves as a bridge for people starting to study these fields by building on the basics of Mathematics, Geometry, Computer Vision, and Computer Graphics to the difficulties encountered in Implicit Representations at the intersection of all these disciplines. This survey provides the history of rendering, Implicit Learning, and NeRFs, the progression of research on NeRFs, and the potential applications and implications of NeRFs in today's world. In doing so, this survey categorizes all the NeRF-related research in terms of the datasets used, objective functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation

Intelligent Circuits and Systems

ICICS-2020 is the third conference initiated by the School of Electronics and Electrical Engineering at Lovely Professional University that explored recent innovations of researchers working for the development of smart and green technologies in the fields of Energy, Electronics, Communications, Computers, and Control. ICICS provides innovators to identify new opportunities for the social and economic benefits of society.　 This conference bridges the gap between academics and R&D institutions, social visionaries, and experts from all strata of society to present their ongoing research activities and foster research relations between them. It provides opportunities for the exchange of new ideas, applications, and experiences in the field of smart technologies and finding global partners for future collaboration. The ICICS-2020 was conducted in two broad categories, Intelligent Circuits & Intelligent Systems and Emerging Technologies in Electrical Engineering

A Digital Triplet for Utilizing Offline Environments to Train Condition Monitoring Systems for Rolling Element Bearings

Manufacturing competitiveness is related to making a quality product while incurring the lowest costs. Unexpected downtime caused by equipment failure negatively impacts manufacturing competitiveness due to the ensuing defects and delays caused by the downtime. Manufacturers have adopted condition monitoring (CM) techniques to reduce unexpected downtime to augment maintenance strategies. The CM adoption has transitioned maintenance from Breakdown Maintenance (BM) to Condition-Based Maintenance (CbM) to anticipate impending failures and provide maintenance actions before equipment failure. CbM is the umbrella term for maintenance strategies that use condition monitoring techniques such as Preventive Maintenance (PM) and Predictive Maintenance (PdM). Preventive Maintenance involves providing periodic checks based on either time or sensory input. Predictive Maintenance utilizes continuous or periodic sensory inputs to determine the machine health state to predict the equipment failure. The overall goal of the work is to improve bearing diagnostic and prognostic predictions for equipment health by utilizing surrogate systems to generate failure data that represents production equipment failure, thereby providing training data for condition monitoring solutions without waiting for real world failure data. This research seeks to address the challenges of obtaining failure data for CM systems by incorporating a third system into monitoring strategies to create a Digital Triplet (DTr) for condition monitoring to increase the amount of possible data for condition monitoring. Bearings are a critical component in rotational manufacturing systems with wide application to other industries outside of manufacturing, such as energy and defense. The reinvented DTr system considers three components: the physical, surrogate, and digital systems. The physical system represents the real-world application in production that cannot fail. The surrogate system represents a physical component in a test system in an offline environment where data is generated to fill in gaps from data unavailable in the real-world system. The digital system is the CM system, which provides maintenance recommendations based on the ingested data from the real world and surrogate systems. In pursuing the research goal, a comprehensive bearing dataset detailing these four failure modes over different collection operating parameters was created. Subsequently, the collections occurred under different operating conditions, such as speed-varying, load-varying, and steadystate. Different frequency and time measures were used to analyze and identify differentiating criteria between the different failure classes over the differing operating conditions. These empirical observations were recreated using simulations to filter out potential outliers. The outputs of the physical model were combined with knowledge from the empirical observations to create ”spectral deltas” to augment existing bearing data and create new failure data that resemble similar frequency criteria to the original data. The primary verification occurred on a laboratory-bearing test stand. A conjecture is provided on how to scale to a larger system by analyzing a larger system from a local manufacturer. From the subsequent analysis of machine learning diagnosis and prognosis models, the original and augmented bearing data can complement each other during model training. The subsequent data substitution verifies that bearing data collected under different operating conditions and sizes can be substituted between different systems. Ostensibly, the full formulation of the digital triplet system is that bearing data generated at a smaller size can be scaled to train predictive failure models for larger bearing sizes. Future work should consider implementing this method for other systems outside of bearings, such as gears, non-rotational equipment, such as pumps, or even larger complex systems, such as computer numerically controlled machine tools or car engines. In addition, the method and process should not be restricted to only mechanical systems and could be applied to electrical systems, such as batteries. Furthermore, an investigation should consider further data-driven approximations to specific bearing characteristics related to the stiffness and damping parameters needed in modeling. A final consideration is for further investigation into the scalability quantities within the data and how to track these changes through different system levels

Acoustic Waves

The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis

Emotion and Stress Recognition Related Sensors and Machine Learning Technologies

This book includes impactful chapters which present scientific concepts, frameworks, architectures and ideas on sensing technologies and machine learning techniques. These are relevant in tackling the following challenges: (i) the field readiness and use of intrusive sensor systems and devices for capturing biosignals, including EEG sensor systems, ECG sensor systems and electrodermal activity sensor systems; (ii) the quality assessment and management of sensor data; (iii) data preprocessing, noise filtering and calibration concepts for biosignals; (iv) the field readiness and use of nonintrusive sensor technologies, including visual sensors, acoustic sensors, vibration sensors and piezoelectric sensors; (v) emotion recognition using mobile phones and smartwatches; (vi) body area sensor networks for emotion and stress studies; (vii) the use of experimental datasets in emotion recognition, including dataset generation principles and concepts, quality insurance and emotion elicitation material and concepts; (viii) machine learning techniques for robust emotion recognition, including graphical models, neural network methods, deep learning methods, statistical learning and multivariate empirical mode decomposition; (ix) subject-independent emotion and stress recognition concepts and systems, including facial expression-based systems, speech-based systems, EEG-based systems, ECG-based systems, electrodermal activity-based systems, multimodal recognition systems and sensor fusion concepts and (x) emotion and stress estimation and forecasting from a nonlinear dynamical system perspective

Review of Particle Physics

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings