Linear Regression over Networks with Communication Guarantees

A key functionality of emerging connected autonomous systems such as smart cities, smart transportation systems, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations. This is increasingly attracting attention under the terms of distributed learning and federated learning. However, in connected autonomous systems, data transfer takes place over communication networks with often limited resources. This paper examines algorithms for communication-efficient learning for linear regression tasks by exploiting the informativeness of the data. The developed algorithms enable a tradeoff between communication and learning with theoretical performance guarantees and efficient practical implementations.Comment: Accepted at 3rd Annual Learning for Dynamics & Control Conference (L4DC) 2021. arXiv admin note: substantial text overlap with arXiv:2101.1000

Resource-Aware Design Of Wireless Control Systems

This work is motivated by modern monitoring and control infrastructures appearing in smart homes, urban environments, and industrial plants. These systems are characterized by multiple sensor and actuator devices at different physical locations, communicating wirelessly with each other. Desired monitoring and control performance requires efficient wireless communication, as the more information the sensors convey the more precise actuation becomes. However wireless communication is constrained by the inherent uncertainty of the wireless medium as well as resource limitations at the devices, e.g., limited power resources. The increased number of wireless devices in such environments further necessitates the management of the shared wireless spectrum with direct account of control performance. To address these challenges, the goal of this work is to provide control-aware and resource-aware communication policies. This is first examined in the fundamental problem of allocating transmit power resources for wireless closed loop control. Opportunistic online adaptation of power to plant and wireless channel conditions is shown to be essential in achieving the optimal tradeoff between control performance and power utilization. Optimal structural properties of channel access mechanisms are also considered for the problem of guaranteeing multiple control performance requirements over a shared wireless medium. This includes scheduling mechanisms implemented by central authorities, as well as decentralized mechanisms implemented independently by the wireless devices with emerging wireless interferences. Again the mechanisms exhibit an opportunistic adaptation to varying wireless channel conditions, especially designed to explore the tradeoffs between different communication links and meet control performance requirements. The structural characterization is augmented with tractable optimization algorithms to compute these channel access mechanisms. Finally, as control is naturally a dynamic task that requires a long term planning, appropriate dynamic algorithms adapting to the varying control system states are examined. Besides adapting dynamically, the proposed algorithms provide guarantees about long term control performance and resource utilization by construction

Resilient Monotone Submodular Function Maximization

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard, and cannot be solved exactly in polynomial time, even though they often involve objective functions that are monotone and submodular. Notwithstanding, in this paper we provide the first scalable, curvature-dependent algorithm for their approximate solution, that is valid for any number of attacks or failures, and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient maximization problems, yet its effect on resilient maximization had hitherto been unknown. We complement our theoretical analyses with supporting empirical evaluations.Comment: Improved suboptimality guarantees on proposed algorithm and corrected typo on Algorithm 1's statemen

Statistical Learning for Analysis of Networked Control Systems over Unknown Channels

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model they are focused on stability analysis and appropriate controller designs. However the availability of such wireless channel modeling is fundamentally challenging in practice as channels are typically unknown a priori and only available through data samples. In this work we aim to develop algorithms that rely on channel sample data to determine the stability and performance of networked control tasks. In this regard our work is the first to characterize the amount of channel modeling that is required to answer such a question. Specifically we examine how many channel data samples are required in order to answer with high confidence whether a given networked control system is stable or not. This analysis is based on the notion of sample complexity from the learning literature and is facilitated by concentration inequalities. Moreover we establish a direct relation between the sample complexity and the networked system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system. This illustrates that it becomes impractical to verify stability under a large range of plant and channel configurations. We validate our theoretical results in numerical simulations

Homomorphically encrypted gradient descent algorithms for quadratic programming

In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption setup. The limit on the multiplication depth of homomorphic encryption circuits is a major challenge for iterative procedures such as gradient descent algorithms. Our analysis not only quantifies these limitations on prototype examples, thus serving as a benchmark for future investigations, but also highlights additional trade-offs like the ones pertaining the choice of gradient descent or accelerated gradient descent methods, opening the road for the use of homomorphic encryption techniques in iterative procedures widely used in optimization based control. In addition, we argue that, among the available homomorphic encryption schemes, the one adopted in this work, namely CKKS, is the only suitable scheme for implementing gradient descent algorithms. The choice of the appropriate step size is crucial to the convergence of the procedure. The paper shows firsthand the feasibility of homomorphically encrypted gradient descent algorithms