25 research outputs found
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Recursive Compressed Sensing
We introduce a recursive algorithm for performing compressed sensing on
streaming data. The approach consists of a) recursive encoding, where we sample
the input stream via overlapping windowing and make use of the previous
measurement in obtaining the next one, and b) recursive decoding, where the
signal estimate from the previous window is utilized in order to achieve faster
convergence in an iterative optimization scheme applied to decode the new one.
To remove estimation bias, a two-step estimation procedure is proposed
comprising support set detection and signal amplitude estimation. Estimation
accuracy is enhanced by a non-linear voting method and averaging estimates over
multiple windows. We analyze the computational complexity and estimation error,
and show that the normalized error variance asymptotically goes to zero for
sublinear sparsity. Our simulation results show speed up of an order of
magnitude over traditional CS, while obtaining significantly lower
reconstruction error under mild conditions on the signal magnitudes and the
noise level.Comment: Submitted to IEEE Transactions on Information Theor
Communication-efficient distributed optimization with adaptability to system heterogeneity
We consider the setting of agents cooperatively minimizing the sum of local
objectives plus a regularizer on a graph. This paper proposes a primal-dual
method in consideration of three distinctive attributes of real-life
multi-agent systems, namely: (i)expensive communication, (ii)lack of
synchronization, and (iii)system heterogeneity. In specific, we propose a
distributed asynchronous algorithm with minimal communication cost, in which
users commit variable amounts of local work on their respective sub-problems.
We illustrate this both theoretically and experimentally in the machine
learning setting, where the agents hold private data and use a stochastic
Newton method as the local solver. Under standard assumptions on Lipschitz
continuous gradients and strong convexity, our analysis establishes linear
convergence in expectation and characterizes the dependency of the rate on the
number of local iterations. We proceed a step further to propose a simple means
for tuning agents' hyperparameters locally, so as to adjust to heterogeneity
and accelerate the overall convergence. Last, we validate our proposed method
on a benchmark machine learning dataset to illustrate the merits in terms of
computation, communication, and run-time saving as well as adaptability to
heterogeneity.Comment: This paper is accepted by the 62nd IEEE Conference on Decision and
Control (CDC 2023
Distributed optimization on directed graphs based on inexact ADMM with partial participation
We consider the problem of minimizing the sum of cost functions pertaining to
agents over a network whose topology is captured by a directed graph (i.e.,
asymmetric communication). We cast the problem into the ADMM setting, via a
consensus constraint, for which both primal subproblems are solved inexactly.
In specific, the computationally demanding local minimization step is replaced
by a single gradient step, while the averaging step is approximated in a
distributed fashion. Furthermore, partial participation is allowed in the
implementation of the algorithm. Under standard assumptions on strong convexity
and Lipschitz continuous gradients, we establish linear convergence and
characterize the rate in terms of the connectivity of the graph and the
conditioning of the problem. Our line of analysis provides a sharper
convergence rate compared to Push-DIGing. Numerical experiments corroborate the
merits of the proposed solution in terms of superior rate as well as
computation and communication savings over baselines