1,007 research outputs found
Stochastic Sensor Scheduling via Distributed Convex Optimization
In this paper, we propose a stochastic scheduling strategy for estimating the
states of N discrete-time linear time invariant (DTLTI) dynamic systems, where
only one system can be observed by the sensor at each time instant due to
practical resource constraints. The idea of our stochastic strategy is that a
system is randomly selected for observation at each time instant according to a
pre-assigned probability distribution. We aim to find the optimal pre-assigned
probability in order to minimize the maximal estimate error covariance among
dynamic systems. We first show that under mild conditions, the stochastic
scheduling problem gives an upper bound on the performance of the optimal
sensor selection problem, notoriously difficult to solve. We next relax the
stochastic scheduling problem into a tractable suboptimal quasi-convex form. We
then show that the new problem can be decomposed into coupled small convex
optimization problems, and it can be solved in a distributed fashion. Finally,
for scheduling implementation, we propose centralized and distributed
deterministic scheduling strategies based on the optimal stochastic solution
and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last
versio
Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective
Distributed algorithms have been playing an increasingly important role in
many applications such as machine learning, signal processing, and control.
Significant research efforts have been devoted to developing and analyzing new
algorithms for various applications. In this work, we provide a fresh
perspective to understand, analyze, and design distributed optimization
algorithms. Through the lens of multi-rate feedback control, we show that a
wide class of distributed algorithms, including popular decentralized/federated
schemes, can be viewed as discretizing a certain continuous-time feedback
control system, possibly with multiple sampling rates, such as decentralized
gradient descent, gradient tracking, and federated averaging. This key
observation not only allows us to develop a generic framework to analyze the
convergence of the entire algorithm class. More importantly, it also leads to
an interesting way of designing new distributed algorithms. We develop the
theory behind our framework and provide examples to highlight how the framework
can be used in practice
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