arXiv subjects

Atiye Alaeddini

Publications and source records attributed to Atiye Alaeddini.

8 recordsLinked to original sources

arXiv2020

Optimal Immunization Policy Using Dynamic Programming

Decisions in public health are almost always made in the context of uncertainty. Policy makers are responsible for making important decisions, faced with the daunting task of choosing from amongst many possible options. This task is called planning under uncertainty, and is particularly acute when addressing complex systems, such as issues of global health and development. Uncertainty leads to cautious or incorrect decisions that cost time, money, and human life. It is with this understanding that we pursue greater clarity on, and methods to address optimal policy making in health. Decision making under uncertainty is a challenging task, and all too often this uncertainty is averaged away to simplify results for policy makers. Our goal in this work is to implement dynamic programming which provides basis for compiling planning results into reactive strategies. We present here a description of an AI-based method and illustrate how this method can improve our ability to find an optimal vaccination strategy. We model the problem as a partially observable Markov decision process, POMDP and show how a re-active policy can be computed using dynamic programming. In this paper, we developed a framework for optimal health policy design in an uncertain dynamic setting. We apply a stochastic dynamic programming approach to identify the optimal time to change the health intervention policy and the value of decision relevant information for improving the impact of the policy.

cs.AI↗

arXiv2019

Augmented State Feedback for Improving Observability of Linear Systems with Nonlinear Measurements

This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based on the assumption that the state is available for measurement. In this paper, we focus on finding a feedback control that avoids state trajectories with undesirable observability properties. In particular, we introduce an optimal control problem that specifically considers an index of observability in the control synthesis. The resulting cost functional is a combination of LQR-like quadratic terms and an index of observability. The main contribution of the paper is presenting a control synthesis procedure that on one hand, provides closed loop asymptotic stability, and addresses the observability of the system--as a transient performance criteria--on the other.

eess.SY↗

arXiv2018

Linear Model Regression on Time-series Data: Non-asymptotic Error Bounds and Applications

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series had been generated, regression on the system model has been particularly popular. In the linear case, the resulting least squares setup for model regression, not only provides a computationally viable method to fit a model to the data, but also provides useful insights into the modal properties of the underlying dynamics. Although probabilistic estimates for this model regression have been reported, deterministic error bounds have not been examined in the literature, particularly as they pertain to the properties of the underlying system. In this paper, we provide deterministic non-asymptotic error bounds for fitting a linear model to the observed time-series data, with a particular attention to the role of symmetry and eigenvalue multiplicity in the underlying system matrix.

math.OC↗

arXiv2018

Parallel Simultaneous Perturbation Optimization

Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function. The objective function, however, is time-intensive to evaluate, and cannot be directly measured. Instead, the stochastic nature of the model means that individual realizations are corrupted by noise. More formally, we consider the problem of optimizing the expected value of an expensive black-box function with continuously-differentiable mean, from which observations are corrupted by Gaussian noise. We present Parallel Simultaneous Perturbation Optimization (PSPO), which extends a well-known stochastic optimization algorithm, simultaneous perturbation stochastic approximation, in several important ways. Our modifications allow the algorithm to fully take advantage of parallel computing resources, like high-performance cloud computing. The resulting PSPO algorithm takes fewer time-consuming iterations to converge, automatically chooses the step size, and can vary the error tolerance by step. Theoretical results are supported by a numerical example. To demonstrate the performance of the algorithm, we implemented the algorithm to maximize the pseudo-likelihood of a stochastic epidemiological model to data of a measles outbreak.

math.OC↗

arXiv2017

Application of a Second-order Stochastic Optimization Algorithm for Fitting Stochastic Epidemiological Models

Epidemiological models have tremendous potential to forecast disease burden and quantify the impact of interventions. Detailed models are increasingly popular, however these models tend to be stochastic and very costly to evaluate. Fortunately, readily available high-performance cloud computing now means that these models can be evaluated many times in parallel. Here, we briefly describe PSPO, an extension to Spall's second-order stochastic optimization algorithm, Simultaneous Perturbation Stochastic Approximation (SPSA), that takes full advantage of parallel computing environments. The main focus of this work is on the use of PSPO to maximize the pseudo-likelihood of a stochastic epidemiological model to data from a 1861 measles outbreak in Hagelloch, Germany. Results indicate that PSPO far outperforms gradient ascent and SPSA on this challenging likelihood maximization problem.

q-bio.QM↗

arXiv2017

Adaptive Communication Networks with Privacy Guarantees

Utilizing the concept of observability, in conjunction with tools from graph theory and optimization, this paper develops an algorithm for network synthesis with privacy guarantees. In particular, we propose an algorithm for the selection of optimal weights for the communication graph in order to maximize the privacy of nodes in the network, from a control theoretic perspective. In this direction, we propose an observability-based design of the communication topology that improves the privacy of the network in presence of an intruder. The resulting adaptive network responds to the intrusion by changing the topology of the network-in an online manner- in order to reduce the information exposed to the intruder.

eess.SY↗

arXiv2016

Optimal Control with Limited Sensing via Empirical Gramians and Piecewise Linear Feedback

This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to ensuring stability of the closed loop system. A recursive algorithm is then proposed to obtain an optimal state feedback controller to maximize the resulting non-quadratic cost functional. The main contribution of the paper is presenting a control synthesis procedure that provides closed loop asymptotic stability, on one hand, and empirical observability of the system, as a transient performance criteria, on the other.

eess.SY↗

arXiv2016

Optimal Disease Outbreak Detection in a Community Using Network Observability

Given a network, we would like to determine which subset of nodes should be measured by limited sensing facilities to maximize information about the entire network. The optimal choice corresponds to the configuration that returns the highest value of a measure of observability of the system. Here, the determinant of the inverse of the observability Gramian is used to evaluate the degree of observability. Additionally, the effects of changes in the topology of the corresponding graph of a network on the observability of the network are investigated. The theory is illustrated on the problem of detection of an epidemic disease in a community. The purpose here is to find the smallest number of people who must be examined to predict the number of infected people in an arbitrary community. Results are demonstrated in simulation.

q-bio.QM↗