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Revisiting Stochastic Realization Theory using Functional Itô Calculus 26

Revisiting Stochastic Realization Theory using Functional It...

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26th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2024

作者： Veeravalli, Tanya Raginsky, Maxim Department of Electrical and Computer Engineering The Coordinated Science Laboratory University of Illinois UrbanaIL61801 United States

This paper considers the problem of constructing finite-dimensional state space realizations for stochastic processes that can be represented as the outputs of a certain type of a causal system driven by a continuous semimartingale input process. The main assumption is that the output process is infinitely differentiable, where the notion of differentiability comes from the functional Itô calculus introduced by Dupire as a causal (nonanticipative) counterpart to Malliavin's stochastic calculus of variations. The proposed approach builds on the ideas of Hijab, who had considered the case of processes driven by a Brownian motion, and makes contact with the realization theory of deterministic systems based on formal power series and Chen-Fliess functional expansions. Copyright © 2024 The Authors.

关键词： Stochastic systems

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Search for Extraterrestrial Intelligence as One-Shot Hypothesis Testing 57

Search for Extraterrestrial Intelligence as One-Shot Hypothe...

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57th Annual Conference on Information Sciences and Systems, CISS 2023

作者： George, Ian Chen, Xinan Varshney, Lav R. Coordinated Science Laboratory Department of Electrical and Computer Engineering UrbanaIL United States

ISBN: (纸本)9781665451819

Both the search for extraterrestrial intelligence (SETI) and messaging extraterrestrial intelligence (METI) struggle with a strong indeterminacy in what data to look for and when to do so. This has led to attempts at finding both fundamental mathematical limits for SETI as well as benchmarks regarding specific signals. Due to the natural correspondence, previous information-theoretic work has been formulated in terms of communication between extraterrestrial and human civilizations. In this work, we instead formalize SETI as a detection problem, specifically (quantum) one-shot asymmetric hypothesis testing. This framework holds for all detection scenarios-in particular, it is relevant for detection of any technosignature, including quantum mechanical signals. To the best of our knowledge, this is the first work to consider the applicability of SETI for quantum signals. Using this formalism, we are able to unify the analysis of fundamental limits and benchmarking specific signals. To show a distinction between METI and SETI, we show that significantly weaker signals may be useful in detection in comparison to communication. Furthermore, the framework is computationally efficient, so it can be implemented by practicing astrobiologists. © 2023 IEEE.

关键词： Quantum optics

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Majorizing Measures, Codes, and Information

Majorizing Measures, Codes, and Information

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2023 IEEE International Symposium on Information Theory, ISIT 2023

作者： Chu, Yifeng Raginsky, Maxim University of Illinois The Department of Electrical and Computer Engineering The Coordinated Science Laboratory UrbanaIL61801 United States

ISBN: (纸本)9781665475549

The majorizing measure theorem of Fernique and Talagrand is a fundamental result in the theory of random processes. It relates the boundedness of random processes indexed by elements of a metric space to complexity measures arising from certain multiscale combinatorial structures, such as packing and covering trees. This paper builds on the ideas first outlined in a little-noticed preprint of Andreas Maurer to present an information-theoretic perspective on the majorizing measure theorem, according to which the boundedness of random processes is phrased in terms of the existence of efficient variable-length codes for the elements of the indexing metric space. © 2023 IEEE.

关键词： Random processes

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A Unified Framework for Information-Theoretic Generalization Bounds 37

A Unified Framework for Information-Theoretic Generalization...

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37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Chu, Yifeng Raginsky, Maxim Department of Electrical and Computer Engineering and Coordinated Science Laboratory University of Illinois UrbanaIL61801 United States

ISBN: (纸本)9781713899921

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of Young's inequality in Lψp Orlicz spaces. Using the decorrelation lemma in combination with other techniques, such as symmetrization, couplings, and chaining in the space of probability measures, we obtain new upper bounds on the generalization error, both in expectation and in high probability, and recover as special cases many of the existing generalization bounds, including the ones based on mutual information, conditional mutual information, stochastic chaining, and PAC-Bayes inequalities. In addition, the Fernique-Talagrand upper bound on the expected supremum of a subgaussian process emerges as a special case. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Stochastic systems

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Stability of nonlinear systems with slow and fast time variation and switching: the common equilibrium case 63

Stability of nonlinear systems with slow and fast time varia...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Liberzon, Daniel Shim, Hyungbo University of Illinois Urbana-Champaign Coordinated Science Laboratory UrbanaIL61801 United States Seoul National University Department of Electrical and Computer Engineering Korea Republic of

ISBN: (纸本)9798350316339

In this paper we consider a class of nonlinear systems with two kinds of inputs: one is slowly-varying, the other is fast-varying and periodic, and both are only piecewise continuous. Under the assumption that the origin is a common equilibrium for all values of the input signals, we provide sufficient conditions under which this equilibrium is semi-globally exponentially stable. Our approach is based on considering the (partial) average system which averages out the fast variation but retains the slow variation, and which can be used to approximate the original system in a certain sense. The stability conditions involve the existence of a suitable Lyapunov function for this average system, along with a bound on the total variation of the slowly-varying input. © 2024 IEEE.

关键词： Lyapunov functions

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Dual Ensemble Kalman Filter for Stochastic Optimal Control 63

Dual Ensemble Kalman Filter for Stochastic Optimal Control

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Joshi, Anant A. Taghvaei, Amirhossein Mehta, Prashant G. Meyn, Sean P. University of Illinois Urbana-Champaign Coordinated Science Laboratory Department of Mechanical Science and Engineering United States University of Washington Department of Aeronautics and Astronautics Seattle United States University of Florida Department of Electrical and Computer Engineering Gainesville United States

ISBN: (纸本)9798350316339

In this paper, stochastic optimal control problems in continuous time and space are considered. In recent years, such problems have received renewed attention from the lens of reinforcement learning (RL) which is also one of our motivation. The main contribution is a simulation-based algorithm - dual ensemble Kalman filter (EnKF) - to numerically approximate the solution of these problems. The paper extends our previous work where the dual EnKF was applied in deterministic settings of the problem. The theoretical results and algorithms are illustrated with numerical experiments. © 2024 IEEE.

关键词： Wiener filtering

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Convergence of Monte Carlo Exploring Starts with TD-Learning 63

Convergence of Monte Carlo Exploring Starts with TD-Learning

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Winnicki, Anna Srikant, R. University of Illinois at Urbana-Champaign Coordinated Science Laboratory Department of Electrical and Computer Engineering United States Uiuc C3.ai Digital Transformation Institute United States

ISBN: (纸本)9798350316339

The use of TD-learning has been widely employed in reinforcement learning algorithms due to its efficiency and practicality. Herein, we study the convergence of a variant of Monte Carlo Exploring Starts when operatornameTD(λ) is used in policy evaluation and policy improvement, and lookahead is used in the policy improvement step. Our results provide a threshold for the amount of lookahead that ensures convergence of Monte Carlo Exploring Starts with T D(λ) as a function of λ in[0,1]. © 2024 IEEE.

关键词： Adversarial machine learning

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How to Make Money From Fresh Data: Subscription Strategies in Age-Based Systems

How to Make Money From Fresh Data: Subscription Strategies i...

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2024 IEEE Global Communications Conference, GLOBECOM 2024

作者： Kaswan, Priyanka Bastopcu, Melih Ulukus, Sennur Etesami, S. Rasoul Basar, Tamer University of Maryland Department of Electrical and Computer Engineering College ParkMD20742 United States University of Illinois Urbana Champaign Coordinated Science Laboratory UrbanaIL61801 United States

ISBN: (纸本)9798350351255

We consider a communication system consisting of a server that tracks and publishes updates about a time-varying data source or event, and a gossip network of users interested in closely tracking the event. The timeliness of the information is measured through the version age of information. The users wish to have their expected version ages remain below a threshold, and have the option to either rely on gossip from their neighbors or subscribe to the server directly to follow updates about the event if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing the number of subscribers and reducing costs associated with the frequent sampling of the event. We model the problem setup as a Stackelberg game between the server and the users, where the server commits to a frequency of sampling the event, and the users make decisions on whether to subscribe or not. As an initial work, we focus on directed networks with unidirectional flow of information and obtain the optimal equilibrium strategies for all the players. We provide simulation results to confirm the theoretical findings and provide additional insights. © 2024 IEEE.

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Global Convergence of Direct Policy Search for State-Feedback H1 Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential 36

Global Convergence of Direct Policy Search for State-Feedbac...

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36th Conference on Neural Information Processing Systems, NeurIPS 2022

作者： Guo, Xingang Hu, Bin Department of Electrical and Computer Engineering Coordinated Science Laboratory University of Illinois at Urbana-Champaign United States

ISBN: (纸本)9781713871088

Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the theoretical properties of direct policy search on nonsmooth robust control synthesis have not been fully understood. The optimal H1 control framework aims at designing a policy to minimize the closed-loop H1 norm, and is arguably the most fundamental robust control paradigm. In this work, we show that direct policy search is guaranteed to find the global solution of the robust H1 state-feedback control design problem. Notice that policy search for optimal H1 control leads to a constrained nonconvex nonsmooth optimization problem, where the nonconvex feasible set consists of all the policies stabilizing the closed-loop dynamics. We show that for this nonsmooth optimization problem, all Clarke stationary points are global minimum. Next, we identify the coerciveness of the closed-loop H1 objective function, and prove that all the sublevel sets of the resultant policy search problem are compact. Based on these properties, we show that Goldstein* subgradient method and its implementable variants can be guaranteed to stay in the nonconvex feasible set and eventually find the global optimal solution of the H1 state-feedback synthesis problem. Our work builds a new connection between nonconvex nonsmooth optimization theory and robust control, leading to an interesting global convergence result for direct policy search on optimal H1 synthesis. © 2022 Neural information processing systems foundation. All rights reserved.

关键词： Robust control

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A Multi-Sequence Prophet Inequality Under Observation Constraints

A Multi-Sequence Prophet Inequality Under Observation Constr...

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IEEE International Symposium on Information Theory

作者： Aristomenis Tsopelakos Olgica Milenkovic Department of Electrical and Computer Engineering Coordinated Science Laboratory University of Illinois at Urbana-Champaign

ISBN: (数字)9798350382846

ISBN: (纸本)9798350382853

In our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each sequence in order to maximize a reward equal to the expected value of the sum of the selections from all sequences. The decision on which element to pick is irrevocable, i.e., rejected observations cannot be revisited. Furthermore, the procedure terminates upon having a single selection from each sequence. Our observation constraint is that we cannot observe the current realization of all sequences at each time instant. Instead, we can observe only a smaller, yet arbitrary, subset of them. Thus, together with a stopping rule that determines whether we choose or reject the sample, the solution requires a sampling rule that determines which sequence to observe at each instant. The problem can be solved via dynamic programming, but with an exponential complexity in the length of the sequences. In order to make the solution computationally tractable, we introduce a decoupling approach and determine each stopping time using either a single-sequence dynamic programming, or a Prophet Inequality inspired threshold method, with polynomial complexity in the length of the sequences. We prove that the decoupling approach guarantees at least 0.745 of the optimal expected reward of the joint problem. In addition, we describe how to efficiently compute the optimal number of samples for each sequence, and its' dependence on the variances.

关键词： Polynomials Finite element analysis Dynamic programming Complexity theory Random variables Information theory

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