Stochastic maximum principle (SMP) specifies a necessary condition for the solution of a stochastic optimal control problem. The condition involves a coupled system of forward and backward stochastic differential equa...
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ISBN:
(数字)9798350316339
ISBN:
(纸本)9798350316346
Stochastic maximum principle (SMP) specifies a necessary condition for the solution of a stochastic optimal control problem. The condition involves a coupled system of forward and backward stochastic differential equations (FBSDE) for the state and the adjoint processes. Numerical solution of the FBSDE is challenging because the boundary condition of the adjoint process is specified at the terminal time, while the solution should be adaptable to the forward in time filtration of a Wiener process. In this paper, a “time-reversal” of the FBSDE system is proposed that involves integration with respect to a backward in time Wiener process. The time-reversal is used to propose an iterative Monte-Carlo procedure to solves the FBSDE system and its time-reversal simultaneously. The procedure involves approximating the Föllmer’s drift and solving a regression problem between the state and its adjoint at each time. The procedure is illustrated for the linear quadratic (LQ) optimal control problem with a numerical example.
In this note we provide and analyze a simple method that given an n × d matrix, outputs approximate p-Lewis weights, a natural measure of the importance of the rows with respect to the p norm, for p ≥ 2. More pr...
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Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances ...
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Bosonic quantum computing, based on the infinite-dimensional qumodes, has shown promise for various practical applications that are classically hard. However, the lack of compiler optimizations has hindered its full p...
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ISBN:
(数字)9798350326581
ISBN:
(纸本)9798350326598
Bosonic quantum computing, based on the infinite-dimensional qumodes, has shown promise for various practical applications that are classically hard. However, the lack of compiler optimizations has hindered its full potential. This paper introduces Bosehedral, an efficient compiler optimization framework for (Gaussian) Boson sampling on Bosonic quantum hardware. Bosehedral overcomes the challenge of handling infinite-dimensional qumode gate matrices by performing all its program analysis and optimizations at a higher algorithmic level, using a compact unitary matrix representation. It optimizes qumode gate decomposition and logical-to-physical qumode mapping, and introduces a tunable probabilistic gate dropout method. Overall, Bosehedral significantly improves the performance by accurately approximating the original program with much fewer gates. Our evaluation shows that Bosehedral can largely reduce the program size but still maintain a high approximation fidelity, which can translate to significant end-to-end application performance improvement.
One of the key challenges when designing a ten (10) hours educational short course, entitled “A Hands-on Approach for Implementing Stochastic Optimization algorithms from Scratch”, which was accepted for inclusion a...
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ISBN:
(数字)9789464593617
ISBN:
(纸本)9798331519773
One of the key challenges when designing a ten (10) hours educational short course, entitled “A Hands-on Approach for Implementing Stochastic Optimization algorithms from Scratch”, which was accepted for inclusion at ICASSP'23, was related to addressing “how to introduce the Stochastic Gradient Descent (SGD) algorithm and variants in a consistent, accessible fashion”? From a simplistic perspective, the SGD algorithm is nothing else than the classical gradient descent (GD) algorithm along with a (very) noisy gradient. Nonetheless, arguably, SGD's most influential variants, e.g. AdaGrad, RMSprop and Adam, nor more recent ones (LookAhead, E-Adam, MadGrad, among several others) may not be explained in such superficial terms. Moreover, such variants are usually given as as black-boxes by most deep-learning (DL) libraries (e.g. TensorFlow, PyTorch, etc.). In this article, based on the experience of the aforementioned short-course, I propose to link the SGD algorithm and variants via an “evolutionary path”, in which each SGD variant may be understood as a set of add-on features over the vanilla SGD, resulting in a generalized algorithm along with a “family tree” graph which are both intuitive and useful when implementing a given SGD variant.
Multiplication plays a pivotal role in diverse fields, including digital signal processing, scientific computing, machine learning, cryptography, computer graphics, control systems, finance, and embedded systems. Opti...
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ISBN:
(数字)9798331529352
ISBN:
(纸本)9798331529390
Multiplication plays a pivotal role in diverse fields, including digital signal processing, scientific computing, machine learning, cryptography, computer graphics, control systems, finance, and embedded systems. Optimizing multiplication operations can significantly enhance performance and efficiency across these domains. This paper presents a VLSI architecture for a hardware multiplier module that utilizes the Dadda algorithm in conjunction with the Divide and Conquer strategy, incorporating Approximate Adders. These adders strike a balance between accuracy and resource efficiency, leading to reductions in power consumption and silicon area. Approximate Adders are essential in optimizing power, area, speed, and heat dissipation in digital systems, particularly in applications where absolute precision is not important. This work underscores the potential of integrating approximate computing with efficient multiplication techniques to advance digital circuit design. The architecture is implemented in Verilog, and its functionality is validated using Vivado 2023.2 and Cadence tools.
This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assu...
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The research offers a unique coevolution-based many-objective optimization (MaOO) approach to benefit from the underlying parallelism of the evolutionary process. The proposed MaOO handles individual objectives in par...
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ISBN:
(数字)9798350373783
ISBN:
(纸本)9798350373790
The research offers a unique coevolution-based many-objective optimization (MaOO) approach to benefit from the underlying parallelism of the evolutionary process. The proposed MaOO handles individual objectives in parallel using artificial bee colony (ABC) algorithm. After achieving convergence, a group of good-quality solutions is carefully chosen from each ABC population, dealing with a specific objective. Next, the groups are combined to form a union set. Finally, a fuzzy membership-induced rank measure is developed to discover the top-ranked equally good members of the union set, showing the approximate Pareto optimal solutions to the given MaOO problem. The proposed MaOO algorithm, referred to as fuzzy-bee colony (FBC) is compared with three state-of-the-art techniques. Experiments undertaken reveal that FBC outperforms its contenders with respect to the performance metrics.
The theory of Kazantzis-Kravaris/Luenberger (KKL) observer design introduces a methodology that uses a nonlinear transformation map and its left inverse to estimate the state of a nonlinear system through the introduc...
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ISBN:
(数字)9783907144107
ISBN:
(纸本)9798331540920
The theory of Kazantzis-Kravaris/Luenberger (KKL) observer design introduces a methodology that uses a nonlinear transformation map and its left inverse to estimate the state of a nonlinear system through the introduction of a linear observer state space. Data-driven approaches using artificial neural networks have demonstrated the ability to accurately approximate these transformation maps. This paper presents a novel approach to observer design for nonlinear dynamical systems through meta-learning, a concept in machine learning that aims to optimize learning models for fast adaptation to a distribution of tasks through an improved focus on the intrinsic properties of the underlying learning problem. We introduce a framework that leverages information from measurements of the system output to design a learning-based KKL observer capable of online adaptation to a variety of system conditions and attributes. To validate the effectiveness of our approach, we present comprehensive experimental results for the estimation of nonlinear system states with varying initial conditions and internal parameters, demonstrating high accuracy, generalization capability, and robustness against noise.
This paper examines the construction of rth-order truncated balanced realizations via tangential interpolation at r specified interpolation points. It is demonstrated that when the truncated Hankel singular values are...
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This paper examines the construction of rth-order truncated balanced realizations via tangential interpolation at r specified interpolation points. It is demonstrated that when the truncated Hankel singular values are negligible—that is, when the discarded states are nearly uncontrollable and unobservable—balanced truncation simplifies to a bi-tangential Hermite interpolation problem at r interpolation points. In such cases, the resulting truncated balanced realization is nearly H2-optimal and thus interpolates the original model at the mirror images of its poles along its residual directions. Additionally, it is shown that existing low-rank balanced truncation algorithms implicitly perform block interpolation to construct a surrogate for the original system, which is subsequently reduced to obtain an approximate truncated balanced realization. Like standard H2-optimal model reduction, where the interpolation points and tangential directions that yield a local optimum are not known, in balanced truncation as well, the interpolation points and tangential directions required to produce a truncated balanced realization remain unknown. To address this, we propose an iterative tangential interpolation-based algorithm for balanced truncation. This algorithm starts with an initial guess of an rth-order truncated balanced realization and iteratively refines the interpolation data by performing tangential interpolation at the mirror images of the poles of the current low-rank truncated balanced realization in the residual directions. In each iteration, the rank of the approximated Gramians is incremented by r, followed by low-rank balanced truncation to generate updated interpolation data for the subsequent step. As the Gramian rank increases and the approximation improves, the relative changes in both the interpolation data and approximate Hankel singular values stagnate. Upon convergence, the algorithm yields a low-rank truncated balanced realization that accurately preser
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