In high-efficiency 12-to-1-1.8-V applications, the small duty ratio (D ≈ 0.1) and high voltage stress on power switches of the conventional buck converter bring significant efficiency penalty. This article proposes a...
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Minimax problems have attracted much attention due to various applications in constrained optimization problems and zero-sum games. Identifying saddle points within these problems is crucial, and saddle flow dynamics ...
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ISBN:
(数字)9798350316339
ISBN:
(纸本)9798350316346
Minimax problems have attracted much attention due to various applications in constrained optimization problems and zero-sum games. Identifying saddle points within these problems is crucial, and saddle flow dynamics offer a straightforward yet useful approach. This study focuses on a class of bilinearly coupled minimax problems with strongly convex-linear objective functions. We design an accelerated algorithm based on saddle flow dynamics, achieving a convergence rate beyond the stereotype limit (the strong convexity constant). The algorithm is derived from a sequential two-step transformation of a given objective function. First, a change of variables is applied to render the objective function better-conditioned, introducing strong concavity (from linearity) while preserving strong convexity. Second, proximal regularization, when staggered with the first step, further enhances the strong convexity of the objective function by shifting some of the obtained strong concavity. After these transformations, saddle flow dynamics based on the new objective function can be tuned for accelerated exponential convergence. Besides, such an approach can be extended to weakly convex-weakly concave functions and still guarantees exponential convergence to one stationary point. The theory is verified by a numerical test on an affine equality-constrained convex optimization problem.
As distributed learning applications such as Federated Learning, the Internet of Things (IoT), and Edge Computing grow, it is critical to address the shortcomings of such technologies from a theoretical perspective. A...
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Low-rank structures have been observed in several recent empirical studies in many machine and deep learning problems, where the loss function demonstrates significant variation only in a lower dimensional subspace. W...
Low-rank structures have been observed in several recent empirical studies in many machine and deep learning problems, where the loss function demonstrates significant variation only in a lower dimensional subspace. While traditional gradient-based optimization algorithms are computationally costly for high-dimensional parameter spaces, such low-rank structures provide an opportunity to mitigate this cost. In this paper, we aim to leverage low-rank structures to alleviate the computational cost of first-order methods and study Adaptive Low-Rank Gradient Descent (AdaLRGD). The main idea of this method is to begin the optimization procedure in a very small subspace and gradually and adaptively augment it by including more directions. We show that for smooth and strongly convex objectives and any target accuracy $\epsilon$ , AdaLRGD's complexity is $\mathcal{O}(r\ln(r/\epsilon))$ for some rank $r$ no more than dimension $d$ . This significantly improves upon gradient descent's complexity of $\mathcal{O}(d\ln(1/\epsilon))$ when $r\ll d$ . We also propose a practical implementation of AdaLRGD and demonstrate its ability to leverage existing low-rank structures in data.
Integrated silicon photonics is recognized as a potential candidate to achieve on-chip optical interconnects. Compared with other optical microcavities, photonic crystal nanobeam cavity (PCNC) has emerged as a promisi...
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We consider the problem of dynamically decoding human intention via electroencephalography (EEG). We present two hierarchical frameworks to approach this problem. One framework processes the activities recorded in the...
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The temporal degree of freedom in photonics has been a recent research hotspot due to its analogy with spatial axes, causality, and open-system characteristics. In particular, the temporal analogues of photonic crysta...
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Our focus in this investigation lies in developing a noise model for a quantum thermal transistor model inspired by its electronic counterpart, with the primary aim of establishing a platform for constructing analogou...
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Our focus in this investigation lies in developing a noise model for a quantum thermal transistor model inspired by its electronic counterpart, with the primary aim of establishing a platform for constructing analogous models. Previous studies on coupled two-level systems-based thermal transistors were focused on their average energy exchange. In this paper, we shift our attention to exploring the stochastic behavior of such thermal transistors due to the disturbances caused to their environment, such as continuous measurements. In the literature, the master equation for the transistor model is derived using the reduced dynamics method. This way, it masks the study of the stochastic nature of the energy flows in the system due to disturbances to the environment. In this paper, we describe a quantum trajectory under measurement theory whose ensemble average unravels the master equation for a quantum thermal transistor. This allows us to analyze the fluctuations and noise levels in the transistor model with greater detail. Then, we produce a numerical solution for the transistor dynamics based on Euler-Maruyama approximation. This helps to establish a model for the thermal transistor, drawing parallels to the small-signal/noise model in an electronic transistor. We define two parameters, thermal conductance and output thermal resistance, to describe the small signal-like model for the thermal transistor. Through these investigations, we seek to gain insights that can help design advanced heat management devices at the quantum level.
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