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ONLINE REGENERATIVE LEARNING

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arXiv 2022年

作者： Shen, Owen Department of Mathematics Stanford University United States

We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs. © 2022, CC BY.

关键词： adaptive algorithms

TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ansätze

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arXiv 2022年

作者： Anastasiou, Panagiotis G. Chen, Yanzhu Mayhall, Nicholas J. Barnes, Edwin Economou, Sophia E. Department of Physics Virginia Tech BlacksburgVA24061 United States Department of Chemistry Virginia Tech BlacksburgVA24061 United States

adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ansätze a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

adaptive LOOCV-based kernel methods for solving time-dependent BVPs

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arXiv 2022年

作者： Cavoretto, Roberto Department of Mathematics "Giuseppe Peano" University of Torino via Carlo Alberto 10 Torino10123 Italy The INdAM Research Group GNCS

In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time derivatives, dealing with each separately. This adaptive algorithm is based on a leave-one-out cross validation (LOOCV) technique, which is employed as an error indicator. By this scheme, we can first detect the domain areas where the error is estimated to be too large – generally due to steep variations or quick changes in the solution – and then accordingly enhance the numerical solution by applying a two-point refinement strategy. Numerical experiments show the efficacy and performance of our adaptive refinement method. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

Approximate Function Evaluation via Multi-Armed Bandits

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arXiv 2022年

作者： Baharav, Tavor Z. Cheng, Gary Pilanci, Mert Tse, David Stanford University United States

We study the problem of estimating the value of a known smooth function f at an unknown point µ ∈ Rn, where each component µi can be sampled via a noisy oracle. Sampling more frequently components of µ corresponding to directions of the function with larger directional derivatives is more sample-efficient. However, as µ is unknown, the optimal sampling frequencies are also unknown. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least 1−δ returns an Ε accurate estimate of f(µ). We generalize our algorithm to adapt to heteroskedastic noise, and prove asymptotic optimality when f is linear. We corroborate our theoretical results with numerical experiments, showing the dramatic gains afforded by adaptivity. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

Contextual Bandits with Smooth Regret: Efficient Learning in Continuous Action Spaces

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arXiv 2022年

作者： Zhu, Yinglun Mineiro, Paul University of Wisconsin-Madison United States Microsoft Research Nyc United States

Designing efficient general-purpose contextual bandit algorithms that work with large-or even continuous-action spaces would facilitate application to important scenarios such as information retrieval, recommendation systems, and continuous control. While obtaining standard regret guarantees can be hopeless, alternative regret notions have been proposed to tackle the large action setting. We propose a smooth regret notion for contextual bandits, which dominates previously proposed alternatives. We design a statistically and computationally efficient algorithm-for the proposed smooth regret-that works with general function approximation under standard supervised oracles. We also present an adaptive algorithm that automatically adapts to any smoothness level. Our algorithms can be used to recover the previous minimax/Pareto optimal guarantees under the standard regret, e.g., in bandit problems with multiple best arms and Lipschitz/Hölder bandits. We conduct large-scale empirical evaluations demonstrating the efficacy of our proposed algorithms. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems

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arXiv 2022年

作者： Müller, Fabio Christiansen, Henrik Schnabel, Stefan Janke, Wolfhard Institut für Theoretische Physik Universität Leipzig IPF 231101 Leipzig04081 Germany

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity O(N log N), where N is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than 104. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations

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arXiv 2022年

作者： Kopteva, Natalia Stynes, Martin Department of Mathematics and Statistics University of Limerick LimerickV94 T9PX Ireland Applied and Computational Mathematics Division Beijing Computational Science Research Center Beijing100193 China

An initial-boundary value problem of subdiffusion type is considered;the temporal component of the differential operator has the form (Equation presented), where the qi are continuous functions, each (Equation presented) is a Caputo derivative, and the αi lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in L2(Ω) and L∞(Ω), where the spatial domain Ω lies in Rd with d ∈ {1, 2, 3}. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm. © 2022, CC BY.

关键词： adaptive algorithms

Sampling Rate Offset Estimation and Compensation for Distributed adaptive Node-Specific Signal Estimation in Wireless Acoustic Sensor Networks

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arXiv 2022年

作者： Didier, Paul van Waterschoot, Toon Doclo, Simon Moonen, Marc KU Leuven Leuven3001 Belgium Signal Processing Group Department of Medical Physics and Acoustics and Cluster of Excellence Hearing4all University of Oldenburg Oldenburg Germany

Sampling rate offsets (SROs) between devices in a heterogeneous wireless acoustic sensor network (WASN) can hinder the ability of distributed adaptive algorithms to perform as intended when they rely on coherent signal processing. In this paper, we present an SRO estimation and compensation method to allow the deployment of the distributed adaptive node-specific signal estimation (DANSE) algorithm in WASNs composed of asynchronous devices. The signals available at each node are first utilised in a coherence-drift-based method to blindly estimate SROs which are then compensated for via phase shifts in the frequency domain. A modification of the weighted overlap-add (WOLA) implementation of DANSE is introduced to account for SRO-induced full-sample drifts, permitting per-sample signal transmission via an approximation of the WOLA process as a time-domain convolution. The performance of the proposed algorithm is evaluated in the context of distributed noise reduction for the estimation of a target speech signal in an asynchronous WASN. © 2022, CC BY.

关键词： adaptive algorithms

Research on adaptive Information Fusion Algorithm Based on Multi-sensor

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Research on Adaptive Information Fusion Algorithm Based on M...

Mobile Networks and Wireless Communications (ICMNWC), IEEE International Conference on

作者： Hongbin Tang Units Command Department Officers College of Chinese People’s Armed Police Force Chengdu China

ISBN: (纸本)9781665491129

I proposed a multi-sensor adaptive state fusion technology that can improve the discovery capability and continuous observation capability of sensor networks. Focusing on the complementarity between the algorithms of adaptive state fusion technology to achieve some kind of optimization. The algorithm can automatically select the most effective algorithm according to the characteristics of the information source and the target, with transparency and openness, is a multi-level multi-model adaptive algorithm. Experiments confirm that: the proposed algorithm will bring greater benefits for command information system information fusion to improve accuracy, anti-stealth, anti-low-altitude intrusion, anti-loss target, etc., besides, it can overcome the shortcomings of sensor performance instability.

关键词： Wireless communication adaptive systems adaptive algorithms Focusing Optimization Information systems