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On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regression. 利用局部多项式回归加速基于梯度的经验风险最小化。

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2022-07-01 Epub Date: 2022-08-05 DOI: 10.23919/ecc55457.2022.9838261

Ekaterina Trimbach, Edward Duc Hien Nguyen, César A Uribe

We study the acceleration of the Local Polynomial Interpolation-based Gradient Descent method (LPI-GD) recently proposed for the approximate solution of empirical risk minimization problems (ERM). We focus on loss functions that are strongly convex and smooth with condition number σ. We additionally assume the loss function is η-Hölder continuous with respect to the data. The oracle complexity of LPI-GD is $\tilde{O} (σ m^{d} log (1 / ε))$ for a desired accuracy ε, where d is the dimension of the parameter space, and m is the cardinality of an approximation grid. The factor m ^d can be shown to scale as O((1/ε) ^d/2η ). LPI-GD has been shown to have better oracle complexity than gradient descent (GD) and stochastic gradient descent (SGD) for certain parameter regimes. We propose two accelerated methods for the ERM problem based on LPI-GD and show an oracle complexity of $\tilde{O} (\sqrt{σ} m^{d} log (1 / ε))$ . Moreover, we provide the first empirical study on local polynomial interpolation-based gradient methods and corroborate that LPI-GD has better performance than GD and SGD in some scenarios, and the proposed methods achieve acceleration.

我们研究了最近为近似解决经验风险最小化问题（ERM）而提出的基于局部多项式插值的梯度下降法（LPI-GD）的加速问题。我们将重点放在条件数为 σ 的强凸平滑损失函数上。此外，我们还假设损失函数相对于数据是 η-Hölder 连续的。对于期望精度 ε，LPI-GD 的甲骨文复杂度为 O ˜ ( σ m d log ( 1 / ε ) ) ，其中 d 是参数空间的维数，m 是近似网格的最小值。m d 因子可按 O((1/ε) d/2η ) 的比例缩放。在某些参数条件下，LPI-GD 比梯度下降法（GD）和随机梯度下降法（SGD）具有更好的算法复杂性。我们提出了两种基于 LPI-GD 的 ERM 问题加速方法，结果表明其算法复杂度为 O ˜ ( σ m d log ( 1 / ε ) ) 。此外，我们首次对基于局部多项式插值的梯度方法进行了实证研究，证实了 LPI-GD 在某些情况下比 GD 和 SGD 具有更好的性能，而且所提出的方法实现了加速。

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引用次数: 0

Model-Based Estimation of Wheel Slip in Locomotives 基于模型的机车轮滑估计

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2022-01-01 DOI: 10.23919/ECC55457.2022.9838075

C. V. V. D. Merwe, J. D. L. Roux

引用次数: 0

Computationally efficient application of Sequential Monte Carlo expectation maximization to confined single particle tracking. 序贯蒙特卡罗期望最大化在受限单粒子跟踪中的高效应用。

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2021-06-01 DOI: 10.23919/ecc54610.2021.9655194

Ye Lin, Sean B Andersson

Single Particle Tracking (SPT) plays a crucial role in biophysics through its ability to reveal dynamic mechanisms and physical properties of biological macromolecules moving inside living cells. Such molecules are often subject to confinement and important information can be revealed by understanding the mobility of the molecules and the size of the domain they are restricted to. In previous work, we introduced a method known as Sequential Monte Carlo-Expectation Maximization (SMC-EM) to simultaneously estimate particle trajectories and model parameters. In this paper, we describe three modifications to SMC-EM aimed at improving its computationally efficiency and demonstrate it through analysis of simulated SPT data of a particle in a three dimensional confined environment. The first two modifications use approximation methods to reduce the complexity of the original motion and measurement models without significant loss of accuracy. The third modification replaces the previous SMC methods with a Gaussian particle filter combined with a backward simulation particle smoother, trading off some level of generality for improved computational performance. In addition, we take advantage of the improved efficiency to investigate the effect of data length on performance in localization and parameter estimation.

单粒子跟踪(SPT)技术能够揭示生物大分子在活细胞内运动的动力学机制和物理特性，在生物物理学中起着至关重要的作用。这样的分子通常受到限制，通过了解分子的迁移性和它们被限制的区域的大小，可以揭示重要的信息。在之前的工作中，我们引入了一种称为顺序蒙特卡罗期望最大化(SMC-EM)的方法来同时估计粒子轨迹和模型参数。本文对SMC-EM进行了三种改进，以提高其计算效率，并通过三维受限环境中粒子的SPT模拟数据进行了验证。前两种修改使用近似方法来降低原始运动和测量模型的复杂性，而不会显著降低精度。第三种修改用高斯粒子滤波器和向后模拟粒子平滑器取代了以前的SMC方法，在一定程度上牺牲了一般性以提高计算性能。此外，我们利用改进的效率研究了数据长度对定位和参数估计性能的影响。

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引用次数: 1

Control of Mobile Plant with use of Interface Brain Computer 基于接口脑机的移动厂房控制

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2020-05-01 DOI: 10.23919/ECC51009.2020.9144000

M. Stepanov, V. Musatov, I. Egorov, S. Pchelintzeva, A. Stepanov, O. Stepanova, A. R. Berkaev, A. Ishanov, A. Nenashev, A. P. Nijazov

引用次数: 0

A novel formalisation of the Markov-Dubins problem 马尔可夫-杜宾斯问题的一种新的形式化

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2020-05-01 DOI: 10.23919/ECC51009.2020.9143597

P. Bevilacqua, Marco Frego, D. Fontanelli, L. Palopoli

引用次数: 4

Estimation of general time-varying single particle tracking linear models using local likelihood. 一般时变单粒子跟踪线性模型的局部似然估计。

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2020-05-01 Epub Date: 2020-07-20 DOI: 10.23919/ecc51009.2020.9143818

Boris I Godoy, Nicholas A Vickers, Y Lin, Sean B Andersson

In this work, we study a general approach to the estimation of single particle tracking models with time-varying parameters. The main idea is to use local Maximum Likelihood (ML), applying a sliding window over the data and estimating the model parameters in each window. We combine local ML with Expectation Maximization to iteratively find the ML estimate in each window, an approach that is amenable to generalization to nonlinear models. Results using controlled-experimental data generated in our lab show that our proposed algorithm is able to track changes in the parameters as they evolve during a trajectory under real-world experimental conditions, outperforming other algorithms of similar nature.

在这项工作中，我们研究了一种估计具有时变参数的单粒子跟踪模型的通用方法。主要思想是使用局部最大似然（ML），在数据上应用滑动窗口，并估计每个窗口中的模型参数。我们将局部ML与期望最大化相结合，在每个窗口中迭代地找到ML估计，这种方法适用于非线性模型的推广。使用我们实验室生成的受控实验数据的结果表明，我们提出的算法能够在真实世界的实验条件下跟踪参数在轨迹中的变化，优于其他类似性质的算法。

引用次数: 3

Subsystem of decision making support of robotics hardware-software 机器人软硬件决策支持子系统

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2020-05-01 DOI: 10.23919/ECC51009.2020.9143938

M. Stepanov, V. Musatov, I. Egorov, S. Pchelintzeva, A. Stepanov, O. Stepanova, A. R. Berkaev, A. Ishanov, A. Nenashev, A. P. Nijazov

引用次数: 0

Optimal Control System Synthesis Based on the Approximation of Extremals by Symbolic Regression 基于符号回归极值逼近的最优控制系统综合

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2020-05-01 DOI: 10.23919/ECC51009.2020.9143798

S. Konstantinov, A. Diveev, Elena A. Sofronova, I. Zelinka

引用次数: 0

Least squares realization of LTI models is an eigenvalue problem LTI模型的最小二乘实现是一个特征值问题

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2019-06-01 DOI: 10.23919/ECC.2019.8795987

B. Moor

We show how least squares optimal realization of autonomous linear time-invariant dynamical systems from given data, reduces to the solution of an eigenvalue problem. In this short paper, we can only schematically sketch the different steps: The first order optimality conditions result in a multi-parameter eigenvalue problem. The eigenvalue $n$ -tuples are calculated from the null space of a quasi-Toeplitz block Macaulay matrix, which is shown to be multishift-invariant. This last property is then exploited via nD ‘exact’ realization theory, leading through several eigenvalue problems to the optimal model parameters.

我们展示了如何从给定数据的最小二乘最优实现自治线性定常动力系统，简化为特征值问题的解。在这篇简短的文章中，我们只能粗略地描述不同的步骤:一阶最优性条件导致多参数特征值问题。从准toeplitz块Macaulay矩阵的零空间计算特征值$n$元组，该矩阵被证明是多移不变的。然后通过nD“精确”实现理论利用最后一个属性，通过几个特征值问题得到最优模型参数。

引用次数: 6

Dynamic extension for direct integrability of singular solutions in optimal control problems 最优控制问题奇异解直接可积性的动态推广

Control Conference (ECC) ... European. European Control Conference

Pub Date : 2019-06-01 DOI: 10.23919/ECC.2019.8795907

P. D. Giamberardino

The paper addresses the problem of optimal control design in presence of singular solutions. For this case, a procedure for avoiding the integration of the costate dynamics is proposed, giving the conditions under which the costate can be directly computed, under controllability condition for the dynamics, and presenting an approach for extending this property by a dynamic extension. The procedure is here described for a single input systems and for the case in which the first step of the iterative procedure is sufficient to get the solution. An example is used to show the feasibility of the approach.

本文研究奇异解存在下的最优控制设计问题。针对这种情况，提出了一种避免协态动力学积分的方法，给出了在动态可控性条件下可直接计算协态的条件，并给出了一种通过动态扩展来扩展这一性质的方法。这里描述的过程适用于单一输入系统，以及迭代过程的第一步足以得到解的情况。算例说明了该方法的可行性。

引用次数: 1

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