Newton based Stochastic Optimization using q-Gaussian Smoothed Functional Algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar et al., 2013), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on smoothed functional algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work and turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of several numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian (Bhatnagar, 2007) and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms (Ghoshdastidar et al., 2013).Comment: This is a longer of version of the paper with the same title accepted in Automatic

Supervised learning with quantum enhanced feature spaces

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.Comment: Fixed typos, added figures and discussion about quantum error mitigatio

A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATION

This paper presents a data-driven PID controller based on Normalized Simultaneous Perturbation Stochastic Approximation (SPSA). Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. The unstable convergence always happened in the data-driven controller tuning, when the closed-loop control system became unstable. In the case of flexible joint manipulator, it will exhibit unstable tip angular position with high magnitude of vibration. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the cost function from the perturbations is normalized to the maximum cost function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to the data-driven PID control scheme of a flexible joint plant. The simulation result shows that the data-driven controller tuning using the normalized SPSA is able to provide a stable convergence with 76.68 % improvement in average cost function. Moreover, it also exhibits lower average and best values for both norms of error and input performances as compared to the existing modified SPSA.A DATA-DRIVEN PID CONTROLLER FOR FLEXIBLE JOINT MANIPULATOR USING NORMALIZED SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATIO

A Data-Driven PID Controller For Flexible Joint Manipulator Using Normalized Simultaneous Perturbation Stochastic Approximation

This paper presents a data-driven PID controller based on Normalized Simultaneous Perturbation Stochastic Approximation (SPSA). Initially, an unstable convergence of conventional SPSA is illustrated, which motivate us to introduce its improved version. The unstable convergence always happened in the data-driven controller tuning, when the closed-loop control system became unstable. In the case of flexible joint manipulator, it will exhibit unstable tip angular position with high magnitude of vibration. Here, the conventional SPSA is modified by introducing a normalized gradient approximation to update the design variable. To be more specific, each measurement of the cost function from the perturbations is normalized to the maximum cost function measurement at the current iteration. As a result, this improvement is expected to avoid the updated control parameter from producing an unstable control performance. The effectiveness of the normalized SPSA is tested to the data-driven PID control scheme of a flexible joint plant. The simulation result shows that the data-driven controller tuning using the normalized SPSA is able to provide a stable convergence with 76.68 % improvement in average cost function. Moreover, it also exhibits lower average and best values for both norms of error and input performances as compared to the existing modified SPSA

Quantum Machine Learning in High Energy Physics

Machine learning has been used in high energy physics since a long time, primarily at the analysis level with supervised classification. Quantum computing was postulated in the early 1980s as way to perform computations that would not be tractable with a classical computer. With the advent of noisy intermediate-scale quantum computing devices, more quantum algorithms are being developed with the aim at exploiting the capacity of the hardware for machine learning applications. An interesting question is whether there are ways to combine quantum machine learning with High Energy Physics. This paper reviews the first generation of ideas that use quantum machine learning on problems in high energy physics and provide an outlook on future applications.Comment: 25 pages, 9 figures, submitted to Machine Learning: Science and Technology, Focus on Machine Learning for Fundamental Physics collectio