Optimization algorithms and methods | Stochastic optimization | Randomized algorithms
Simultaneous perturbation stochastic approximation (SPSA) is an algorithmic method for optimizing systems with multiple unknown parameters. It is a type of stochastic approximation algorithm. As an optimization method, it is appropriately suited to large-scale population models, adaptive modeling, simulation optimization, and atmospheric modeling. Many examples are presented at the SPSA website http://www.jhuapl.edu/SPSA. A comprehensive book on the subject is Bhatnagar et al. (2013). An early paper on the subject is Spall (1987) and the foundational paper providing the key theory and justification is Spall (1992). SPSA is a descent method capable of finding global minima, sharing this property with other methods as simulated annealing. Its main feature is the gradient approximation that requires only two measurements of the objective function, regardless of the dimension of the optimization problem. Recall that we want to find the optimal control with lossfunction : Both Finite Differences Stochastic Approximation (FDSA)and SPSA use the same iterative process: where represents the iterate, is the estimate of the gradient of the objective function evaluated at , and is a positive number sequence converging to 0. If is a p-dimensional vector, the component of the symmetric finite difference gradient estimator is: FD: 1 ≤i ≤p, where is the unit vector with a 1 in the place, and is a small positive number that decreases with n. With this method, 2p evaluations of J for each are needed. Clearly, when p is large, this estimator loses efficiency. Let now be a random perturbation vector. The component of the stochastic perturbation gradient estimator is: SP: Remark that FD perturbs only one direction at a time, while the SP estimator disturbs all directions at the same time (the numerator is identical in all p components). The number of loss function measurements needed in the SPSA method for each is always 2, independent of the dimension p. Thus, SPSA uses p times fewer function evaluations than FDSA, which makes it a lot more efficient. Simple experiments with p=2 showed that SPSA converges in the same number of iterations as FDSA. The latter follows approximately the steepest descent direction, behaving like the gradient method. On the other hand, SPSA, with the random search direction, does not follow exactly the gradient path. In average though, it tracks it nearly because the gradient approximation is an almost unbiasedestimator of the gradient, as shown in the following lemma. (Wikipedia).
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
Stochastic Approximation-based algorithms, when the Monte (...) - Fort - Workshop 2 - CEB T1 2019
Gersende Fort (CNRS, Univ. Toulouse) / 13.03.2019 Stochastic Approximation-based algorithms, when the Monte Carlo bias does not vanish. Stochastic Approximation algorithms, whose stochastic gradient descent methods with decreasing stepsize are an example, are iterative methods to comput
From playlist 2019 - T1 - The Mathematics of Imaging
Jana Cslovjecsek: Efficient algorithms for multistage stochastic integer programming using proximity
We consider the problem of solving integer programs of the form min {c^T x : Ax = b; x geq 0}, where A is a multistage stochastic matrix. We give an algorithm that solves this problem in fixed-parameter time f(d; ||A||_infty) n log^O(2d) n, where f is a computable function, d is the treed
From playlist Workshop: Parametrized complexity and discrete optimization
OHM2013: Introduction to Quantum Perturbation
For more information visit: http://bit.ly/OHM13_web To download the video visit: http://bit.ly/OHM13_down Playlist OHM 2013: http://bit.ly/OHM13_pl Speaker: Karnei Gozman A birds eye view of the diagrammatic representation of Rayleigh-Schrödinger Perturbation Theory(RSPT), a general form
From playlist OHM 2013
Benjamin Stamm: A perturbation-method-based post-processing of planewave approximations for
Benjamin Stamm: A perturbation-method-based post-processing of planewave approximations for Density Functional Theory (DFT) models The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Non-local Material Models and Concurrent Multisc
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Victor Beresnevich: Simultaneous rational approximations to several functions of a real variable
Abstract: As is well known, simultaneous rational approximations to the values of smooth functions of real variables involve counting and/or understanding the distribution of rational points lying near the manifold parameterised by these functions. I will discuss recent results in this are
From playlist Number Theory
Perturbation Theory in Quantum Mechanics - Cheat Sheet
In this video we present all the equations you need to know when you want to do time (in)dependent, (non-)degenerate perturbation theory in non-relativistic #QuantumMechanics References: [1] Sakurai, Napolitano, "Modern Quantum Mechanics". Table of Contents: 00:00 Introduction 00:57 T
From playlist Quantum Mechanics, Quantum Field Theory
Multivariable Calculus | Definition of partial derivatives.
We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Worldwide Calculus: Partial Anti-Derivatives & Iterated Integrals
Lecture on 'Partial Anti-Derivatives & Iterated Integrals' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Integrals
Benjamin Gess - Fluctuations in non-equilibrium and stochastic PDE
Macroscopic fluctuation theory provides a general framework for far from equilibrium thermodynamics, based on a fundamental formula for large fluctuations around (local) equilibria. This fundamental postulate can be informally justified from the framework of fluctuating hydrodynamics, link
From playlist Research Spotlight
Probing the Early Universe with Gravitational Wave Background and Primordial by Nilanjandev Bhaumik
PROGRAM LESS TRAVELLED PATH TO THE DARK UNIVERSE ORGANIZERS: Arka Banerjee (IISER Pune), Subinoy Das (IIA, Bangalore), Koushik Dutta (IISER, Kolkata), Raghavan Rangarajan (Ahmedabad University) and Vikram Rentala (IIT Bombay) DATE & TIME: 13 March 2023 to 24 March 2023 VENUE: Ramanujan
From playlist LESS TRAVELLED PATH TO THE DARK UNIVERSE
The Sherrington-Kirkpatrick model and its diluted version II
Dmitry Panchenko Texas A&M University March 12, 2014 I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main goals in these models is to find a formula for the maximum of the process, or th
From playlist Mathematics
Stochastic Gradient Descent and Machine Learning (Lecture 4) by Praneeth Netrapalli
PROGRAM: BANGALORE SCHOOL ON STATISTICAL PHYSICS - XIII (HYBRID) ORGANIZERS: Abhishek Dhar (ICTS-TIFR, India) and Sanjib Sabhapandit (RRI, India) DATE & TIME: 11 July 2022 to 22 July 2022 VENUE: Madhava Lecture Hall and Online This school is the thirteenth in the series. The schoo
From playlist Bangalore School on Statistical Physics - XIII - 2022 (Live Streamed)
Martin HAIRER - Random Loops and T-algebras
The stochastic quantization of the 1d non-linear sigma model (i.e. the natural Langevin dynamic on loop space) naturally leads to the study of an algebraic structure we call a T-algebra. We will discuss how they arise, a few of their properties, as well as a concrete example of their appli
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Luca Mazzucato - Computational Principles Underlying the Temporal Organization of Behavior
Naturalistic animal behavior exhibits a striking amount of variability in the temporal domain along at least three independent axes: hierarchical, contextual, and stochastic. First, a vast hierarchy of timescales links movements into behavioral sequences and long-term activities, from mill
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Fluid Turbulence, Thermal Noise and Spontaneous Stochasticity - Gregory Eyink
Workshop on Turbulence Topic: Fluid Turbulence, Thermal Noise and Spontaneous Stochasticity Speaker: Gregory Eyink Affiliation: Johns Hopkins University Date: December 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Sixteenth Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, March 3, 2021, 10:00am EDT Speaker: Simon Arridge, University College London Title: Coupled Physics Imaging with Sound and Light - Deterministic and Stochastic Approaches Abstract: Coupled Physics Imaging (CPI) refers to methods that generate contrast through one phy
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
Reservoir computing in noisy real-world systems: network inference and dynamical. by Sarthak Chandra
DISCUSSION MEETING NEUROSCIENCE, DATA SCIENCE AND DYNAMICS (ONLINE) ORGANIZERS: Amit Apte (IISER-Pune, India), Neelima Gupte (IIT-Madras, India) and Ramakrishna Ramaswamy (IIT-Delhi, India) DATE : 07 February 2022 to 10 February 2022 VENUE: Online This discussion meeting on Neuroscien
From playlist Neuroscience, Data Science and Dynamics (ONLINE)
Spatio-temporal chaos in a driven dissipative Duffing chain: an OTOC... by Amit Kumar Chatterjee
DISCUSSION MEETING: 7TH INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS : Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Sanjib Sabhapandit, Samriddhi Sankar Ray and Prerna Sharma DATE: 19 February 2020 to 21 February 2020 VENUE: Ramanujan Lecture Hall, ICTS Ba
From playlist 7th Indian Statistical Physics Community Meeting 2020
Numeric Modeling in Mathematica: Q&A with Mathematica Experts
Mathematica experts answer user-submitted questions about numeric computations during Mathematica Experts Live: Numeric Modeling in Mathematica. For more information about Mathematica, please visit: http://www.wolfram.com/mathematica
From playlist Mathematica Experts Live: Numeric Modeling in Mathematica