Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration
Smoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nester...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
IEEE
2021-01-01
|
Series: | IEEE Access |
Subjects: | |
Online Access: | https://ieeexplore.ieee.org/document/9509526/ |
id |
doaj-dfa89383fd804b58b77ec0cfde6b21a0 |
---|---|
record_format |
Article |
spelling |
doaj-dfa89383fd804b58b77ec0cfde6b21a02021-08-18T23:00:14ZengIEEEIEEE Access2169-35362021-01-01911348911349910.1109/ACCESS.2021.31037679509526Multi-Time Scale Smoothed Functional With Nesterov’s AccelerationAbhinav Sharma0K. Lakshmanan1Ruchir Gupta2https://orcid.org/0000-0001-9970-3889Atul Gupta3Department of Computer Science, PDPM Indian Institute of Information Technology at Jabalpur, Jabalpur, Madhya Pradesh, IndiaDepartment of Computer Science, IIT Banaras Hindu University (BHU) at Varanasi, Varanasi, Uttar Pradesh, IndiaDepartment of Computer Science, Jawaharlal Nehru University (JNU), Delhi, IndiaDepartment of Computer Science, PDPM Indian Institute of Information Technology at Jabalpur, Jabalpur, Madhya Pradesh, IndiaSmoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nesterov’s acceleration for stochastic optimization problems. The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations’ (o.d.e.) stability for a non-autonomous system. We compare our algorithm with other smoothed functional algorithms such as Quasi-Newton SF, Gradient SF and Jacobi Variant of Newton SF on two different optimization problems: first, on a simple stochastic function minimization problem, and second, on the problem of optimal routing in a queueing network. Additionally, we compared the algorithms on real weather data in a weather prediction task. Experimental results show that our algorithm performs significantly better than these baseline algorithms.https://ieeexplore.ieee.org/document/9509526/Multi-Stage queueing networksNesterov’s accelerationsimulationsmoothed functional algorithmstochastic approximation algorithmsstochastic optimization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Abhinav Sharma K. Lakshmanan Ruchir Gupta Atul Gupta |
spellingShingle |
Abhinav Sharma K. Lakshmanan Ruchir Gupta Atul Gupta Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration IEEE Access Multi-Stage queueing networks Nesterov’s acceleration simulation smoothed functional algorithm stochastic approximation algorithms stochastic optimization |
author_facet |
Abhinav Sharma K. Lakshmanan Ruchir Gupta Atul Gupta |
author_sort |
Abhinav Sharma |
title |
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration |
title_short |
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration |
title_full |
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration |
title_fullStr |
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration |
title_full_unstemmed |
Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration |
title_sort |
multi-time scale smoothed functional with nesterov’s acceleration |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2021-01-01 |
description |
Smoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nesterov’s acceleration for stochastic optimization problems. The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations’ (o.d.e.) stability for a non-autonomous system. We compare our algorithm with other smoothed functional algorithms such as Quasi-Newton SF, Gradient SF and Jacobi Variant of Newton SF on two different optimization problems: first, on a simple stochastic function minimization problem, and second, on the problem of optimal routing in a queueing network. Additionally, we compared the algorithms on real weather data in a weather prediction task. Experimental results show that our algorithm performs significantly better than these baseline algorithms. |
topic |
Multi-Stage queueing networks Nesterov’s acceleration simulation smoothed functional algorithm stochastic approximation algorithms stochastic optimization |
url |
https://ieeexplore.ieee.org/document/9509526/ |
work_keys_str_mv |
AT abhinavsharma multitimescalesmoothedfunctionalwithnesterovx2019sacceleration AT klakshmanan multitimescalesmoothedfunctionalwithnesterovx2019sacceleration AT ruchirgupta multitimescalesmoothedfunctionalwithnesterovx2019sacceleration AT atulgupta multitimescalesmoothedfunctionalwithnesterovx2019sacceleration |
_version_ |
1721202573018398720 |