Developing insight into effective SPSA parameters through ... · Developing insight into effective...
19
Developing insight into effective SPSA parameters through sensitivity analysis Ioulia MARKOU Constantinos ANTONIOU National Technical University of Athens, Greece MT-ITS 2015 3-5. June 2015, Budapest
Transcript of Developing insight into effective SPSA parameters through ... · Developing insight into effective...
Developing insight into effective SPSA parametersthrough sensitivity analysis
Ioulia MARKOU Constantinos ANTONIOUNational Technical University of Athens, Greece
MT-ITS 2015 3-5. June 2015, Budapest
Outline
Motivation
Overview
Methodology
Experimental set-up
Application and results
Conclusion and future research prospects
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 2
Motivation
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 3
Driving Characteristics
Key factor for transportation systems
Models’ values represent driving and
travel behavior parameters’ diversity
Parameter calibration is a
crucial step
MotivationSimultaneous Perturbation Stochastic Approximation
SPSA
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 4
An optimization method that has attracted considerable international attention
Its performance depends on the appropriate set of parameters
Overview
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 5
Macroscopic, mesoscopic and microscopic traffic flow models
Their default parameter values are not suitable for all applications
Driving and travel behavior parameters are constantly changing
Calibration procedure aims to appropriately specify the modelparameter values, so that the representation of the network and trafficflow characteristics is as accurate as the model structure allows
Overview
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 6
Formulation as an optimization problem
Optimization algorithms
Least-squares method Deterministic Complex algorithm of Box Nelder-Mead algorithm … Stochastic approximation
S - imultaneousP - erturbationS - tochasticA - pproximation
Spall, J. C. (1998)
Overview
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 7
Member of the iterative stochastic optimization algorithms family
Applicable solution when the objective function does not have an analytical form
Saves computational time for large-scale problems over traditional gradient methods
1SPSA, 2SPSA, W–SPSA, c–SPSA, etc.
SPSA Algorithm
Overview
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 8
SPSA Algorithm
Overview
aA
alphac
gamma
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 6
SPSA Algorithm
Methodology
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 6
Determination of calibration parameters
Collection of historical measurements
Selection of calibration algorithm
Choice of Loss Function
Start of Calibration
Experimental set-up
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 11
Ozguven and Ozbay (2008)
Application
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 12
RMSNusing the suggested
SPSA parameter
values
Application
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 13
Parameter a
RM
SN
0,4
0,3
0,2
0,1
0
a = 2a = 0,01 a = 5 a = 10a = 7a = 0,5
Application
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 14
Parameter alpha
RM
SN
0,4
0,3
0,2
0,1
0
alpha = 0,3 alpha = 0,4 alpha = 0,5 alpha = 0,6 alpha = 0,8 alpha = 1
Application
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 15
Sensitivity analysis of the three important parameters
Results
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 16
Conclusion
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 17
Certain parameters significantly affect SPSA’s convergence
The parameter c does not appear to improve convergence
Parameters alpha, gamma and a seem to contribute
significantly to the convergence of the algorithm.
Future research prospects
MT-ITS 2015 3-5. JUNE 2015, BUDAPEST 18
Further experimental analysis Larger problems Different noise structures Dynamic phenomena
Application in other SPSA variants (e.g. W-SPSA, c-SPSA)
Developing insight into effective SPSA parametersthrough sensitivity analysis
Ioulia MARKOU Constantinos ANTONIOU
National Technical University of Athens, Greece
MT-ITS 2015 3-5. June 2015, Budapest
