Tutorial on Function Approximation Optimization for Computationally Expensive Nonlinear Models Including Applications to Uncertainty Analysis and to Groundwater Transport

2006 ◽  
Author(s):  
Christine A. Shoemaker
Keyword(s):  
Uncertainty Analysis ◽  
Function Approximation ◽  
Nonlinear Models ◽  
Groundwater Transport ◽  
Computationally Expensive ◽  
Approximation Optimization

scholarly journals Uncertainty Analysis for Computationally Expensive Models with Multiple Outputs

2012 ◽  
Vol 17 (4) ◽  
pp. 623-640 ◽  
Author(s):  
David Ruppert ◽  
Christine A. Shoemaker ◽  
Yilun Wang ◽  
Yingxing Li ◽  
Nikolay Bliznyuk
Keyword(s):  
Uncertainty Analysis ◽  
Multiple Outputs ◽  
Computationally Expensive

scholarly journals Scalable Initial State Interdiction for Factored MDPs

2018 ◽  
Author(s):  
Swetasudha Panda ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Optimal Policy ◽  
Function Approximation ◽  
Stackelberg Game ◽  
Game Model ◽  
Initial State ◽  
Novel Approach ◽  
Linear Function Approximation ◽  
Computationally Expensive

We propose a novel Stackelberg game model of MDP interdiction in which the defender modifies the initial state of the planner, who then responds by computing an optimal policy starting with that state. We first develop a novel approach for MDP interdiction in factored state space that allows the defender to modify the initial state. The resulting approach can be computationally expensive for large factored MDPs. To address this, we develop several interdiction algorithms that leverage variations of reinforcement learning using both linear and non-linear function approximation. Finally, we extend the interdiction framework to consider a Bayesian interdiction problem in which the interdictor is uncertain about some of the planner's initial state features. Extensive experiments demonstrate the effectiveness of our approaches.

Approximation of Computationally Expensive and Noisy Functions for Constrained Nonlinear Optimization

1987 ◽  
Vol 109 (4) ◽  
pp. 528-532 ◽  
Author(s):  
J. W. Free ◽  
A. R. Parkinson ◽  
G. R. Bryce ◽  
R. J. Balling
Keyword(s):  
Nonlinear Programming ◽  
Approximation Method ◽  
Function Approximation ◽  
Experimental Designs ◽  
Test Problems ◽  
Constrained Nonlinear Optimization ◽  
Noisy Functions ◽  
Computationally Expensive ◽  
And Function ◽  
Programming Algorithms

The use of statistical experimental designs is explored as a method of approximating computationally expensive and noisy functions. The advantages of experimental designs and function approximation for use in optimization are discussed. Several test problems are reported showing the approximation method to be competitive with the most efficient optimization algorithms when no noise is present. When noise is introduced, the approximation method is more efficient and solves more problems than conventional nonlinear programming algorithms.

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