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## A Nonparametric Approach to Noisy and Costly Optimization (2000)

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Citations: | 21 - 3 self |

### Citations

1372 | Numerical Recipes - Press, Teukolsky, et al. - 1992 |

960 |
A Stochastic Approximation Method
- Robbins, Munro
- 1951
(Show Context)
Citation Context ...-Marquardt (Press et al., 1992) have fast convergence properties, but they can oscillate or diverge to in nity. Furthermore, current numerical methods cannot survive noise. Stochastic approximation: (=-=Robbins & Monro, 1951-=-) nds roots without the use of derivative estimates. Keifer-Wolfowitz (KW) (Kushner & Clark, 1978) is a related algorithm for noisy optimization. It estimates the gradient by performing experiments in... |

804 |
Empirical Model-building and Response Surfaces
- Box, Draper
- 1987
(Show Context)
Citation Context ...ones, and ooze along ridges. Amoeba is sensitive to noise, and it is also not e cient with its experiments� it only keeps the most recent k +1 results. Experiment design and Response surface methods (=-=Box & Draper, 1987-=-): A region of interest (ROI) is established at a starting point and experiments are made at positions that can best be used to identify local function properties with low-order polynomial regression.... |

480 |
A New Measure of Rank Correlation.
- Kendall
- 1938
(Show Context)
Citation Context ...ethod to test the positive monotonic association between kx ; x k and f(x). A typical nonparametric measure used for this purpose is Kendall's correlation coe cient, otherwise known as Kendall's tau (=-=Kendall, 1938-=-). We will denote the Kendall's tau for the relationship between kx ; x k and y(x) in the data set D as x �D. In this paper, the subscript D will be omitted whenever possible. Figure 1. Example calcul... |

366 |
Stochastic approximation methods for constrained and unconstrained systems.
- Kushner, Clark
- 1978
(Show Context)
Citation Context ...ge to in nity. Furthermore, current numerical methods cannot survive noise. Stochastic approximation: (Robbins & Monro, 1951) nds roots without the use of derivative estimates. Keifer-Wolfowitz (KW) (=-=Kushner & Clark, 1978-=-) is a related algorithm for noisy optimization. It estimates the gradient by performing experiments in both directions along each dimension of the input space. Based on the estimate, it moves its exp... |

105 |
Applied Nonparametric Statistical Methods.
- Sprent
- 1989
(Show Context)
Citation Context ...tal e ciency appears to be competitive with Amoeba and PMAX. 3. Nonparametric Statistics Nonparametric statistics have been heavily used in many areas of data analysis and machine learning for years (=-=Sprent, 1989-=-). They rely on taking numerical operations on the data and then testing for evidence of some e ect. They usually do so by empirically looking at the distribution of this property implied by the null ... |

56 | Stochastic Optimization. - Schneider, Kirkpatrick - 2006 |

54 | Self-improving factory simulation using continuous-time average-reward reinforcement learning - Mahadevan, Marchalleck, et al. - 1997 |

41 | An empirical investigation of brute force to choose features, smoothers and function approximators
- Moore, Hill, et al.
- 1992
(Show Context)
Citation Context ...isticated alternatives (Moore &Schneider, 1996). However it has some serious drawbacks: First, one must solve the bias-variance tradeo . This is often determined automatically using cross-validation (=-=Moore et al., 1994-=-), but this proves di cult with a set of very few, weirdly distributed datapoints obtained during optimization. Empirically we haveobserved dismal performance when attempting this. Second, PMAX is ver... |

11 | Active exploration and learning in real-valued spaces using multi-armed bandit allocation indices - Salganicoff, Ungar - 1995 |

5 |
Q2: A memory-based active learning algorithm for blackbox noisy optimization
- Moore, Schneider, et al.
- 1998
(Show Context)
Citation Context ...sted experiment. Third, PMAX can get stuck in \hallucinated" optima. Fourth, and most importantly, it assumes a locally smooth function. Discontinuities are disastrous for PMAX. Q2: the Q2 algorithm (=-=Moore et al., 1998-=-) attempts to achieve second order (quadratic) convergence by tting local quadratics in a Newton-like method. Unlike RSM it attempts to entirely automatically determine a good region of interest, i.e.... |

4 |
Learning in embedded systems. Doctoral dissertation
- Kaelbling
- 1990
(Show Context)
Citation Context ...imum, but instead where the con dence intervals are widest, or where the top of the con dence interval is maximized (Moore & Schneider, 1996), or in accordance with the Interval Estimation heuristic (=-=Kaelbling, 1990-=-). Empirically, wehave found that PMAX using locally weighted regression as the function approximator is often faster than more sophisticated alternatives (Moore &Schneider, 1996). However it has some... |