On weighted averaging in optimization

731 views

Published on

@inproceedings{teytaud:inria-00451416,
hal_id = {inria-00451416},
url = {http://hal.inria.fr/inria-00451416},
title = {{Bias and variance in continuous EDA}},
author = {Teytaud, Fabien and Teytaud, Olivier},
abstract = {{Estimation of Distribution Algorithms are based on statistical estimates. We show that when combining classical tools from statistics, namely bias/variance decomposition, reweighting and quasi-randomization, we can strongly improve the convergence rate. All modifications are easy, compliant with most algorithms, and experimentally very efficient in particular in the parallel case (large offsprings).}},
language = {Anglais},
affiliation = {TAO - INRIA Futurs , Laboratoire de Recherche en Informatique - LRI , TAO - INRIA Saclay - Ile de France},
booktitle = {{EA 09}},
address = {Strasbourg, France},
audience = {internationale },
year = {2009},
month = May,
pdf = {http://hal.inria.fr/inria-00451416/PDF/decsigma.pdf},
}

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
731
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • I am Frederic Lemoine, PhD student at the University Paris Sud. I will present you my work on GenoQuery, a new querying module adapted to a functional genomics warehouse
  • On weighted averaging in optimization

    1. 1. Why one mustuse reweighting F. Teytaud, O. Teytaud Montréal, 2009Tao, Inria Saclay Ile-De-France, LRI (Université Paris Sud, France),UMR CNRS 8623, I&A team, Digiteo, Pascal Network of Excellence.
    2. 2. Outline Idea of averaging in evolutionary algorithms This idea introduces a bias How to remove this bias The results Conclusions Teytaud and Teytaud Gecco 09 is great 2
    3. 3. Idea in ES Average of selected points = good approximation of optimum Teytaud and Teytaud Gecco 09 is great 3
    4. 4. Idea in ES Lets assume this is true (for the moment)... nonetheless, theres a bias. Teytaud and Teytaud Gecco 09 is great 4
    5. 5. EMNA (P. Larranaga and J.-A. Lozano, 2001) While (not finished) - generate population - select best individuals - estimate mean / variance (and possibly covariance) Teytaud and Teytaud Gecco 09 is great 5
    6. 6. EMNA (P. Larranaga and J.-A. Lozano, 2001) Teytaud and Teytaud Gecco 09 is great 6
    7. 7. EMNA (P. Larranaga and J.-A. Lozano, 2001) While (not finished) - generate population - select best individuals - estimate mean / variance (and possibly covariance)Highly parallel (more than most ES; T. et al, EvoStar 2001)Very simpleCan handle covariance matrix easily Teytaud and Teytaud Gecco 09 is great 7
    8. 8. Please wake up during 3 slides :-) Idea of averaging in evolutionary algorithms This idea introduces a bias How to remove this bias The results Conclusions Teytaud and Teytaud Gecco 09 is great 8
    9. 9. Bias due to bad (Gaussian) distribution High density Teytaud and Teytaud Gecco 09 is great 9
    10. 10. Bias due to bad distribution Teytaud and Teytaud Gecco 09 is great 10
    11. 11. Bias due to bad distribution Teytaud and Teytaud Gecco 09 is great 11
    12. 12. Bias due to bad distribution AVERAGE (biased by the distribution) Teytaud and Teytaud Gecco 09 is great 12
    13. 13. Corrected by weighted average AVERAGE (the one we really want !) Teytaud and Teytaud Gecco 09 is great 13
    14. 14. Outline Idea of averaging in evolutionary algorithms This idea introduces a bias How to remove this bias The results Conclusions Teytaud and Teytaud Gecco 09 is great 14
    15. 15. American Election of 1936 (fun) Literary digest: pop size = 2 000 000 ==> predicts Landon Gallup: pop size = 50 000 ==> predicts Roosevelt (and was proved right) Teytaud and Teytaud Gecco 09 is great 15
    16. 16. American Election of 1936 Literary digest: pop size = 2 300 000 ==> predicts Landon Gallup: pop size = 50 000 ==> predicts Roosevelt (and was proved right) The Literary digest failed because of a biased sampling. (much more affluent people and much more republicans among Literary Digest readers) Correction: Weight of individual = real density / biased density. Teytaud and Teytaud Gecco 09 is great 16
    17. 17. REMNA (reweighted EMNA) Inverse Gaussian density Gaussian density (=weight for removing the bias!) Teytaud and Teytaud Gecco 09 is great 17
    18. 18. REMNA (reweighted EMNA) Very simple modification: - compute weight ( individual ) = 1 / density - compute mean, variance, covariance with these weights ==> not only for Gaussians ==> ok for all surrogate models / EDA ==> just an application of standard statistics Teytaud and Teytaud Gecco 09 is great 18
    19. 19. REMNA Teytaud and Teytaud Gecco 09 is great 19
    20. 20. Outline Idea of averaging in evolutionary algorithms This idea introduces a bias How to remove this bias The results: less premature convergence Conclusions Teytaud and Teytaud Gecco 09 is great 20
    21. 21. The results We do not prove that “theres no more premature convergence.” We just show that, for a fixed generation, “ IF the center of the level set is the optimum, THEN the asymptotic value of the estimated optimum = the optimum.” ==> is the condition really necessary ? Teytaud and Teytaud Gecco 09 is great 21
    22. 22. Yes: center = optimum and Yes: situation better Yes and yes Teytaud and Teytaud Gecco 09 is great 22
    23. 23. No: center ≠optimum but Yes: situation better (assumption not really necessary) No... but yes Teytaud and Teytaud Gecco 09 is great 23
    24. 24. Results: convergence rate with  = d 2 Teytaud and Teytaud Gecco 09 is great 24
    25. 25. Conclusions Idea of averaging in evolutionary algorithms This idea introduces a bias How to remove this bias The results Conclusions Teytaud and Teytaud Gecco 09 is great 25
    26. 26. ConclusionsReduces the risk of premature convergenceNo proof on the complete algorithm (just step-wise consistency)Empirically quite good for EMNA (should be tested on other EDA / surrogate)Simple, sound, widely applicableBias of step-size adaptation not yetanalyzed (==> seemingly works quite well!) Teytaud and Teytaud Gecco 09 is great 26
    27. 27. Related work Papers from D.V. Arnold et al. around reweighting for improved convergence rate (sphere, ridge) of ES (to be combined ?) Work from CMA-people around weights for improved conv. rate in CMA-ES Thanks! Questions ? Teytaud and Teytaud Gecco 09 is great 27

    ×