Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Intensive Surrogate Model Exploitation in Self-adaptive Surrogate-assisted CMA-ES (saACM-ES) Ilya

493 views

Published on

Published in: Business, Technology
  • Hello! I have searched hard to find a reliable and best research paper writing service and finally i got a good option for my needs as ⇒ www.HelpWriting.net ⇐
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • A very good resource can do the writings for ⇒ www.HelpWriting.net ⇐ But use it only if u rly cant write anything down.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Be the first to like this

Intensive Surrogate Model Exploitation in Self-adaptive Surrogate-assisted CMA-ES (saACM-ES) Ilya

  1. 1. State-of-the-art Intensive surrogate model exploitation Intensive Surrogate Model Exploitation in Self-adaptive Surrogate-assisted CMA-ES (saACM-ES) Ilya Loshchilov1 , Marc Schoenauer2 and Michèle Sebag 2 1 LIS, École Polytechnique Fédérale de Lausanne 2 TAO, INRIA − CNRS − Université Paris-Sud July 9th, 2013 Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 1/ 19
  2. 2. State-of-the-art Intensive surrogate model exploitation Historical overview: PPSN’2010, GECCO’2012 PPSN’2010 CMA-ES assisted with comparison-based surrogate models (ACM algorithm) 1 . Good performance but exploitation is independent on surrogate model quality, surrogate hyper-parameters are fixed. GECCO’2012 Self-adaptive surrogate-assisted CMA-ES (IPOP-saACM-ES and BIPOP-saACM-ES) on noiseless2 and noisy testbeds3 . BIPOP-saACM-ES demonstrates good performance w.r.t. all algorithms tested during the BBOB-2009, 2010 and 2012. 1[Loshchilov, Schoenauer and Sebag; PPSN 2010] "Comparison-based optimizers need comparison-based surrogates" 2[Loshchilov, Schoenauer and Sebag; GECCO-BBOB 2012] "Black-box optimization benchmarking of IPOP-saACM-ES and BIPOP-saACM-ES on the BBOB-2012 noiseless testbed" 3[Loshchilov, Schoenauer and Sebag; GECCO-BBOB 2012] "Black-box optimization benchmarking of IPOP-saACM-ES on the BBOB-2012 noisy testbed" Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 2/ 19
  3. 3. State-of-the-art Intensive surrogate model exploitation Content 1 State-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES 2 Intensive surrogate model exploitation Intensive surrogate model exploitation Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 3/ 19
  4. 4. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES (µ, λ)-Covariance Matrix Adaptation Evolution Strategy Rank-µ Update 4 5 yi ∼ N (0, C) , C = I xi = m + σ yi, σ = 1 sampling of λ solutions Cµ = 1 µ yi:λyT i:λ C ← (1 − 1) × C + 1 × Cµ calculating C from best µ out of λ mnew ← m + 1 µ yi:λ new distribution The adaptation increases the probability of successful steps to appear again. Other components of CMA-ES: step-size adaptation, evolution path. 4[Hansen et al., ECJ 2003] "Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES)" 5 the slide adopted by courtesy of Nikolaus Hansen Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 4/ 19
  5. 5. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES Invariance: Guarantee for Generalization Invariance properties of CMA-ES Invariance to order-preserving transformations in function space true for all comparison-based algorithms Translation and rotation invariance thanks to C −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 CMA-ES is almost parameterless (as a consequence of invariances) Tuning on a small set of functions Hansen & Ostermeier 2001 Default values generalize to whole classes Exception: population size for multi-modal functions a b a[Auger & Hansen, CEC 2005] "A restart CMA evolution strategy with increasing population size" b[Loshchilov et al., PPSN 2012] "Alternative Restart Strategies for CMA-ES" Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 5/ 19
  6. 6. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES Contents 1 State-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES 2 Intensive surrogate model exploitation Intensive surrogate model exploitation Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 6/ 19
  7. 7. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES s∗ ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES Using Ranking SVM as the surrogate model Build a global model using Ranking SVM 6 xi ≻ xj iff ˆF(xi) < ˆF(xj) Comparison-based surrogate models → invariance to rank-preserving transformations of F(x) How to choose an appropriate Kernel? Use covariance matrix C adapted by CMA-ES in Gaussian kernel7 K(xi, xj) = e− (xi−xj )T (xi−xj) 2σ2 ; KC(xi, xj) = e− (xi−xj )T C−1(xi−xj ) 2σ2 Invariance to rotation of the search space thanks to C 6[Runarsson et al., PPSN 2006] "Ordinal Regression in Evolutionary Computation" 7[Loshchilov et al., PPSN 2010] "Comparison-based optimizers need comparison-based surrogates" Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 7/ 19
  8. 8. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES s∗ ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES Surrogate-assisted CMA-ES with online adaptation of model hyper-parameters a a[Loshchilov et al., GECCO 2012] "Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy" Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 8/ 19
  9. 9. State-of-the-art Intensive surrogate model exploitation Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES Results on Black-Box Optimization Competition BIPOP-s∗aACM and IPOP-s∗aACM (with restarts) on 24 noiseless 20 dimensional functions 0 1 2 3 4 5 6 7 8 9 log10 of (ERT / dimension) 0.0 0.5 1.0 Proportionoffunctions RANDOMSEARCH SPSA BAYEDA DIRECT DE-PSO GA LSfminbnd LSstep RCGA Rosenbrock MCS ABC PSO POEMS EDA-PSO NELDERDOERR NELDER oPOEMS FULLNEWUOA ALPS GLOBAL PSO_Bounds BFGS ONEFIFTH Cauchy-EDA NBC-CMA CMA-ESPLUSSEL NEWUOA AVGNEWUOA G3PCX 1komma4mirser 1plus1 CMAEGS DEuniform DE-F-AUC MA-LS-CHAIN VNS iAMALGAM IPOP-CMA-ES AMALGAM IPOP-ACTCMA-ES IPOP-saACM-ES MOS BIPOP-CMA-ES BIPOP-saACM-ES best 2009 f1-24 Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 9/ 19
  10. 10. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Contents 1 State-of-the-art Covariance Matrix Adaptation Evolution Strategy (CMA-ES) s∗ ACM-ES: Self-Adaptive Surrogate-Assisted CMA-ES 2 Intensive surrogate model exploitation Intensive surrogate model exploitation Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 10/ 19
  11. 11. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Intensive surrogate model exploitation When optimizing ˆF, λ = kλλdef , µ = µdef Parameter settings: kλ = 1 for D<10 and kλ = 10, 100, 1000 for 10, 20, 40-D. An interpretation: trust-region search. Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 11/ 19
  12. 12. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Divergence prevention Surrogate model error estimation can be imprecise The proposed simple fix: Exploit surrogate only if the model is "reasonably" precise: kλ > 1 is used only of ˆn ≥ ˆnkλ Parameter settings: ˆnkλ = 4. Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 12/ 19
  13. 13. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Surrogate model hyper-parameters adaptation: the original saACM Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 13/ 19
  14. 14. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Surrogate model hyper-parameters adaptation: the proposed saACM-k CPU time per function evaluation: 1.22 sec. (kλ = 1), 0.313 sec. (kλ = 10), 0.311 sec. (kλ = 100), 0.367 sec. (kλ = 1000), 1.52 sec. (kλ = 10000). Here, for kλ = 100 it is even computationally cheaper! Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 14/ 19
  15. 15. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Ill-conditioned problems Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 15/ 19
  16. 16. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation All BBOB problems * smaller budget for surrogate-assisted search: 104 D for BIPOP-saACM-k versus 106 D for BIPOP-saACM. Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 16/ 19
  17. 17. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Hybridization HCMA = NEWUOA (first 10n evaluations) + STEP (to exploit separability if any) + BIPOP-saACM-k. 0 1 2 3 4 5 6 7 8 log10 of (# f-evals / dimension) 0.0 0.2 0.4 0.6 0.8 1.0 Proportionoffunction+targetpairs fmincon lmm-CMA-ES IPOP-texp MOS BIPOP-saACM-k HCMA best 2009f1-24,20-D * smaller budget for surrogate-assisted search: 104 D forIlya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 17/ 19
  18. 18. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Conclusion Pros: Faster convergence, especially on ill-condition problems. Potentially smaller CPU per function evaluation. Cons: Decrease of performance if surrogate error estimation is imprecise. Perspective Kullback-Leibler divergence measure for surrogate model control.8 8[Loshchilov, Schoenauer and Sebag; CAP 2013] "KL-based Control of the Learning Schedule for Surrogate Black-Box Optimization" Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 18/ 19
  19. 19. State-of-the-art Intensive surrogate model exploitation Intensive surrogate model exploitation Thank you for your attention! Questions? Ilya Loshchilov, Marc Schoenauer and Michèle Sebag Intensive Surrogate Model Exploitation in saACM-ES 19/ 19

×