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論文紹介:Speeding up Automatic Hyperparameter Optimization of Deep Neural Networks by Extrapolation of Learning Curves

S.Shota
May 12, 2017

論文紹介:Speeding up Automatic Hyperparameter Optimization of Deep Neural Networks by Extrapolation of Learning Curves

2017/05/12の論文紹介ゼミで使用したスライドです.
論文:T. Domhan, J. T. Springenberg, and F. Hutter,
“Speeding up Automatic Hyperparameter Optimization of Deep Neural Networks by Extrapolation of Learning Curves,”
Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015) (2015)

http://ml.informatik.uni-freiburg.de/papers/15-IJCAI-Extrapolation_of_Learning_Curves.pdf

S.Shota

May 12, 2017
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  21. • ͕༩͑ΒΕͨͱ͖ɼ ͕ Λ௒͑Δ
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    View Slide


  22. ࠷ߴਫ਼౓ ͱ͢Δʢ ͷॳظ஋͸ ʣ
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  23. •ظ଴஋͸࣍ࣜͰۙࣅɿ
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    •%//ͷ܇࿅Λ(16Ͱߦ͍ͬͯΔؒʹɼ
    .$.$ʹΑΔαϯϓϦϯά͸$16Ͱ
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    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    4QFFEJOHVQ)ZQFSQBSBNFUFS 0QUJNJ[BUJPO
    E
    [
    ym | y
    1:
    n
    ]
    ⇡ 1
    S
    S
    X
    s=
    1
    f
    comb(
    m | ⇠S
    )

    View Slide


  24. •͍͔ͭ͘ͷ%//Ϟσϧɼσʔληοτ
    ʹ͍࣮ͭͯݧ
    •༻͍ΔϋΠύʔύϥϝʔλ࠷దԽख๏͸
    ͭʢ4."$ͱ51&ʣ
    •ϞσϧͱϋΠύʔύϥϝʔλ࠷దԽख๏
    Λ૊Έ߹Θ࣮ͤͯݧ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    &YQFSJFODF

    View Slide


  25. •࢖༻͢Δσʔληοτ
    • $*'"3
    • $*'"3
    • ./*45
    •%//ͷ࣮૷͸$BGGFΛ࢖༻
    • (16ͭͷΈ࢖༻
    •ϋΠύʔύϥϝʔλ࠷దԽͷ࣮૷͸
    )10-*#Λ࢖༻
    •.$.$ͷ࣮૷͸&.$&&Λ࢖༻
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    &YQFSJNFOUBM4FUVQ
    Ұൠը૾ೝࣝͷσʔληοτ
    खॻ͖਺ࣈͷσʔληοτ

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  26. •શͯͷ࣮ݧͰ͖͍͠஋ ͸ʹઃఆ
    •QSFEJDUJWFUFSNJOBUJPODSJUFSJPO͸ɼ
    ΤϙοΫ͝ͱʹ࣮ߦ
    •ςετσʔλʹΑΔධՁ͸Ϟσϧ͝ͱʹ
    ઃఆ
    • શ݁߹ωοτϫʔΫɿ
    • ৞ΈࠐΈωοτϫʔΫɿ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    &YQFSJNFOUBM4FUVQ
    k = 10
    k = 2

    View Slide


  27. •$*'"3Ͱ͸લॲཧΛ࣮ߦ
    • Yͷখ͞ͳը૾ΛϥϯμϜͰऔΓग़͠ɼ
    ॏ৺ݸͷLNFBOTΛ࣮ߦ
    • $*'"3ͷ֤ը૾Λ֤ॏ৺Ͱ৞ΈࠐΈɼ
    ը૾ͷԠ౴ΛฏۉԽ
    • ͜ͷ݁ՌΛωοτϫʔΫʹೖྗ
    •ϋΠύʔύϥϝʔλͷ୳ࡧճ਺͸ճ
    •࠷େΤϙοΫ਺͸ΤϙοΫ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    'VMMZ$POOFDUFE/FUXPSLT

    View Slide


  28. •./*45͸લॲཧͳ͠
    • ҰճͷωοτϫʔΫͷ܇࿅ʹ͸d෼
    •ϋΠύʔύϥϝʔλͷ୳ࡧճ਺͸߹ܭ
    ճ·Ͱ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    'VMMZ$POOFDUFE/FUXPSLT

    View Slide


  29. •֬཰తޯ഑߱Լ๏͸.PNFOUVN4(%
    Λ࢖༻
    •ֶश཰͸࣍ࣜͰεέδϡʔϦϯά
    • ͱ൒ݮظ͔Β ͕ܾఆ
    • ൒ݮظΛϋΠύʔύϥϝʔλͱͯ͠࠾༻
    •׆ੑԽؔ਺͸3F-6ʢதؒ૚ʣͱ
    4PGUNBYʢग़ྗ૚ʣΛ࢖༻
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    %//)ZQFSQBSBNFUFST
    ↵t = ↵0
    (1 + t) p
    p

    View Slide


  30. •֤ύϥϝʔλͷ
    ఆٛҬͱॳظ஋
    •ܾఆ໦ϕʔεͷ
    ࠷దԽ๏ͳΒ͹
    ੍໿͖ͭͷ
    ࠷దԽ΋Մೳ
    • Ϣχοτ਺ͳͲ
    ͸ϨΠϠʔ਺ʹ
    ґଘ͢Δ
    ύϥϝʔλ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    %//)ZQFSQBSBNFUFST

    View Slide


  31. •ϋΠύʔύϥϝʔλ࠷దԽث͝ͱʹ
    ϥϯμϜͳγʔυͰճ࣮ݧ
    •ճͷςετΤϥʔͷฏۉͱඪ४ภࠩΛ
    ՄࢹԽ
    •4."$ɼ51&ͷͲͪΒΛ࢖ͬͯ΋ɼ
    ఏҊख๏ͳ͠ʹൺ΂ͯ໿ഒͷߴ଎Խ
    • ఏҊख๏ͳ͠Ͱ࣌ؒޙͷੑೳͱ
    ఏҊख๏͋ΓͰ࣌ؒޙͷੑೳ͕ಉ͡
    •࠷ऴతͳςετΤϥʔ͸4."$͕࠷খ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPSQSFQSPDFTTFE$*'"3

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  32. •ςετΤϥʔͱܦա࣌ؒͷਪҠ
    •&BSMZ4UPQQJOHWTఏҊख๏
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPSQSFQSPDFTTFE$*'"3

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  33. •֤छख๏Ͱݟ͚ͭͨ࠷ྑͷϞσϧʹ
    ର͢ΔςετΤϥʔͷൺֱ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPSQSFQSPDFTTFE$*'"3

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  34. •ఏҊख๏ͳ͋͠ΓͰͷֶशۂઢͷ༷ࢠ
    •ੑೳ͕ѱ͍ͱ͖͸ૣ͘ଧͪ੾ΒΕ͍ͯΔ
    ͜ͱ͕Θ͔Δ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPSQSFQSPDFTTFE$*'"3

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  35. •$*'"3Ͱͷ݁ՌΛ౿·͑ɼϋΠύʔ
    ύϥϝʔλ࠷దԽث͸4."$Λ࢖༻
    •࣮ݧճ਺͸ճ
    •ఏҊख๏ͳ͠Ͱ4."$Λ࢖ͬͨ৔߹ͱ
    ൺֱͯ͠ɼ໿ͷ࣌ؒͰಉ͡ੑೳΛ
    ୡ੒
    • QSFEJDUJWFUFSNJOBUJPODSJUFSJPOʹΑΔ
    ߴ଎Խ͕༗ޮ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUGPS./*45

    View Slide


  36. •4."$ͷΈ WTఏҊख๏4."$
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUGPS./*45

    View Slide


  37. •৞ΈࠐΈχϡʔϥϧωοτͰͷ࣮ݧ
    •$*'"3ɼ$*'"3Λ࢖༻
    • ͲͪΒ΋ന৭Խͷલॲཧ
    •ଞͷ$//Ϟσϧ͸σʔλΛͦͷ··
    ࢖༻
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    4NBMM$POWPMVUJPOBM/FVSBM/FUXPSLT

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  38. •৞ΈࠐΈ૚ͷ͋ͱʹશ݁߹૚ΛೖΕͳ͍
    ϞσϧΛ࢖༻
    • ৞ΈࠐΈ૚ͷΧʔωϧαΠζ͸Y
    •৞ΈࠐΈ૚ͷޙʹ͸ϓʔϦϯά૚Λૠೖ
    • NBYQPPMJOHΛ࣮ߦ
    • ϓʔϦϯά૚ͷ૚਺͸࠷దԽͷର৅
    •Ұճͷ܇࿅͸෼Ͱऴྃ͢Δখ͞ͳ
    Ϟσϧ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    4NBMM$//)ZQFSQBSBNFUFST

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  39. •ϋΠύʔύϥϝʔλͷఆٛҬͱॳظ஋
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    4NBMM$//)ZQFSQBSBNFUFST

    View Slide


  40. •4."$ɼ51&ͰͦΕͧΕճ࣮ͣͭݧ
    •ϋΠύʔύϥϝʔλͷ୳ࡧճ਺͸ճ
    •࠷େΤϙοΫ਺͸ΤϙοΫ
    •ςετΤϥʔͷฏۉΛൺֱ͢Δͱɼ
    4."$͕51&ΑΓ΋एׯྑ͍݁Ռ
    • 4."$ɿœ
    • 51&ɿœ ˋ
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  41. •4."$ͷΈ WTఏҊख๏4."$ B

    •ఏҊख๏ʹΑΓதஅ͞Εֶͨशɿ C

    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  42. •࠷ྑͷϋΠύʔύϥϝʔλʹ͓͚Δ
    ςετΤϥʔͷൺֱ
    • ϕʔεϥΠϯ͕
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  43. •$*'"3Ͱͷ݁ՌΛ౿·͑ɼ
    4."$ͷΈΛ࢖༻
    •࣮ݧճ਺͸ճ
    •ϋΠύʔύϥϝʔλͷ୳ࡧճ਺͸ճ
    ·Ͱ
    •ఏҊख๏ͳ͠ͱൺֱͯ͠ɼ
    ಉ͡ςετΤϥʔʹୡ͢Δ଎͕͞໿ഒ
    •ςετσʔλʹର͢Δਪఆਫ਼౓΋޲্
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  44. •4."$ͷΈ WTఏҊख๏4."$
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  45. •࠷ྑͷϋΠύʔύϥϝʔλʹ͓͚Δ
    ςετΤϥʔͷൺֱ
    • ϕʔεϥΠϯ͕
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS4NBMM$//TPO$*'"3

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  46. •࠷ઌ୺ͷϞσϧͱͷൺֱ
    •$*'"3σʔληοτΛ࢖༻
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    -BSHF$POWPMVUJPOBM/FUXPSLT

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  47. •ଟ͘ͷϋΠύʔύϥϝʔλͷఆٛҬ͸
    5BCMFʹै͏
    •࢖༻͢ΔϞσϧ͸"MM$//ϕʔε
    • ͨͩ͠ϓʔϦϯά૚͸௥Ճͷ৞ΈࠐΈ૚ʹ
    มߋ
    • ௥Ճͷ৞ΈࠐΈ૚ͷετϥΠυ͸
    •৞ΈࠐΈ૚ͷΧʔωϧαΠζ͸Yʹ
    มߋ
    •ग़ྗ૚ͷલʹ΋৞ΈࠐΈ૚
    ࿦จ঺հɿ4QFFEJOHVQ"VUPNBUJD)ZQFSQBSBNFUFS0QUJNJ[BUJPOPG%FFQ
    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    -BSHF$//)ZQFSQBSBNFUFST

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  48. •4."$ͷΈΛ࢖༻
    •࣮ݧ͸ճ
    •࠷େΤϙοΫ਺͸ΤϙοΫ
    •ϋΠύʔύϥϝʔλͷ୳ࡧճ਺͸ճ
    •σʔλ֦ுͳ͠Ͱൺֱͨ͠ͱ͜Ζ
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    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    3FTVMUTGPS-BSHF$//TPO$*'"3

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  49. •࠷ઌ୺ͷωοτϫʔΫͱͷςετΤϥʔ
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    3FTVMUTGPS-BSHF$//TPO$*'"3

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  50. •ੑೳ͕վળ͠ͳ͍͜ͱΛࣗಈతʹݕ஌͠
    ϋΠύʔύϥϝʔλͷධՁΛૣظऴྃ͢
    Δख๏ΛఏҊ
    •ఏҊख๏ʹΑΓ%//ʹ͓͚ΔϋΠύʔ
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    •ϋΠύʔύϥϝʔλ࠷దԽثʹґଘ
    ͠ͳ͍ख๏Ͱɼͭͷख๏ͷͲͪΒͱ΋
    ߴ଎ԽΛ࣮ݱ
    •$*'"3ʹ͓͍ͯ࠷ઌ୺ͷ݁Ռ
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    /FVSBM/FUXPSLTCZ&YUSBQPMBUJPOPG-FBSOJOH$VSWFT
    $PODMVTJPO

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