Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Optunaによる多目的最適化
Search
Yoshihiko Ozaki
June 29, 2021
Research
5
3.5k
Optunaによる多目的最適化
Optuna Meetup #1 での発表資料です。
Yoshihiko Ozaki
June 29, 2021
Tweet
Share
Other Decks in Research
See All in Research
言語モデルの内部機序:解析と解釈
eumesy
PRO
32
13k
Weekly AI Agents News! 2月号 アーカイブ
masatoto
1
110
AWS 音声基盤モデル トーク解析AI MiiTelの音声処理について
ken57
0
170
한국어 오픈소스 거대 언어 모델의 가능성: 새로운 시대의 언어 이해와 생성
inureyes
PRO
0
260
サーブレシーブ成功率は勝敗に影響するか?
vball_panda
0
600
Zipf 白色化:タイプとトークンの区別がもたらす良質な埋め込み空間と損失関数
eumesy
PRO
8
1.5k
IM2024
mamoruk
0
250
さくらインターネット研究所 アップデート2025年
matsumoto_r
PRO
0
430
チュートリアル:Mamba, Vision Mamba (Vim)
hf149
6
3.2k
博士学位論文予備審査 / Scaling Telemetry Workloads in Cloud Applications: Techniques for Instrumentation, Storage, and Mining
yuukit
1
1.8k
公立高校入試等に対する受入保留アルゴリズム(DA)導入の提言
shunyanoda
0
310
ベイズ的方法に基づく統計的因果推論の基礎
holyshun
0
920
Featured
See All Featured
How To Stay Up To Date on Web Technology
chriscoyier
790
250k
Build The Right Thing And Hit Your Dates
maggiecrowley
34
2.6k
Building a Scalable Design System with Sketch
lauravandoore
462
33k
Unsuck your backbone
ammeep
670
57k
Six Lessons from altMBA
skipperchong
27
3.7k
Intergalactic Javascript Robots from Outer Space
tanoku
270
27k
Embracing the Ebb and Flow
colly
85
4.6k
Speed Design
sergeychernyshev
28
860
The Web Performance Landscape in 2024 [PerfNow 2024]
tammyeverts
4
490
Visualization
eitanlees
146
15k
Optimising Largest Contentful Paint
csswizardry
35
3.2k
Being A Developer After 40
akosma
90
590k
Transcript
OptunaʹΑΔଟత࠷దԽ Optuna Meetup #1 2021/06/26 ඌ࡚ Յ 1
ඌ࡚ Յ • ॴଐ • άϦʔגࣜձࣾʗ࢈ۀٕज़૯߹ݚڀॴਓೳηϯλʔ • ࠷ۙͷݚڀ • Ozaki,
Y., Tanigaki, Y., Watanabe, S., & Onishi, M. (2020). Multiobjective tree-structured parzen estimator for computationally expensive optimization problems. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference (pp. 533-541). • Ozaki, Y., Suzuki, Y., Hawai, T., Saito, K., Onishi, M., & Ono, K. (2020). Automated crystal structure analysis based on blackbox optimisation. npj Computational Materials, 6(1), 1-7. • ඌ࡚Յ, ଜক, & େਖ਼ً. (2020). ػցֶशʹ͓͚ΔϋΠύύϥϝʔλ࠷దԽख๏: ֓ཁͱಛ . ిࢠใ௨৴ֶձจࢽ D, 103(9), 615-631. 2
࣍ • ͡Ίʹɿଟత࠷దԽ • Optunaɿଟత࠷దԽख๏ • Optunaɿଟత࠷దԽؔ࿈ػೳ • ·ͱΊ 3
͡Ίʹɿଟత࠷దԽ 4
ଟత࠷దԽ • త࠷దԽ • ಉ࣌ʹ࠷దԽ͞ΕΔ ݸͷత͕ؔଘࡏ͢Δ • ྫɿాۭߓ 㱺 ϑϥϯΫϑϧτؒͷҠಈϓϥϯ
• ✔ Ҡಈ࣌ؒͷ࠷খԽ 㱻 ✔ අ༻ͷ࠷খԽʢ2ͭͷతτϨʔυΦϑͷؔʣ m m 5
ଟత࠷దԽ • త࠷దԽ • ಉ࣌ʹ࠷దԽ͞ΕΔ ݸͷత͕ؔଘࡏ͢Δ m m తۭؒ (f1
(x), f2 (x)) ୈ2తɿf2 (x) ୈ1తɿf1 (x) 2త࠷খԽ Minimize/Maximize subject to ɿ ൪ͷతؔ ɿܾఆม ɿ࣮ߦՄೳྖҬ f1 (x), f2 (x), …, fm (x) x ∈ X fi (x) i x X ୳ࡧۭؒ X x1 x2 ࣸ૾ 6
ଟత࠷దԽ • ଟత࠷దԽͰɼ୯Ұͷ࠷దղҰൠʹଘࡏ͠ͳ͍ • ଞͷҙͷղʹ༏ӽ͞Εͳ͍શͯͷղͷू߹ΛύϨʔτηοτͱݺͼ ύϨʔτηοτͷతۭؒͰͷ૾ΛύϨʔτϑϩϯτͱݺͿ ύϨʔτϑϩϯτ ྉۚ Ҡಈ࣌ؒ 2తʢҠಈ࣌ؒɼྉۚʣ࠷খԽ
༏ӽؔ • ABΛ༏ӽ͢Δ • AͱCൺֱෆՄೳͷؔ ଟత࠷దԽΛղ͘ͱύϨʔτηοτ ΛٻΊΔʢۙࣅ͢Δʣ͜ͱ 7
Optunaɿଟత࠷దԽख๏ 8
Optunaͱଟత࠷దԽɿػցֶशʹ͓͚ΔԠ༻ • λεΫ • Hyperparameter Optimization • Neural Architecture Search
• తؔ • Ϟσϧਫ਼ • ϞσϧαΠζʢɼফඅిྗʣ https://arxiv.org/abs/2105.01015 9
ଟత࠷దԽख๏ • ݱࡏOptunaͰར༻Մೳͳख๏ • ਐԽܕଟత࠷దԽɿNSGA-II • ଟతϕΠζ࠷దԽɿMOTPEɼqEHVI (integration.botorch) 10
ਐԽܕଟత࠷దԽ • ਐԽܭࢉΛ༻͍Δ͜ͱͰɼύϨʔτϑϩϯτΛۙࣅ͢Δղू߹ΛҰ ͷ࣮ߦͰಉ࣌ʹ֫ಘ͢Δ͜ͱΛతͱͨ͠ख๏ 11
• ղͷ༏ྼΛɼඇ༏ӽϥϯΫʹجͮ͘ऩଋੑɼࠞࡶڑʹجͮ͘ଟ༷ੑ ͷ؍͔Βܾఆ͠ɼ༏ΕͨղΛݩʹ࣍ੈͷݸମΛੜ NSGA-II (Deb et al., 2002) ඇ༏ӽϥϯΫɿ༏ӽ͞Ε͍ͯͳ͍ղΛRank 1ͱͯͦ͜͠
͔Βॱʹऩଋੑʢ༏ӽؔʣʹԠͯ͡ϥϯΫ͕ܾ·Δ ࠞࡶڑɿྡΓ߹͏ݸମؒͷϚϯϋολϯڑͱͯ͠ ܭࢉ͞ΕΔʢ ʣɼ྆ʹ͍ͭͯ ͱଋ͢Δ a + b ∞ 12
Optunaʹ͓͍ͯ NSGA-IIΛ͏ import optuna def objective(trial): x = trial.suggest_float("x", 0,
5) y = trial.suggest_float("y", 0, 3) v0 = 4 * x ** 2 + 4 * y ** 2 v1 = (x - 5) ** 2 + (y - 5) ** 2 return v0, v1 # objectiveશͯͷతؔΛฦ͢ # NSGAIISamplerΛ͏ sampler = optuna.samplers.NSGAIISampler(seed=1234) study = optuna.create_study( sampler=sampler, directions=["minimize", "minimize"] ) study.optimize(objective, n_trials=250) 13
ଟతϕΠζ࠷దԽ • తؔ୳ࡧۭؒʹ͍ͭͯϕΠζతͳϞσϧΛߏங͠ɼ֫ಘؔͱ ݺΕΔج४Λ༻͍ͯ༗ͳղΛޮతʹαϯϓϧ͢Δख๏ • తؔΛϞσϧԽɿຆͲͷଟతϕΠζ࠷దԽख๏ • ୳ࡧۭؒΛϞσϧԽɿMOTPE 14
MOTPE (Ozaki et al., 2020) • Optunaͷ୯త࠷దԽʹ͓͚Δඪ४ΞϧΰϦζϜͰ͋ΔTPEΛଟత ࠷దԽʹ֦ுͨ͠ͷ • Ϟσϧ୳ࡧۭؒͷ༗ɾඇ༗ͳղʹ͍ͭͯΧʔωϧີਪఆ
༗ ඇ༗ ୳ࡧۭؒʹ͓͍ͯରԠ͢Δ༗ͳղͷू߹ʹ ͍ͭͯΧʔωϧີਪఆ ୳ࡧۭؒʹ͓͍ͯରԠ͢Δඇ༗ͳղͷू߹ʹ ͍ͭͯΧʔωϧີਪఆ 15
MOTPE (Ozaki et al., 2020) • ࣍ʹධՁ͢ΔղExpected Hypervolume Improvement (EHVI)
֫ಘؔʹΑܾͬͯΊΔ • ू߹ ʹ ΛՃ͑ͨͱ͖ͷϋΠύϘϦϡʔϜ૿ՃྔͷظʹରԠɼ͜ΕΛ࠷େԽ͢Δ Λ࠾༻ • ࣮༗ɾඇ༗ྖҬͷ֬ີΛ ɼ ͱͨ͠ͱ͖ɼ ͕Γཱͭ EHVIY* (x) := ∫ max(IH (Y* ∪ {y}) − IH (Y*),0)p(y ∣ x)dy Y* y = f(x) x l(x) g(x) argmaxx EHVI(x) = argmaxx l(x)/g(x) Y r • ϋΠύϘϦϡʔϜ ʹଐ͢ΔϕΫτϧͱࢀর ʹғ·ΕͨྖҬ ͷମੵʢփ৭෦ʣ • ύϨʔτϑϩϯτମੵΛ࠷େԽ͢Δ Y r 16
Optunaʹ͓͍ͯ MOTPEΛ͏ ... # MOTPESamplerʹมߋ͢Δ͚ͩ sampler = optuna.samplers.MOTPESampler(seed=1234) study =
optuna.create_study( sampler=sampler, directions=["minimize", “minimize"] ) study.optimize(objective, n_trials=250) 17
ൺֱɿNSGA-IIͱMOTPE ؆୯ͳͰ͋ΕͲͪΒͰ͙͢ղ͚Δ 18
ൺֱɿNSGA-IIͱMOTPE • ऩଋMOTPEͷํ͕͍ ʢAutoML͖ʣ ͖ͬ͞ΑΓ͍͠ʢධՁճ250ʣ 19
ൺֱɿNSGA-IIͱMOTPE • ऩଋMOTPEͷํ͕͍ ʢAutoML͖ʣ • MOTPEධՁճʹݶք͋Γ ʢNSGA-IIزΒͰʣ MOTPE1000ճͰ15-20ఔɼଞͷଟత ϕΠζ࠷దԽख๏ʢPESMOSMS-EGOʣΑΓ ѹతʹ͍͕NSGA-IIͱൺΔͱʹͳΒͳ͍
20
ൺֱɿNSGA-IIͱMOTPE • ऩଋMOTPEͷํ͕͍ ʢAutoML͖ʣ • MOTPEධՁճʹݶք͋Γ ʢNSGA-IIزΒͰʣ • ७ਮͳࢄ࠷దԽNSGA-II͕ Α͍ʢMOTPEہॴղʹऩଋʣ
0-1φοϓαοΫʢ2త࠷େԽʣ 21
Optunaɿଟత࠷దԽؔ࿈ػೳ 22
ՄࢹԽ • ࢄਤ • (Parallel coordinate) ... sampler = optuna.samplers.MOTPESampler(seed=1234)
study = optuna.create_study(sampler=sampler, directions=["minimize", "minimize"]) study.optimize(objective, n_trials=250) # plotlyϕʔεͷՄࢹԽ fig = optuna.visualization.plot_pareto_front(study) fig.show() # matplotlibϕʔεͷՄࢹԽ optuna.visualization.matplotlib.plot_pareto_front( study ) plt.show() 23
ධՁ • ϋΠύϘϦϡʔϜ ... # ϋΠύϘϦϡʔϜܭࢉ͍ؔ·ͷͱ͜Ζ։ൃऀ͚API # কདྷతʹoptuna/_hypervolume/wfg.pyʹҠಈ͞ΕΔ༧ఆ wfg =
optuna.multi_objective._hypervolume.WFG() reference_point = np.array([3, 5]) trials = study.trials hvs = [] for i in range(1, len(trials) + 1): vector_set = np.array( [t.values for t in trials[:i]] ) hvs.append( wfg.compute(vector_set, reference_point) ) plt.style.use(“ggplot") plt.xlabel("Number of valuations") plt.ylabel("Hypervolume") plt.plot(range(1, len(hvs) + 1), hvs) plt.show() 24
·ͱΊ • ଟత࠷దԽύϨʔτ࠷దղͷू߹Λ֫ಘ͢Δ͜ͱ͕ඪ • OptunaਐԽܕଟత࠷దԽͱଟతϕΠζ࠷దԽͷ2λΠϓͷख๏Λఏڙ • લऀ൚༻తɼNSGA-IIͦͷ࠷දతͳख๏Ͱ20ؒͷ࣮͕͋Δ • ޙऀAutoML͖ɼMOTPEϋΠύύϥϝʔλ࠷దԽख๏TPEͷଟత൛ •
Optunaͷଟత࠷దԽؔ࿈ػೳΛհ • ଟత࠷దԽɼ୯త࠷దԽʹൺͯ׆༻ࣄྫ։ൃऀগͳ͍ɼࠓճΛ ͖͔͚ͬʹϢʔβ։ൃऀ͕૿͑Δͱخ͍͠ 25