ฏΒ͞ͷ֬ೝ 8FJHIU-PTT-BOETDBQF ρ(w) = 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw (x′  ), yi ) ఢରతࣄྫΛϞσϧʹೖྗͨ͠߹ͷଛࣦҎԼͷΑ͏ʹఆࣜԽՄೳ ఢରతࣄྫΛೖྗ͢Δͱ͍͏ҙຯ ρ(w + αd) = 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw+αd (x′  ), yi ) ϞσϧͷॏΈͷपลͷଛࣦҎԼͷΑ͏ʹఆࣜԽՄೳ ύϥϝʔλʔXΛֶ࣋ͭशࡁΈϞσϧ ͞ЋํE͚ͩۙͷଛࣦ͕ܭࢉͰ͖Δ
ͷఆࣜԽ ॏΈͷۙͷଛࣦ͕ฏΒͰ͋ΔΑ͏ͳֶशʹ͍ͨ͠ argmin w max v∈ 𝒱 ρ(w + v) ۙʹ͓͚Δଛࣦͷ࠷େΛ ࠷খԽ͢ΔXΛݟ͚ͭΖ argmin w max v∈ 𝒱 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw+v (x′  ), yi ) ЛΛల։ ্ه͕ղ͚Εɺఢରతࣄྫʹؤ݈ͳX͕ಘΒΕΔͣ
ͷղ͖ํ *OQVU1FSUVSCBUJPO argmin w max v∈ 𝒱 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw+v (x′  ), yi ) ఢରతࣄྫΛೖྗ͢Δͱ͍͏ҙຯ ࠷ॳͷ࠷େԽطଘݚڀͱಉ͘͡ɺఢରతࣄྫͷೖྗΛҙຯ͢Δ จͰ༻͍͍ͯͨ1(%BUUBDLͷ߹ԼهͷY`Λೖྗ͢Εྑ͍ x′  i ← Πϵ (x′  i + η1 sign(∇x′  i ℓ(fw+v (x′  i ), yi )) ˞จʹ߹Θͤͨදهʹ͍ͯ͠Δɻ ૯ͷҙຯͰͳ͍ɻ
argmin w max v∈ 𝒱 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw+v (x′  ), yi ) ͷղ͖ํ 8FJHIU1FSUVSCBUJPO ॏΈʹઁಈΛՃ͑ͯ࠷ϞσϧΛѱ͍ͨ͘͠ ͭͷ࠷େԽXۙͰϞσϧGΛ࠷ѱ͘͢Δ͜ͱΛҙਤ 8VΒޯΛ༻͍ͯҎԼͷΑ͏ʹWΛࢉग़ v ← Πγ v + η2 ∇v 1 m ∑m i=1 ℓ(fw+v (x′  i ), yi ) ∇v 1 m ∑m i=1 ℓ(fw+v (x′  i ), yi ) ∥w∥ ˞จʹ߹Θͤͨදهʹ͍ͯ͠Δɻ ૯ͷҙຯͰͳ͍ɻ
ͷղ͖ํ ॏΈͷߋ৽ argmin w max v∈ 𝒱 1 n n ∑ i=1 max ∥x′  i −xi ∥p ≤ϵ ℓ(fw+v (x′  ), yi ) *OQVU1FSUVSCBUJPOͱ8FJHIU1FSUVSCBUJPOΛߦ্ͬͨͰɺ ௨ৗͷֶशͱಉ༷ʹόοΫϓϩοϓ͢Εྑ͍ ղܾ w ← w − η3 ∇w+v 1 m m ∑ i=1 ℓ(fw+v (x′  i ), yi ) *OQVU1FSUVSCBUJPOͱ8FJHIU1FSUVSCBUJPOΛ
ͷఆࣜԽ ॏΈͷۙͷଛࣦ͕ฏΒͰ͋ΔΑ͏ͳֶशʹ͍ͨ͠ argmin w max v∈ 𝒱 ρ(w + v) ۙʹ͓͚Δଛࣦͷ࠷େΛ ࠷খԽ͢ΔXΛݟ͚ͭΖ ۩ମతʹ w ← w − η3 ∇w+v 1 m m ∑ i=1 ℓ(fw+v (x′  i ), yi ) Ͱύϥϝʔλʔߋ৽Λߦ͍͍͑
"81ͷ࣮ BUUBDL@CBDLXBSEͰԿΛ͍ͬͯΔͷ͔ʁ Ϟσϧ Λอଘ fw ʹվม fw+v ޙʹCBDLXBSE͍ͯ͠Δͱ͍͏͜ͱ ∇w+v 1 m m ∑ i=1 ℓ( fw+v (xi ), yi ) 1 m m ∑ i=1 ℓ( fw+v (xi ), yi ) ΛಘΔ͜ͱʹͳΔ ˠॏΈXۙͰ ४ ࠷ѱͷଛࣦΛܭࢉ͍ͯ͠Δ