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
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 ɹཧղͷͨΊʹແࢹͯ͠ྑ͍ɻ Π
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 ɹཧղͷͨΊʹແࢹͯ͠ྑ͍ɻ Π
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 ߦͬͨͱ͖ͷXͷޯ