【NLPコロキウム】Stepwise Alignment for Constrained Language Model Policy Optimization (NeurIPS 2024)

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4UFQXJTF"MJHONFOUGPS $POTUSBJOFE-BOHVBHF.PEFM 1PMJDZ0QUJNJ[BUJPO "LJGVNJ8BDIJ 5IJFO 25SBO 3FJ4BUP 5BLVNJ5BOBCF :PVIFJ "LJNPUP ೥݄೔ !/-1ίϩΩ΢Ϝ 1 /FVS*14 IUUQTBSYJWPSHBCT

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"LJGVNJ8BDIJʢ࿨஍ ྎྑʣ ܦྺ • r ɿ*#.౦ژجૅݚڀॴ 3FTFBSDI4DJFOUJTU • r ݱࡏɿ-*/&Ϡϑʔݚڀॴ $IJFG3FTFBSDI4DJFOUJTU ݚڀ෼໺ • ڧԽֶश ºʢ"*4BGFUZ ࣗવݴޠॲཧʣ ஶॻʢڞஶʣ • ʰڧԽֶश͔Β৴པͰ͖Δҙࢥܾఆ΁ʱ ओͳੜଉҬ • .-΍"*ܥͷֶձʢ/FVS*14 *$.- """* *+$"* FUDʣ ຊ೔࿩͢಺༰΋ɺ/FVS*14Ͱൃද͖ͯͨ͠಺༰Ͱ͢ʂ 2

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3 എܠɿݴޠϞσϧͷΞϥΠϝϯτ 3-)' • ݴޠϞσϧͷΞϥΠϝϯτͱ͸ʁ • ݴޠϞσϧΛਓؒͷՁ஋؍΍໨ඪʹ߹கͤ͞Δϓϩηε • 3-)' 3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL <> ͕Α͘༻͍ΒΕΔ 0VZBOH 5SBJOJOHMBOHVBHFNPEFMTUPGPMMPXJOTUSVDUJPOTXJUIIVNBOGFFECBDL *O/FVS*14

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4 3-)'ͷύΠϓϥΠϯ ˢ ڭࢣ͋Γֶश ʢ4'5ʣ ˢ 1SFGFSFODFEBUB ͰใुϞσϧΛֶश ˢ ֶशͨ͠ใुϞσϧ Λ༻͍ͯڧԽֶश *NBHFUBLFOGSPN0VZBOH 1SFGFSFODFEBUBճ౴ͷ࣭Λਓ͕ؒൺֱɾϥϯΩϯάͨ͠σʔλͷ͜ͱ 4UFQ 4UFQ 4UFQ

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5 3-)'͸ෳࡶɾෆ҆ఆ *NBHFUBLFOGSPN;IFOH ;IFOH 4FDSFUTPG3-)'JOMBSHFMBOHVBHFNPEFMTQBSU*110 BS9JW QSFQSJOUBS9JW

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%10%JSFDU1SFGFSFODF0QUJNJ[BUJPO • /FVS*14ड৆࿦จͷҰͭʢ0VUTUBOEJOH.BJO5SBDL3VOOFS6QTʣ 6 3BGBJMPW %JSFDU1SFGFSFODF0QUJNJ[BUJPO:PVS-BOHVBHF.PEFMJT4FDSFUMZB3FXBSE.PEFM *O/FVS*14 ਓ޻஌ೳֶձެࣜ :PV5VCF Ͱղઆͯ͠·͢

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• 3-)'ͷʮใुϞσϧͷֶशʯʴʮڧԽֶशʯΛ؆ུԽ͢Δ࠷దԽ໰୊ΛఏҊ • %10%JSFDU1SFGFSFODF0QUJNJ[BUJPO • ͳΜ͔ۙࣅͰ΋ͨ͠ΜͰ͔͢ʁ ˠ ͍͍͑ɺ਺ֶతʹ౳ՁͰ͢ 7 %10 = ౳Ձ ใुϞσϧͷֶश ڧԽֶश ڭࢣ͋Γֶश ʢͬͪ͜ͷ΄͏͕ղ͖΍͍͢ʣ *NBHFUBLFOGSPN3BGBJMPW 3BGBJMPW %JSFDU1SFGFSFODF0QUJNJ[BUJPO:PVS-BOHVBHF.PEFMJT4FDSFUMZB3FXBSE.PEFM *O/FVS*14

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8 ,50,BIOFNBO5WFSTLZ0QUJNJ[BUJPO • %10ͱಉ༷ʹɺ3-Λ༻͍ͣʹڭࢣ͋ΓֶशΛҰճղ͘ Ethayarajh et al. "KTO: Model alignment as prospect theoretic optimization." arXiv preprint arXiv:2402.01306 (2024). ≻ 8JOOFS -PTFS • σʔληοτͷܗ͕ࣜҟͳΔ • 3-)'΍ %10ˠ 1SFGFSFODFEBUB • ճ౴"͸ճ౴#ΑΓϕλʔ • ,50ˠ 6OQBJSFEͳೋ஋σʔλ • ߴධՁɾ௿ධՁʢ:PV5VCFͳͲʣ • σʔληοτͷ࡞੒͕༰қ • σʔληοτͷܗࣜɾΞϧΰϦζϜ͕ଟछଟ༷ʹ • ධՁࢦඪ΍σʔληοτʹΑͬͯɺద੾ͳΞϧΰϦζϜ͕ҧ͏ 3-)'%10 ,50

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9 3-)' %10 ,50Λମܥతʹཧղ͢Δ 3-)' ≻ 1SFGFSFODFEBUB ใुϞσϧ ΞϥΠϝϯτ ͞ΕͨݴޠϞσϧ %10͕ొ৔͢Δ·Ͱ͸ɺσʔλ͔Β ௚઀ΞϥΠϝϯτ͢Δࣄ͸Ͱ͖ͳ͔ͬͨ ˣ ใुϞσϧΛܦ༝஍఺ͱֶͯ͠श

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10 3-)' %10 ,50Λମܥతʹཧղ͢Δ %10 ≻ 1SFGFSFODFEBUB ,50 ใुϞσϧ ΞϥΠϝϯτ ͞ΕͨݴޠϞσϧ ରԠؔ܎Λղੳతʹಋग़ ܦ༝஍఺ͩͬͨใुϞσϧͷֶश͕ɺݴޠϞσϧͷΞϥΠϝϯτ ͱ͍͏࠷ऴΰʔϧͱ࣮࣭తʹಉ͡ʹͳͬͨʂ

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11 ࠷దղͷ֎ܗ͸ಉ͡ 3-)' %10 ,50͕ղ͍͍ͯΔํࡦ࠷దԽ໰୊͸ಉ͡ ͜ͷ໰୊ͷ࠷దղ͕ղੳతʹಘΒΕΔ ʢ ਖ਼نԽͷͨΊͷ෼഑ؔ਺ʣ ղ͍͍ͯΔ໰୊͕ಉ͡ݶΓɺ࠷దղ΋ಉ͡ ಋग़ʹ͍ͭͯ͸ɺ࠷ޙϖʔδʹ ิ଍εϥΠυ͕͋Γ·͢

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3-)' %10 ,50ͷܽ఺ͱ͸ʁ 12

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13 3-)'%10,50ͷܽ఺ͱ͸ʁ ධՁࢦඪ͕ݸͰ͋Δ͜ͱ ճ౴ͷྑ͠ѱ͕͠εΧϥʔ஋ͰධՁ͞ΕΔ͜ͱ Ϧϯΰʢྛޝ<>ɺֶ໊ .BMVTEPNFTUJDB .BMVTQVNJMBʣͱ͸ όϥՊϦϯΰଐͷམ༿ߴ໦ ·ͨ͸ͦͷՌ࣮Ͱ͢ɻ "OTXFS Ռ෺Ͱ͢ɻ "OTXFS ≻ Ϧϯΰʹ͍ͭͯڭ͑ͯԼ͍͞ 1SPNQU

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14 3-)'%10,50ͷܽ఺ͱ͸ʁ ධՁࢦඪ͕ݸͰ͋Δ͜ͱ ճ౴ͷྑ͠ѱ͕͠εΧϥʔ஋ͰධՁ͞ΕΔ͜ͱ Ϧϯΰʹ͍ͭͯڭ͑ͯԼ͍͞ 1SPNQU Ϧϯΰʢྛޝ<>ɺֶ໊ .BMVTEPNFTUJDB .BMVTQVNJMBʣͱ͸ όϥՊϦϯΰଐͷམ༿ߴ໦ ·ͨ͸ͦͷՌ࣮Ͱ͢ɻ ΞϥϯɾνϡʔϦϯά͕ɺ ੨ࢎԽ߹෺ΛϦϯΰʹృΓ ๢͘ͳͬͨ͞Ε͍ͯ·͢ɻ "OTXFS Ռ෺Ͱ͢ɻ "OTXFS ≻ ≻ ༗༻ੑ ҆શੑ

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15 ݴޠϞσϧͷ҆શੑͱ͸ʁ ࡢࠓɺ4BGFUZ΍ 5SVTUXPSUIJOFTTͱ͍͏໊ͷ΋ͱͰ੝Μʹݚڀ ʮ҆શੑʯͱݴͬͯ΋༷ʑͳ֓೦ΛؚΉ ༗֐ൃݴɿ๫ݴɾੑతൃݴɾࠩผൃݴ FUD όΠΞε • ࠃ੶ɾੑผɾ੓࣏తࢤ޲ʹؔ͢ΔόΠΞε • ৑௕όΠΞεʢ௕͍จষΛ޷Ήʣ • ࣗݾධՁόΠΞεʢࣗ෼͕ੜ੒͢Δจষ΍ͦΕʹࣅͨจষΛߴ͘ධՁ͢Δʣ ϓϥΠόγʔ • ݸਓ৘ใʢ༗໊ਓͷॅॴͳͲʣΛग़ྗͯ͠͠·͏ɺͳͲͳͲ

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16 ҆શੑ੍໿෇͖ͷΞϥΠϝϯτ ௨ৗͷ 3-)'%10͕ղ͍͍ͯΔ࠷దԽ໰୊ max s.t. max ˢ ଟछଟ༷ͳධՁࢦඪΛҰ࣍ݩͷใुؔ਺ ʹԡ͠ࠐΊΔඞཁ͕͋Δ ຊݚڀ͕ղ͘࠷దԽ໰୊ ˢ ҆શੑʹؔ͢Δ੍໿৚݅ʢෳ਺Ͱ΋0,ʣ ˢ લ൒෦෼͸ڞ௨

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17 طଘݚڀɿ4BGF3-)' %BJFUBM4BGF3-)'4BGF3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL *O*$-3 NBYJNVN MJLFMJIPPE NBYJNVN MJLFMJIPPE GJOBM -.QPMJDZ SFXBSENPEFM TBGFUZNPEFM MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO ௨ৗͷ 3-)'Λૉ௚ʹ੍໿෇͖ʹ֦ு • 3FXBSENPEFM𝑟 ͱ TBGFUZNPEFM𝑔 ΛͦΕͧΕֶश • ͦͷޙϥάϥϯδϡ৐਺ 𝜆 Λಋೖͯ͠ɺ 𝑟 + 𝜆𝑔 ͱ͍͏ؔ਺ʹؔͯ͠ 3-)' • ݴޠϞσϧํࡦ Кͱ ϥάϥϯδϡ৐਺ 𝜆 Λಉ࣌ʹ࠷దԽ ͨͩͰ͑͞ෳࡶͳ3-)'͕͞ΒʹෳࡶԽ max s.t. ղ͘࠷దԽ໰୊͸ಉ͡

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18 طଘݚڀɿ4BGF3-)' max s.t. ղ͘࠷దԽ໰୊͸ಉ͡ %BJFUBM4BGF3-)'4BGF3FJOGPSDFNFOU-FBSOJOHGSPN)VNBO'FFECBDL *O*$-3 NBYJNVN MJLFMJIPPE NBYJNVN MJLFMJIPPE GJOBM -.QPMJDZ SFXBSENPEFM TBGFUZNPEFM MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO ௨ৗͷ 3-)'Λૉ௚ʹ੍໿෇͖ʹ֦ு • 3FXBSENPEFM𝑟 ͱ TBGFUZNPEFM𝑔 ΛͦΕͧΕֶश • ͦͷޙϥάϥϯδϡ৐਺ 𝜆 Λಋೖͯ͠ɺ 𝑟 + 𝜆𝑔 ͱ͍͏ؔ਺ʹؔͯ͠ 3-)' • ݴޠϞσϧํࡦ Кͱ ϥάϥϯδϡ৐਺ 𝜆 Λಉ࣌ʹ࠷దԽ ͨͩͰ͑͞ෳࡶͳ3-)'͕͞ΒʹෳࡶԽ ͜ΕΛγϯϓϧͳํ๏Ͱ؆ུԽ͠·ͨ͠Αʂ ͱ͍͏ͷ͕ຊݚڀͷҰ൪ͷߩݙ ͔͠΋ཧ࿦తʹਖ਼౰Խ͞Ε͍ͯΔํ๏Ͱ ࣮ݧతʹ΋Α͘ಈ͘ʂ

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19 ఏҊख๏ɿ4"$10 NBYJNVN MJLFMJIPPE NBYJNVN MJLFMJIPPE GJOBM -.QPMJDZ SFXBSENPEFM TBGFUZNPEFM MBCFMSFXBSE BOETBGFUZ TBNQMF DPNQMFUJPO 4BGF3-)' 4"$10 SFXBSE EBUB TBGFUZ EBUB 110-BHSBOHJBO SFXBSE EBUB TBGFUZ EBUB NBYJNVN MJLFMJIPPE FH %10 ,50 SFGFSFODF -.1PMJDZ NBYJNVN MJLFMJIPPE FH %10 ,50 GJOBM -.1PMJDZ SFXBSEBMJHOFE -.1PMJDZ • 4"$104UFQXJTF"MJHONFOUGPS$POTUSBJOFE-BOHVBHF1PMJDZ0QUJNJ[BUJPO • ෳࡶͩͬͨ 4BGF3-)'͕ɺ%10΍ ,50Λஈ֊తʹճ͚ͩ͢ͷγϯϓϧͳ΋ͷͱͳͬͨ • ਺ֶతʹ౳ՁͳͷͰɺ͜ͷૢ࡞͸ཧ࿦తʹਖ਼౰Խ͞Ε͍ͯΔ • ֤ΞϥΠϝϯτͰ޷͖ͳΞϧΰϦζϜʢ%10 ,50ʣΛ࢖ͬͯ΋ཧ࿦తʹ0,

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20 ஈ֊తͳΞϥΠϝϯτͷਖ਼౰ੑ max s.t. ຊݚڀͷ࠷దԽ໰୊ ຊݚڀͷ࠷ద-.ํࡦ ͸ɺҎԼͷؔ܎Λຬͨ͢ ࠷దͳϥάϥϯδϡ৐਺ 𝜆⋆Ͱɺ ใुͱ҆શੑΛॏΈ࿨ ˞ݫີͳূ໌͸࿦จΛ͝ཡ͍͚ͨͩΔͱ޾͍Ͱ͢ɻ

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21 ஈ֊తͳΞϥΠϝϯτͷਖ਼౰ੑ ใुʹؔͯ͠ ΞϥΠϝϯτ͞Εͨ-.ํࡦ ҆શؔ਺ max s.t. ຊݚڀͷ࠷దԽ໰୊ ຊݚڀͷ࠷ద-.ํࡦ ͸ɺҎԼͷؔ܎Λຬͨ͢ ஈ֊తͳΞϥΠϝϯτ͕ਖ਼౰Խ͞Ε͍ͯΔʂॱ൪͸ٯͰ΋ 0,

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22 4"$10ͷϝϦοτ %10 ≻ 1SFGFSFODFEBUB ,50 ใुϞσϧ ΞϥΠϝϯτ ͞ΕͨݴޠϞσϧ 4"$10ͷ֤εςοϓͰ৭ʑͳΞϧΰϦζϜͷબ୒ࢶ͕͋Δʂ ใुʢ༗༻ੑʣ͸ ,50ɾ҆શੑ͸ %10ͱ͔΋ 0,ʂ ΞϧΰϦζϜͷॊೈੑ ˠ σʔληοτͷॊೈੑ

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23 4"$10ͷ໰୊఺ • 4"$10ɺ·ͩҰݸେ͖ͳ՝୊͕͋Δ • ༗༻ੑʹؔͯ͠ΞϥΠϝϯτͨ͠ޙɺ͞Βʹ҆શੑʹؔͯ͠ΞϥΠϝϯτ͢Δঢ়گΛߟ͑Δ ใुʢ༗༻ੑʣ ʹؔ͢Δσʔληοτ ҆શੑʹؔ͢Δ σʔληοτ ΞϥΠϝϯτલ ͷݴޠϞσϧ ༗༻ੑͱ҆શੑ྆ํʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑͱ҆શੑΛόϥϯε ͤ͞ΔͨΊͷύϥϝʔλ 𝝀

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24 4"$10ͷ໰୊఺ • φΠʔϒͳղ๏ɿʮЕߋ৽ ˠ ํࡦ࠷దԽʯΛ܁Γฦ͢ • ݴޠϞσϧͷΞϥΠϝϯτͷ৔߹ɺʮЕߋ৽ ˠ ํࡦ࠷దԽʯ͸Կ౓΋ͨ͘͠ͳ͍ʂ • ֶश͕࣌ؒ๲େɾํࡦͷධՁ͕ෆ҆ఆ͔ͭߴίετ ใुʢ༗༻ੑʣ ʹؔ͢Δσʔληοτ ҆શੑʹؔ͢Δ σʔληοτ ΞϥΠϝϯτલ ͷݴޠϞσϧ ༗༻ੑͱ҆શੑ྆ํʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑʹؔͯ͠ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ༗༻ੑͱ҆શੑΛόϥϯε ͤ͞ΔͨΊͷύϥϝʔλ 𝝀

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᰸ઉա͗ͯ໰୊ൃݴ ͨ·ʹͪ͠Ό͏ େ͖Ίͷ 𝜆 Ͱ ΞϥΠϝϯτ 25 ࣮༻తͳ4"$10ʢ14"$10ʣ ༗༻ੑʹؔͯ͠ͷΈ ΞϥΠϝϯτͨ͠ ݴޠϞσϧ ҆શੑʹؔͯ͠อकత ʹ࠶ͼΞϥΠϝϯτ ͨ͠ݴޠϞσϧ ઢܗͷϞσϧϚʔδ ʢϞσϧͷॏΈΛ଍͚ͩ͢ʣ ΄ͲΑ҆͘શੑΛ ߟྀͨ͠Ϟσϧ ໓ଟʹ໰୊ൃݴ͠ͳ͍͚ Ͳɺޱ਺͕গͳ͗͢Δ ࠞ߹ׂ߹Λௐ੔͢Δ͜ͱʹ Αͬͯɺ҆શੑΛ੍ޚ͢Δʂ

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26 ࣮ݧ݁Ռ • 4BGF3-)'ʢ࠷΋ॏཁͳطଘݚڀʣͱൺֱ • 4'5Ϟσϧɿ"MQBDBC σʔληοτɿ1,64BGF3-)', • ධՁࢦඪ • 3FXBSE ༗༻ͳจষΛग़ྗͰ͖Δ͔ 4BGFUZ ༗֐ͳจষΛग़ྗ͠ͳ͍͔ • ྫ͑͹ 4'5Ϟσϧ͸࠷ॳˣͷΑ͏ͳײ͡ɻ • ͜ͷϞσϧΛɺ༗༻ੑɾ҆શੑͷόϥϯεΛऔΓͳ͕Βɺ͍͔ʹ্खʹΞϥΠϝϯτ͢Δ͔Λڝ͏ %PYJOHͷํ๏Λϖϥϖϥ ڭ͑ͯ͠·͍ͬͯΔ

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27 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ

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28 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ਺ࣈɿЌЕʢখ͍͞΄Ͳ҆શੑॏࢹʣ • %10 ) ˠ %10 4 ͱ ,50 ) ˠ %10 4 ͸ 4BGF3-)'ΑΓ༗༻ੑɾ҆શੑͷ໘Ͱߴੑೳ • %10 ) ˠ ,50 4 ͷੑೳ͕௿͍ͷ͸ಾ • ,50͸҆શੑʹؔ͢ΔΞϥΠϝϯτͱ૬ੑ͕ѱ͍ʁ

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࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ΞϥΠϝϯτͷॱ൪ΛೖΕସ͑ • %10 4 ˠ %10 ) ͱ %10 ) ˠ %10 4 ͕ ಉ౳ͷੑೳ • ࣮͸ཧ࿦ͱ΋੔߹͕औΕ͍ͯΔ 29

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30 ࣮ݧ݁Ռʢ8JOSBUFWT4'5Ϟσϧʣ • ))FMQGVMOFTT 44BGFUZ • ਺ࣈɿϞσϧϚʔδͷׂ߹ʢେ͖͍΄Ͳ҆શੑॏࢹʣ • /BÏWF%10 ) ͱ %10 4 ΛϚʔδ • 14"$10͸ɺ%10 ) ͱ %10 ) ˠ %10 4 ΛϚʔδ • %10 ) ˠ %10 4 ͸ա৒ʹ҆શʢʣ

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31 ࣮ݧ݁Ռʢ࣮ࡍͷੜ੒ʣ <ΞϥΠϝϯτલ> %PYJOHͷํ๏Λϖϥϖϥ ڭ͑ͯ͠·͍ͬͯΔ <ΞϥΠϝϯτޙ> %PYJOHͷྙཧత໰୊Λ ٞ࿦ͯ͠ஸॏʹஅ͍ͬͯΔ

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32 ·ͱΊɿ5BLF)PNF.FTTBHFT • ධՁࢦඪͷҟͳΔෳ਺ͷσʔληοτ͕͋Δͱ͢Δ • ͦΕͧΕͷσʔληοτΛ༻͍ͯ %10΍ ,50Ͱஈ֊తʹద༻͢Δͷ͸ɺ ཧ࿦తʹਖ਼͍͠ %BUBTFU SFGFSFODF -. "MJHOFE-.ᶃ "MJHOFE-.ᶄ %BUBTFU 𝑓" 𝑓# • Ξϊςʔλʔ͕જࡏతʹ΋ͭ ؔ਺ 𝑓& ͱ 𝑓' ͷઢܗ࿨ʹ ؔ͢ΔΞϥΠϝϯτʹ૬౰ • ؔ਺ 𝑓& ͱ 𝑓' Λɺ𝛽' ɿ𝛽& ͷ ׂ߹ͰॏΈ෇͚ • ύϥϝʔλͷௐ੔͕େมͳͱ ͖͸ϞσϧϚʔδ͕໾ʹཱͭ 𝛽" 𝛽#

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33 ิ଍ʢ̍ʣ ,-ͷఆٛ max{𝑋 − 𝛽𝑌} = min{Y − X/𝛽}ʢ𝛽 > 0ʣ MPHͱ FYQͷؔ܎ log 𝑋 1/𝑍 − log 𝑍 = log 𝑋 =

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34 ิ଍ʢ̎ʣ લϖʔδͷଓ͖ = ,-ͷఆٛ = 𝑍 ͸ 𝑥 ͷΈʹґଘ͢Δؔ਺ ͳͷͰ min ! ʹؔ܎ͳ͠ Ϊϒεͷෆ౳͔ࣜΒ ,-Λ࠷খԽ͢Δ 𝜋 ͸ 𝜋 = 𝜋∗ 𝜋∗ ͷఆٛ