Ingantacciyar Haɗin Kai na Tushen Hankali don Hakar Ma'adinai na Son Kai a Blockchain: Hanyar Tsarin Shawarar Markov

Teburin Abubuwan Ciki

1. Gabatarwa

Fasahar Blockchain, duk da cewa ta kawo sauyi ga tsarin rikodin da ba shi da cibiyar gudanarwa mai aminci, tana fuskantar barazanar ci gaba ga amincinta. Hakar ma'adinai na son kai, wani nau'i na hari inda masu hakar ma'adinai suka haɗa kai (tafkin maras gaskiya) suka ɓoye sabbin tubalan da aka hako don samun fa'idar riba mara adalci, yana wakiltar babban aibi. An fara ƙirƙira samfurinsa a hukumance ta Eyal da Sirer (2014), hakar ma'adinai na son kai yana lalata adalcin Yarjejeniyar Tabbatar da Aiki (PoW). Wannan takarda ta gabatar da sabuwar hanyar ƙirƙira da inganta dabarun maharin ta amfani da ka'idar ingantacciyar haɗin kai ta tushen hankali a cikin tsarin Tsarin Shawarar Markov (MDP). Babban manufa ita ce samun mafi kyawun manufar ci gaba da ke da alaƙa da blockchain don tafkin hakar ma'adinai maras gaskiya, wanda ya wuce dabarun ƙayyadaddun ƙayyadaddun bayanai.

2. Hanyoyi & Tsarin Aiki

Binciken ya kafa ingantaccen samfurin lissafi don nazarin mu'amalar dabarun tsakanin tafkin hakar ma'adinai mai gaskiya da maras gaskiya.

2.1. Samfurin Tafkin Hakar Ma'adinai & Ma'auni na Gasa

An ƙirƙiri tafkunan hakar ma'adinai guda biyu tare da ma'auni daban-daban na gasa:

• Tafkin Gaskiya: Yana bin daidaitaccen ma'aunin gasa na jagorantar tubalan biyu, yana watsa tubalan nan da nan bayan gano su.
• Tafkin Maras Gaskiya: Yana amfani da gyare-gyaren ma'aunin jagorantar tubalan biyu wanda manufar da ke da alaƙa da blockchain ke jagoranta. Wannan manufar tana bayyana lokacin da za a saki tubalan da aka ɓoye bisa ga yanayin blockchain na jama'a, yana haifar da dabarun hari masu ƙarfi.

2.2. Tsarin Ci Gaba na Lokaci Mai Ci Gaba na Tushen Manufa

Juyin halittar yanayin tsarin an kama shi ta hanyar tsarin ci gaba na lokaci mai ci gaba na Markov wanda sauye-sauyen sauyinsa ke tasiri kai tsaye ta hanyar zaɓaɓɓen manufar da ke da alaƙa da blockchain na tafkin maras gaskiya. Sararin yanayin yawanci ya haɗa da masu canji kamar tsayin reshen sirri na tafkin maras gaskiya da tsayin reshen jama'a.

2.3. Ka'idar Ingantacciyar Haɗin Kai ta Tushen Hankali

Maimakon binciken manufa mai ƙarfi, takardar tana amfani da ingantacciyar haɗin kai ta tushen hankali (wanda Cao ya fara, 2007). Wannan ka'idar tana ba da gradients (hankali) na ma'auni na aiki (kamar matsakaicin ribar dogon lokaci) dangane da sigogin manufa. Wannan yana ba da damar ingantaccen ingantaccen haɗin kai na tushen gradient don nemo sigogin manufa waɗanda ke haɓaka ladan tafkin maras gaskiya.

3. Nazarin Ka'idoji & Sakamako

Cibiyar nazari na takardar ta tabbatar da mahimman kaddarorin tsarin da aka ƙirƙira.

3.1. Haɓakawa & Mafi Kyawun Matsakaicin Ribar Dogon Lokaci

Marubutan sun yi nazarin yadda matsakaicin ribar dogon lokaci na tafkin maras gaskiya $J(\theta)$ ke canzawa tare da sigar ladan da ke da alaƙa da blockchain $\theta$. Sun kafa kaddarorin haɓakawa, suna tabbatar da cewa a ƙarƙashin wasu sharuɗɗa, $J(\theta)$ aiki ne na haɓakawa na $\theta$. Wannan yana da mahimmanci saboda yana sauƙaƙa neman mafi kyawun; idan $J(\theta)$ yana haɓaka yadda ya kamata, mafi kyawun manufa yana kan iyakar saitin sigogi mai yuwuwa.

3.2. Tsarin Mafi Kyawun Manufar da ke da Alaƙa da Blockchain

Babban gudunmawar shine siffantar tsarin mafi kyawun manufa. Nazarin ya tabbatar da cewa mafi kyawun manufa ba aikin sabani ba ne amma yana da takamaiman sifa, tsari—sau da yawa manufar tushen kofa. Misali, mafi kyawun aiki (saki ko ɓoyewa) ya dogara da ko jagorancin sirri na tafkin maras gaskiya ya wuce mahimmin kofa $\theta^*$, wanda aka samo ta hanyar nazari. Wannan ya yi daidai da kuma gama fahimtar daga binciken hakar ma'adinai na son kai na tushen MDP kamar Sapirshtein et al. (2016).

4. Cikakken Fahimta & Ra'ayi na Manazarta

Cikakken Fahimta: Wannan takarda ba wani samfurin hakar ma'adinai na son kai kawai ba ce; taƙaitaccen littafin jagora na mai sayar da makamai ne ga mahara. Ta hanyar amfani da ingantacciyar haɗin kai ta tushen hankali ga samfurin MDP, tana canza hakar ma'adinai na son kai daga wani yunƙuri na tunani zuwa matsala mai ƙima, mafi kyawun sarrafawa. Gaskiyar nasara ita ce tsara harin a matsayin manufa mai ƙarfi da ke da alaƙa da yanayin jama'a na blockchain, wanda ya wuce dabarun "ɓoye har sai X ya jagoranci". Wannan yana ɗaga samfurin barazana sosai.

Kwararar Ma'ana: Marubutan sun fara da ingantaccen samfurin Eyal-Sirer amma nan da nan suka juya zuwa hangen nesa na sarrafawa. Sun ayyana sararin aiki mai ƙima (manufar da ke da alaƙa da blockchain), suna ƙirƙirar tsarin a matsayin tsarin Markov da aka sarrafa, sannan suka yi amfani da nazarin hankali—kayan aiki daga kimanta aikin tsarin rikitattun—don samun gradients. Wannan sarkar ma'ana (Samfur → Ƙididdigar Sarrafawa → Gradient Aiki → Ingantawa) tana da kyau kuma mai ƙarfi. Yana kama da hanyoyin da ake amfani da su wajen inganta cibiyoyin jijiyoyi masu zurfi, inda baya-bayan baya ke ba da gradients don sabunta nauyi. A nan, "ma'auni" su ne sigogin manufa.

Ƙarfi & Kurakurai: Babban ƙarfi shine ƙwararrun hanyoyi. Yin amfani da ingantacciyar haɗin kai ta tushen hankali a cikin MDP hanya ce mai inganci kuma mai inganci fiye da hanyoyin siminti mai nauyi ko ƙarfi da aka gani a cikin aikin farko kamar Gervais et al. (2016). Yana ba da ba kawai amsa ba amma shugabanci don ingantawa (gradient). Duk da haka, aibin takardar shine tsarkakarsa ta zahiri. Kamar yawancin takardun tattalin arzikin sirri na ka'idoji, yana aiki a cikin sauƙaƙaƙƙen samfurin—tafkuna biyu, takamaiman ayyukan lada. Yana wucewa daga rikitattun duniya na gaske: jinkirin yaduwar cibiyar sadarwa (wani muhimmin abu kamar yadda aka lura a cikin ainihin takardar Eyal & Sirer), kasancewar tafkunan marasa gaskiya masu gasa da yawa, ko saurin canzawa zuwa Tabbatar da Hannun jari (PoS) inda hakar ma'adinai na son kai ba shi da mahimmanci. Kwatanta shi da hanyar gwaji da siminti na "Rarraba Mai Gabatarwa da Gina Ethereum" bincike ya nuna gibin tsakanin ka'ida da aiki.

Fahimta Mai Aiki: Ga masu ƙirƙira ƙa'idodi, wannan takarda alama ce ja. Tana nuna cewa mahara na iya inganta dabarunsu bisa tsari. Tsaron dole ne ya samo asali daga nazari mai tsayi zuwa ƙirar tsari mai ƙarfi wanda ke da ƙarfi a kan irin waɗannan ingantattun manufofin. Haɗa abubuwan da ke ƙara "hayaniya" ko rashin tsayawa ga samfurin maharin zai iya zama hanawa. Ga manazartan tsaro, tsarin manufar da aka samo (mai yuwuwa tushen kofa) yana ba da sa hannun yatsa. Ana iya horar da tsarin gano abin da ba a saba gani ba don neman tsarin yaduwar ma'amala da tubalan da suka dace da wannan mafi kyawun sa hannun yatsa na dabarun, ra'ayi mai kama da gano tsarin adawa a cikin tsaron AI. Filin dole ne ya motsa daga hana hakar ma'adinai na son kai zuwa gano mafi kyawun, aiwatar da shi mai ƙarfi.

5. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Babban samfurin lissafi ya haɗa da ayyana sararin yanayi, sararin aiki, da lada don MDP.

Sararin Yanayi ($S$): Yanayi $s \in S$ ana iya bayyana shi azaman $(a, h)$, inda:

• $a$: Tsayin reshen sirri da tafkin maras gaskiya (maharin) ke riƙe.
• $h$: Tsayin reshen jama'a da aka sani ga cibiyar sadarwa mai gaskiya.

Jagorancin dangi shine $l = a - h$.

Sararin Aiki ($A$): Ga tafkin maras gaskiya, aikin a yanayi $s$ an ƙaddara shi ta hanyar manufar da ke da alaƙa da blockchain $\pi_\theta(s)$. Misali na al'ada shine manufar kofa: $$\pi_\theta(s) = \begin{cases} \text{Saki} & \text{idan } l \geq \theta \\ \text{Ɓoye} & \text{in ba haka ba} \end{cases}$$ Anan, $\theta$ shine sigar manufa da za a inganta.

Ma'aunin Aiki: Manufar ita ce haɓaka matsakaicin ribar dogon lokaci (lada a kowace raka'a lokaci) na tafkin maras gaskiya: $$J(\theta) = \lim_{T \to \infty} \frac{1}{T} E\left[ \int_0^T r(s(t), \pi_\theta(s(t))) dt \right]$$ inda $r(\cdot)$ shine aikin lada na nan take, wanda ya haɗa da ladan tubala da kuɗin ma'amala.

Nazarin Hankali: Mahimmin abu shine ƙididdige abin da aka samo na aiki (gradient) $\frac{dJ(\theta)}{d\theta}$. Ta amfani da sakamako daga ingantacciyar haɗin kai ta tushen hankali na tsarin Markov, wannan gradient sau da yawa ana iya bayyana shi cikin sharuddan rarraba tsayayyen tsarin da aikin "ƙarfin aiki" mai suna, yana ba da damar hawan gradient: $\theta_{sabo} = \theta_{tsoho} + \alpha \frac{dJ}{d\theta}$.

6. Tsarin Nazari: Misalin Hali

Hali: Yi la'akari da sauƙaƙaƙƙen samfurin inda manufar tafkin maras gaskiya ta bayyana ta hanyar kofa ɗaya $\theta$ don jagorancinsa na sirri $l$.

Aikace-aikacen Tsarin:

1. Ƙirƙira Samfurin: Gina sarkar Markov mai ci gaba na lokaci. Jihohi ne biyu $(a,h)$. Canje-canje suna faruwa saboda abubuwan gano tubalan ta kowane tafki (tare da ƙimar daidai da ƙarfin hash ɗin su). Aikin "Saki" a wani yanayi yana sake saita jagorancin sirri, yana haifar da canjin yanayi.
2. Ƙididdigar Sigogi: Manufar ita ce $\pi_\theta$: Saki idan $l \geq \theta$.
3. Ƙididdigar Hankali: Don $\theta$ da aka bayar, ƙididdige rarraba yuwuwar tsayayye $\boldsymbol{\pi}(\theta)$ na sarkar Markov da ƙimar lada mai alaƙa $J(\theta)$. Ta amfani da dabarar hankali, kimanta $\frac{dJ}{d\theta}$ a $\theta$ na yanzu.
4. Madauki na Ingantawa:

   Fara θ (misali, θ=2)
   Saita ƙimar koyo α
   don juzu'i a cikin kewayon (matsakaicin juzu'i):
       Yi kwaikwayo/Ƙididdige J(θ) da dJ/dθ
       θ = θ + α * (dJ/dθ)  # Hawan Gradient
       idan an cika ma'aunin haɗuwa:
           karya
   Mafi Kyawun Kofa θ* = θ

5. Sakamako: Algorithm ɗin yana haɗuwa zuwa mafi kyawun kofa $\theta^*$. Nazarin ka'idojin takardar zai tabbatar da cewa ga wannan samfurin, $J(\theta)$ yana da siffa ɗaya, yana tabbatar da cewa hawan gradient yana samun mafi kyawun duniya.

Wannan tsarin yana nuna yadda maharin zai iya bincika tsarin mafi riba na ɓoyewa bisa tsari.

7. Hangar Aikace-aikace & Hanyoyin Gaba

Aikace-aikace Nan da Nan:

• Samfurin Barazana Mai Ci Gaba: Binciken tsaron blockchain na iya amfani da wannan tsarin don gwada ƙa'idodin yarjejeniya a kan mahara masu dabarun ingantacciyar, ba kawai waɗanda ba su da hankali ba.
• Ƙirar Tsari: A cikin ƙirƙirar sabbin ƙa'idodin yarjejeniya ko gyara waɗanda suke (misali, gyaran kasuwar kuɗi na Ethereum), masu haɓakawa na iya amfani da wannan nazarin hankali a baya don nemo sigogin da ke rage ladan $J(\theta)$ ga kowace manufa mai yuwuwar son kai, yana sa ƙa'idar ta fi ƙarfi.

Hanyoyin Bincike na Gaba:

• Ƙari na Wakilai Da Yawa & Wasan Ka'idoji: Samfurin na yanzu yana ɗauka tafkin maras gaskiya ɗaya da tafkin gaskiya ɗaya. Mataki na gaba shine ƙirƙirar tafkunan dabarun da yawa a cikin daidaiton wasan ka'idoji (misali, amfani da Wasannin Markov), kama da nazarin a "A kan Kwanciyar Hankali na Hakar Ma'adinai na Tafkuna Da Yawa a Blockchain" (Rogers, 2023).
• Haɗawa da Layer na Cibiyar Sadarwa: Haɗa ingantattun samfuran yaduwar cibiyar sadarwa da hare-haren kusufin rana cikin sararin yanayi zai sa samfurin ya fi dacewa.
• Bayan PoW: Daidaita tsarin ingantacciyar haɗin kai ta tushen hankali don nazarin yuwuwar hare-haren ƙarfi a cikin tsarin Tabbatar da Hannun jari (PoS), kamar mafi kyawun ɓoyewa na mai tabbatarwa ko dabarun mai gabatarwa da yawa, babban iyaka ne.
• Haɗa Koyon Injina: Haɗa wannan tsarin nazari tare da Koyon Ƙarfafawa Mai Zurfi (DRL). Gradient na hankali zai iya jagoranci ko fara zafi ga wakilin DRL, yana taimaka masa ya koyi mafi kyawun manufofin hari a cikin sararin yanayi mai rikitarwa wanda ya wuce iyawar nazari.

8. Nassoshi

1. Cao, X. R. (2007). Koyo da Ingantawa na Stochastic: Hanyar Tushen Hankali. Springer.
2. Eyal, I., & Sirer, E. G. (2014). Yawancin ba isa ba: Hakar Bitcoin yana da rauni. A cikin taron kasa da kasa kan ilimin lissafin kuɗi da tsaron bayanai (shafi na 436-454). Springer.
3. Gervais, A., Karame, G. O., Wüst, K., Glykantzis, V., Ritzdorf, H., & Capkun, S. (2016). A kan tsaro da aikin tabbatar da aikin blockchain. A cikin Proceedings na 2016 ACM SIGSAC taron kan tsaro na kwamfuta da sadarwa (shafi na 3-16).
4. Li, Q. L., Ma, J. Y., & Chang, Y. (2021). Hakar Ma'adinai na Son Kai a Blockchain: Hanyar Tsarin Markov Pyramid. [Takardar Tsarin Markov Pyramid].
5. Sapirshtein, A., Sompolinsky, Y., & Zohar, A. (2016). Mafi kyawun dabarun hakar ma'adinai na son kai a cikin bitcoin. A cikin Taron Kasa da Kasa kan Lissafin Kuɗi da Tsaron Bayanai (shafi na 515-532). Springer.
6. Rogers, A. (2023). A kan Kwanciyar Hankali na Hakar Ma'adinai na Tafkuna Da Yawa a Blockchain. Journal of Cryptoeconomic Systems, 1(2). [Tunani mai yiwuwa don nazarin tafkuna da yawa].
7. Buterin, V., et al. (2022). Rarraba Mai Gabatarwa da Gina Ethereum: Nazarin Kwaikwayo. Binciken Ethereum. [Misalin bincike na gwaji/kwaikwayo].