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Byzantine Machine Learning: MultiKrum and an optimal notion of robustness

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  • Haebom
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์ €์ž

Gilles Bareilles, Wassim Bouaziz, Julien Fageot, El-Mahdi El-Mhamdi

๐Ÿ’ก ๊ฐœ์š”

๋ณธ ์—ฐ๊ตฌ๋Š” ๋ถ„์‚ฐ ํ•™์Šต ํ™˜๊ฒฝ์—์„œ ๋น„์ž”ํ‹ด ๊ณต๊ฒฉ์ž์— ๋Œ€ํ•œ ๊ฒฌ๊ณ ์„ฑ์„ ๋ณด์žฅํ•˜๋Š” ์ง‘๊ณ„ ๊ทœ์น™์ธ MultiKrum์˜ ์ด๋ก ์  ๋ณด์ฆ์ด ์—†๋‹ค๋Š” ํ•œ๊ณ„๋ฅผ ๊ทน๋ณตํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. ์ด๋ฅผ ์œ„ํ•ด ์ ๋Œ€์  ํ™˜๊ฒฝ์—์„œ์˜ ํ‰๊ท  ์ถ”์ • ์ •ํ™•๋„๋ฅผ ์ •๋Ÿ‰ํ™”ํ•˜๋Š” ์ƒˆ๋กœ์šด ๊ฐœ๋…์ธ ์ตœ์ ์˜ ๊ฒฌ๊ณ ์„ฑ ๊ณ„์ˆ˜ $\kappa^\star$๋ฅผ ๋„์ž…ํ•˜๊ณ , MultiKrum์˜ ๊ฒฌ๊ณ ์„ฑ ๊ณ„์ˆ˜์— ๋Œ€ํ•œ ์ƒํ•˜ํ•œ์„ ์ฆ๋ช…ํ•ฉ๋‹ˆ๋‹ค. ๊ทธ ๊ฒฐ๊ณผ MultiKrum์ด Krum๋ณด๋‹ค ๋” ๋‚˜์€ ๊ฒฌ๊ณ ์„ฑ์„ ๊ฐ€์ง€๋ฉฐ, ์‹ค์ œ ํ™˜๊ฒฝ์—์„œ๋„ ๋” ์šฐ์ˆ˜ํ•œ ์„ฑ๋Šฅ์„ ๋ณด์ž„์„ ์ด๋ก ์ ์œผ๋กœ ์ž…์ฆํ•ฉ๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

โ€ข
MultiKrum์€ ๊ธฐ์กด Krum๋ณด๋‹ค ํ–ฅ์ƒ๋œ ์ด๋ก ์  ๊ฒฌ๊ณ ์„ฑ ๋ณด์ฆ์„ ๊ฐ€์ง€๋ฉฐ, ์ด๋Š” ๋น„์ž”ํ‹ด ๊ณต๊ฒฉ์ด ์กด์žฌํ•˜๋Š” ๋ถ„์‚ฐ ํ•™์Šต ์‹œ์Šคํ…œ์˜ ์‹ ๋ขฐ์„ฑ์„ ๋†’์ด๋Š” ๋ฐ ๊ธฐ์—ฌํ•ฉ๋‹ˆ๋‹ค.
โ€ข
์ƒˆ๋กœ์šด ๊ฒฌ๊ณ ์„ฑ ๊ณ„์ˆ˜ $\kappa^\star$์˜ ๋„์ž…์€ ์ ๋Œ€์  ํ™˜๊ฒฝ์—์„œ์˜ ํ‰๊ท  ์ถ”์ • ๋Šฅ๋ ฅ์„ ๋” ์ •๋ฐ€ํ•˜๊ฒŒ ์ธก์ •ํ•˜๊ณ  ๋น„๊ตํ•˜๋Š” ์ƒˆ๋กœ์šด ํ”„๋ ˆ์ž„์›Œํฌ๋ฅผ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค.
โ€ข
์ œ์•ˆ๋œ ์ƒํ•˜ํ•œ์ด ํ•ญ์ƒ ์ตœ์ ๊ฐ’๊ณผ ์ผ์น˜ํ•˜์ง€ ์•Š์„ ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์‹คํ—˜์„ ํ†ตํ•ด ํ•˜ํ•œ์˜ ํ’ˆ์งˆ์„ ๋ณด์—ฌ์ฃผ์ง€๋งŒ, ์‹ค์ œ ํ™˜๊ฒฝ์—์„œ์˜ ์ตœ์ ์˜ ๊ฒฌ๊ณ ์„ฑ ๊ณ„์ˆ˜๋ฅผ ์ •ํ™•ํžˆ ๊ฒฐ์ •ํ•˜๊ธฐ ์œ„ํ•œ ์ถ”๊ฐ€์ ์ธ ์—ฐ๊ตฌ๊ฐ€ ํ•„์š”ํ•ฉ๋‹ˆ๋‹ค.
๐Ÿ‘