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New Insight of Variance reduce in Zero-Order Hard-Thresholding: Mitigating Gradient Error and Expansivity Contradictions

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Xinzhe Yuan (Harbin Institute of Technology), William de Vazelhes (Mohamed bin Zayed University of Artificial Intelligence), Bin Gu (Mohamed bin Zayed University of Artificial Intelligence, Jilin University), Huan Xiong (Harbin Institute of Technology, Mohamed bin Zayed University of Artificial Intelligence)

πŸ’‘ κ°œμš”

λ³Έ μ—°κ΅¬λŠ” $\ell_0$ μ œμ•½ μ΅œμ ν™” 문제 해결에 μ‚¬μš©λ˜λŠ” ν•˜λ“œ-μŠ€λ ˆμˆ„λ”© μ•Œκ³ λ¦¬μ¦˜μ—μ„œ 0μ°¨(ZO) 기울기 근사λ₯Ό μ‚¬μš©ν•  λ•Œ λ°œμƒν•˜λŠ” λΆ„μ‚°(variance) 문제λ₯Ό λ‹€λ£Ήλ‹ˆλ‹€. κΈ°μ‘΄ SZOHT μ•Œκ³ λ¦¬μ¦˜μ€ ZO 기울기의 νŽΈμ°¨μ™€ ν•˜λ“œ-μŠ€λ ˆμˆ„λ”© μ—°μ‚°μžμ˜ ν™•μž₯μ„± κ°„μ˜ 상좩 κ΄€κ³„λ‘œ 인해 랜덀 λ°©ν–₯의 μˆ˜μ— μ œμ•½μ΄ μžˆμ—ˆμŠ΅λ‹ˆλ‹€. λ³Έ 논문은 λΆ„μ‚° κ°μ†Œμ— λŒ€ν•œ μƒˆλ‘œμš΄ 관점을 μ œμ‹œν•˜κ³ , 이λ₯Ό 톡해 ZO κΈ°μšΈκΈ°μ™€ ν•˜λ“œ-μŠ€λ ˆμˆ„λ”© κ°„μ˜ κ³ μœ ν•œ μΆ©λŒμ„ μ™„ν™”ν•˜λŠ” μΌλ°˜ν™”λœ λΆ„μ‚° κ°μ†Œ ZO ν•˜λ“œ-μŠ€λ ˆμˆ„λ”© μ•Œκ³ λ¦¬μ¦˜μ„ μ œμ•ˆν•©λ‹ˆλ‹€.

πŸ”‘ μ‹œμ‚¬μ  및 ν•œκ³„

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μ œμ•ˆλœ μ•Œκ³ λ¦¬μ¦˜μ€ 랜덀 λ°©ν–₯ μˆ˜μ— λŒ€ν•œ μ œμ•½μ„ μ œκ±°ν•˜μ—¬ SZOHT λŒ€λΉ„ κ°œμ„ λœ 수렴 속도와 넓은 적용 κ°€λŠ₯성을 μ œκ³΅ν•©λ‹ˆλ‹€.
β€’
ZO 기울기 근사와 ν•˜λ“œ-μŠ€λ ˆμˆ„λ”© μ—°μ‚°μž κ°„μ˜ μΆ©λŒμ„ μ™„ν™”ν•˜λŠ” λΆ„μ‚° κ°μ†Œ λ©”μ»€λ‹ˆμ¦˜μ„ 톡해 더 μ•ˆμ •μ μΈ μ΅œμ ν™” μ„±λŠ₯을 κΈ°λŒ€ν•  수 μžˆμŠ΅λ‹ˆλ‹€.
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μ œμ•ˆλœ λ°©λ²•μ˜ 싀증적 νš¨μš©μ„±μ€ 릿지 νšŒκ·€ 및 λΈ”λž™λ°•μŠ€ μ λŒ€μ  곡격 λ¬Έμ œμ—μ„œ μž…μ¦λ˜μ—ˆμœΌλ©°, μ΄λŠ” μ‹€μ œ μ‘μš©μ—μ„œμ˜ 잠재λ ₯을 μ‹œμ‚¬ν•©λ‹ˆλ‹€.
β€’
(ν•œκ³„μ  λ˜λŠ” ν–₯ν›„ 과제) 아직 νƒμƒ‰λ˜μ§€ μ•Šμ€ 더 λ³΅μž‘ν•œ μ΅œμ ν™” λ¬Έμ œλ‚˜ λ‹€μ–‘ν•œ μ’…λ₯˜μ˜ μ œμ•½ 쑰건에 λŒ€ν•œ μ•Œκ³ λ¦¬μ¦˜μ˜ μΌλ°˜ν™” 및 μ„±λŠ₯ 검증이 ν•„μš”ν•©λ‹ˆλ‹€.
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