Group online adaptive learning
نویسندگان
چکیده
منابع مشابه
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Proof (of Lemma 1) The proof is by induction on t. For t = 1, we have˜W 1 = ˜ w 1 ([1, 1]) = 1. Next, we assume that the claim holds for any t ≤ t and prove it for t+1. Since |{[q, s] ∈ I : q = t}| ≤ log(t)+ 1 for all t ≥ 1, we have˜W t+1 = I=[q,s] ∈I˜w t+1 (I) = I=[t+1,s] ∈I˜w t+1 (I) + I=[q,s]∈I: q≤t˜w t+1 (I) ≤ log(t + 1) + 1 + I=[q,s]∈I: q≤t˜w t+1 (I) .
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Lemma 1. If ρ = 0, then Mt = M0 +M′t (∀t ≥ 1). When ρ > 0, then Mt = M ′ t (∀t ≥ 1). Proof. 1. Case ρ = 0: Since γt = 1 (∀t ≥ 1), thus Mt = M0 + ∑t i=1 Ni. We also have that ( i t 0 = 1 (∀i ≥ 1), and therefore M′t = ∑t i=1 Ni, which completes the proof. 2. Case ρ > 0: The proof proceeds by induction. • t = 1: In this case γ1 = 0, M1 = 0 × M0 + N1 = N1 and M′1 = N1, which proves that M1 = M ′ 1....
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ژورنال
عنوان ژورنال: Machine Learning
سال: 2017
ISSN: 0885-6125,1573-0565
DOI: 10.1007/s10994-017-5661-5