An Optimal Agnostic PAC Algorithm
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TL;DR - A theoretical paper constructing a learner for agnostic PAC learning over hypothesis classes of finite VC dimension d that attains the statistically optimal excess-risk bound, closing the long-standing gap between upper and lower bounds up to universal constants.
- For a class $H\subseteq{-1,+1}^X$ with VC dimension $d\ge1$, the learner achieves, with probability $\ge 1-\delta$, $L(\widehat h)\le L^+7\cdot10^8\big(\sqrt{L^(d+\log(1/\delta))/n}+(d+\log(1/\delta))/n\big)$ from an i.i.d. sample of size $n$.
- The bound is "first-order"/optimistic: it interpolates between the fast $O((d+\log(1/\delta))/n)$ rate in the realizable case ($L^=0$) and the slow $\sqrt{\cdot/n}$ rate as $L^$ grows.
- The result settles agnostic PAC sample complexity up to universal constants at every fixed $L^*$, matching the lower bounds of Devroye, Györfi, and Lugosi (1996).
- The constant $7\cdot10^8$ is explicitly large, so the contribution is asymptotic/constant-factor optimality rather than practical tightness; no empirical results are claimed in the provided abstract.
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An Optimal Agnostic PAC Algorithm
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TL;DR - A theoretical paper constructing a learner for agnostic PAC learning over hypothesis classes of finite VC dimension d that attains the statistically optimal excess-risk bound, closing the long-standing gap between upper and lower bounds up to universal constants.
- For a class $H\subseteq{-1,+1}^X$ with VC dimension $d\ge1$, the learner achieves, with probability $\ge 1-\delta$, $L(\widehat h)\le L^+7\cdot10^8\big(\sqrt{L^(d+\log(1/\delta))/n}+(d+\log(1/\delta))/n\big)$ from an i.i.d. sample of size $n$.
- The bound is "first-order"/optimistic: it interpolates between the fast $O((d+\log(1/\delta))/n)$ rate in the realizable case ($L^=0$) and the slow $\sqrt{\cdot/n}$ rate as $L^$ grows.
- The result settles agnostic PAC sample complexity up to universal constants at every fixed $L^*$, matching the lower bounds of Devroye, Györfi, and Lugosi (1996).
- The constant $7\cdot10^8$ is explicitly large, so the contribution is asymptotic/constant-factor optimality rather than practical tightness; no empirical results are claimed in the provided abstract.