Suggest a procedure that agnostic PAC learns the problem with sample complexity of mH(_, δ), assuming that the loss function is bounded by 1.

1. Show that the resulting learning problem is convex-Lipschitz-bounded.

2. Show that no computable algorithm can learn the problem.

3. From Bounded Expected Risk to Agnostic PAC Learning: Let be an algorithm that guarantees the following: If ≥ mH(_) then for every distribution it holds that E SDm [LD(A(S))]≤ min hH LD(h)+_. _ Show that for every δ ∈ (01), if ≥ mH(_ δ) then with probability of at least 1−δ it holds that LD(A(S))≤ minhH LD(h)+_Hint: Observe that the random variable LD(A(S))−minhH LD(h) is nonnegative and rely on Markov’s inequality.

_ For every δ ∈ (01) let

mH(_, δ) = mH(_/2)_log2 (1)_+

 

log(4)+log(_log2 (1)_)

_2

 

. Suggest a procedure that agnostic PAC learns the problem with sample complexity of mH(_, δ), assuming that the loss function is bounded by 1. Hint: Let = _log2 (1)_. Divide the data into +1 chunks, where each of the first chunks is of size mH(_/2) examples. Train the first chunks using A. On the basis of the previous question argue that the probability that for all of these chunks we have LD(A(S))>minhH LD(h)+is at most 2−δ/2. Finally, use the last chunk as a validation set.

find the cost of your paper

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