Let A be an algorithm that guarantees the following: If m m(e) then for every distribution...

 

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Let A be an algorithm that guarantees the following: If m m(e) then for every distribution D it holds that E [LD(A(S))] min LD (h) + . S~Dm hH Show that for every 8 = (0,1), if m m(d) then with probability of at least 18 it holds that LD (A(S)) minhH LD (h) + e. Hint: Observe that the random variable LD (A(S)) - minH LD (h) is nonnegative and rely on Markov's inequality. Let A be an algorithm that guarantees the following: If m m(e) then for every distribution D it holds that E [LD(A(S))] min LD (h) + . S~Dm hH Show that for every 8 = (0,1), if m m(d) then with probability of at least 18 it holds that LD (A(S)) minhH LD (h) + e. Hint: Observe that the random variable LD (A(S)) - minH LD (h) is nonnegative and rely on Markov's inequality.