
#1




Problem 1.3 c
w(t)^2
= w(t1) + y(t1)x(t1)^2 < this is from the PLA iteration <=(w(t1) + y(t1)x(t1))^2 < a property: a + b <= a + b = w(t1)^2 + 2y(t1)w(t1)x(t1) + y(t1)^2x(t1)^2 = w(t1)^2 + 2y(t1)w(t1)x(t1) + x(t1)^2 Now, it seems like 2y(t1)w(t1)x(t1) is somehow <= 0. w(t1)x(t1) is >= 0 tho. hence, it seems like 2y(t1) is somehow <= 0. It seems like I am on the wrong track as I am not using the hint mentioned in the question at all. Any pointer? Thanks! 
#2




Re: Problem 1.3 c
This inequality a + b <= a + b is quite loose in general and you may want to consider not using it. Hope this helps.
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#3




Re: Problem 1.3 c
Hi,
I just revisited this problem again. If I substitute w(t1) with x(t1) with I could get and then use the hint to get the answer. However, the dimension of x and w can be more than 3. I just wonder whether there is a more generic proof. Thanks in advance. Last edited by henry2015; 06102016 at 02:38 AM. Reason: syntax error 
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