LFD Book Forum Impact of Alpha on PLA Converging
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#1
04-07-2012, 08:02 PM
 tcristo Member Join Date: Apr 2012 Posts: 23
Impact of Alpha on PLA Converging

Two of the questions (7 & 9) ask how many iterations it takes for the PLA to converge. I would expect this to be a function of both the size of N that was mandated as well as the alpha (learning rate) that is selected. Is this not correct?
#2
04-07-2012, 08:18 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Impact of Alpha on PLA Converging

Quote:
 Originally Posted by tcristo Two of the questions (7 & 9) ask how many iterations it takes for the PLA to converge. I would expect this to be a function of both the size of N that was mandated as well as the alpha (learning rate) that is selected. Is this not correct?
The PLA rule we use does not have a learning rate (or has a learning rate of 1 if you will). The size indeed affects the number of iterations, and the homework questions specify particular values for .
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#3
04-07-2012, 08:32 PM
 tcristo Member Join Date: Apr 2012 Posts: 23
Re: Impact of Alpha on PLA Converging

Quote:
 Originally Posted by yaser The PLA rule we use does not have a learning rate (or has a learning rate of 1 if you will). The size indeed affects the number of iterations, and the homework questions specify particular values for .
Thanks! I didn't realize that the learning rate wasn't present in the model you had discussed during the first lecture. I had previously run all my data at .5 so it will be interesting to see what the difference is when I set it to 1.
#4
04-08-2012, 12:25 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Impact of Alpha on PLA Converging

If you take a deeper look at the steps of the PLA algorithm, you'll find that setting the learning rate to any positive value gives you equivalent results (subject to the same random sequence and equivalent starting weights, of course). For instance, if you start with the zero vector, the final weights that you get for learning rate 1 are simply twice the final weights that you get for learning rate 0.5.
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#5
04-08-2012, 08:32 AM
 tcristo Member Join Date: Apr 2012 Posts: 23
Re: Impact of Alpha on PLA Converging

Quote:
 Originally Posted by htlin If you take a deeper look at the steps of the PLA algorithm, you'll find that setting the learning rate to any positive value gives you equivalent results (subject to the same random sequence and equivalent starting weights, of course). For instance, if you start with the zero vector, the final weights that you get for learning rate 1 are simply twice the final weights that you get for learning rate 0.5.
I agree. However, I wouldn't think that would necessarily result in halving the the number of iterations required to converge or result in the "best" answer.

I would expect that if your learning rate is too large it would be possible to "overshoot" the convergence values and therefore require some back and forth before they settle. Depending upon the extent of that oscillation it may or may not require more iterations than a smaller value.

I guess you could also say a similar thing about too small a learning value. It could slowly inch up to one possible set of convergence weight values and get stuck in a "local minima" of sorts without truly finding the "global minima".
#6
04-08-2012, 09:45 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601
Re: Impact of Alpha on PLA Converging

Quote:
 Originally Posted by tcristo I agree. However, I wouldn't think that would necessarily result in halving the the number of iterations required to converge or result in the "best" answer.
Hinted in my reply is that for PLA in particular, using any positive alpha gives you the same (equivalent) answer with exactly the same number of iterations. So convergence-wise, alpha doesn't affect PLA at all. Not necessarily true for other algorithms, of course.
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