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optimization-parameter-scaling [2017/11/13 09:57]
awf
optimization-parameter-scaling [2017/11/13 10:43] (current)
awf
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 So instead I far prefer to place some onus on you, the user of the routine. ​ Your job is this: So instead I far prefer to place some onus on you, the user of the routine. ​ Your job is this:
  
-> *Scale x so its values ​are "​around 1"*+**Scale x so its components ​are "​around 1"**
  
 This is actually pretty easy in practice.  ​ This is actually pretty easy in practice.  ​
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 But if you add 1e-5 seconds, it will probably change the objective by very little, maybe by 1e-12 gigawatts, and the optimizer will be in trouble. But if you add 1e-5 seconds, it will probably change the objective by very little, maybe by 1e-12 gigawatts, and the optimizer will be in trouble.
  
-Your days were a better choice (about 86400 times better), giving a change of 1e-7 GW when you add 1e-5 days (about a second).+Your first idea (do it in days) was actually ​a better choice (about 86400 times better), giving a change of 1e-7 GW when you add 1e-5 days (about a second). ​ Can we do even better?
  
-Ultimately you're probably anyway looking ​at terms in the objective ​which include the phase of the moon as+Well, look at how the parameter appears ​in the objective ​funciton. ​ For phase of the moon, that's normally in some term like:
  
-  ​cos(eta * phoon)^beta+$$  \cos(\eta * \mathtt{phoon})^\beta  $$
  
-so perhaps ​a range of 0..1/eta is sensible.   +so a sensible ​range might be to $2\pi/\eta$.   
-The point is just to think about how a change in phoon affects the objective.+The point is just to think about how a change in ''​phoon'' ​affects the objective.
  
 === But that's the easy case, what about dimensionless parameters? === === But that's the easy case, what about dimensionless parameters? ===
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 So.  In conclusion. ​ Think about the parameters, and try to keep them in sensible units. So.  In conclusion. ​ Think about the parameters, and try to keep them in sensible units.
 +
 +~~DISCUSSION~~