Solver loses track to histogram operations about cppad

[bradbell]

Are you trying, in some sense, to
minimize || y - f(x) || with respect x
where || * || is some measure of the difference between y and f(x) ?

[dreamwingc]

Not only to measure the difference, but also to calculate the differences into several bins, and the cost function is related to the bin vectors. This process is called histogram.

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On Thu, Dec 20, 2018 at 6:10 PM Brad Bell ***@***.***> wrote: Are you trying, in some sense, to minimize || y - f(x) || with respect x where || * || is some measure of the difference between y and f(x) ? — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#40 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AGZhmvW3xat72EhAGzNqYhcH41eoJZPvks5u7EMegaJpZM4ZdHDO> .

[bradbell]

Sounds like you are trying to do multi-objective optimization
https://en.wikipedia.org/wiki/Multi-objective_optimization

[dreamwingc]

Sounds like you are trying to do multi-objective optimization
https://en.wikipedia.org/wiki/Multi-objective_optimization

I am not sure about if the situation I wanna optimize is multi or single optimization, but there is only one cost function/loss function to be optimized. Since the histogram is calculated, the direct relationship between vars and fg is "broken". In this case, the optimizer consider fg is a constant and refuse to do any optimization.

The histogram calculation cannot be represent by any equation directly. There are several bins in one histogram, and the value of each bin is based on how many elements which values are within the bin edges. Consider a vector a = [5, 6, 6, 7, 7, 7, 8, 8, 8, 8], if the number of bin set to be 4, hist(a) will be [1, 2, 3, 4]. In my case, vars are applied to vector a, so that the histogram calculation cannot be represent by vars directly.

I am wondering if there is any way to let the optimizer know the histogram calculation is one of the step to calculate the final cost function, and actually, there is indirect relationship between vars and histogram.

Thank you.

[bradbell]

You have defined a function for which the derivative is zero almost everywhere. Where the derivative is non-zero, it is a generalized function (like a delta function). It is standard, in optimization, to reformulate such a problem to a space where the function is absolutely continuous; i.e., changes it the function value are equal to the integral of its derivative.

[dreamwingc]

Thanks for your comments. I think I need to find other way to solve it.