scipy.optimize.fmin_bfgs单个函数同时计算f和fprime [英] scipy.optimize.fmin_bfgs single function computes both f and fprime

问题描述

我正在使用scipy.optimize.fmin_bfgs(f, init_theta, fprime)最小化具有渐变fprime的f.我在单个函数中计算f和fprime，因为大多数计算是相同的，因此无需重复两次.

I'm using scipy.optimize.fmin_bfgs(f, init_theta, fprime) to minimize f, which has gradient fprime. I compute f and fprime in a single function because most of the computation is the same so there's no need to do it twice.

是否有任何方法可以调用fmin_bfgs()并指定一个同时返回f和fprime的单个函数?

Is there any way to call fmin_bfgs() specifying a single function that returns both f and fprime?

推荐答案

如果您要节省计算时间，而不仅仅是为了代码方便而组合f和f'的计算，那么您似乎需要函数周围有一个额外的包装器来缓存值，因为fmin_bfgs似乎不允许您传递这样的函数(与其他一些优化函数不同).

If you're trying to save on computation time rather than just combine the calculation of f and f' for code convenience, it seems like you need an extra wrapper around your function to cache values, since fmin_bfgs doesn't seem to allow you to pass such a function (unlike some other optimization functions).

这是一种方法，可以在一个小缓存中保留最近评估的10个点. (我不确定对该函数的调用是否需要是线程安全的:可能不是，但是，如果是这样，我想您可能需要在此处添加一些锁定.)

Here's one way to do that, maintaining the 10 most recently evaluated points in a little cache. (I'm not sure whether calls to this function need to be thread-safe: probably not, but if so, you'll probably need to add some locking in here, I guess.)

def func_wrapper(f, cache_size=10):
    evals = {}
    last_points = collections.deque()

    def get(pt, which):
        s = pt.tostring() # get binary string of numpy array, to make it hashable
        if s not in evals:
            evals[s] = f(pt)
            last_points.append(s)
            if len(last_points) >= cache_size:
                del evals[last_points.popleft()]
        return evals[s][which]

    return functools.partial(get, which=0), functools.partial(get, which=1)

如果可以的话

>>> def f(x):
...    print "evaluating", x
...    return (x-3)**2, 2*(x-3)

>>> f_, fprime = func_wrapper(f)

>>> optimize.fmin_bfgs(f_, 1000, fprime)
evaluating [ 994.93480441]
evaluating [ 974.67402207]
evaluating [ 893.63089268]
evaluating [ 665.93446894]
evaluating [ 126.99931561]
evaluating [ 3.]
Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 4
         Function evaluations: 7
         Gradient evaluations: 7
array([ 3.])

我们可以看到我们没有重复任何评估.

we can see that we don't repeat any evaluations.

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