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Multi-iteration Stochastic Estimator

Project description

Multi-iteration Stochastic Estimator

The Multi-Iteration stochastiC Estimator (MICE) is an estimator of gradients to be used in stochastic optimization. It uses control variates to build a hierarchy of iterations, adaptively sampling to keep the statistical variance below tolerance in an optimal fashion, cost-wise. The tolerance on the statistical error decreases proportionally to the square of the gradient norm, thus, SGD-MICE converges linearly in strongly convex L-smooth functions.

This python implementation of MICE is able to

  • estimate expectations or finite sums of gradients of functions;

  • choose the optimal sample sizes in order to minimize the sampling cost;

  • build a hierarchy of iterations that minimizes the total work;

  • use a resampling technique to compute the gradient norm, thus enforcing stability;

  • define a tolerance on the norm of the gradient estimate or a maximum number of evaluations as a stopping criterion.

Using MICE

Using MICE is as simple as

>>> import numpy as np
>>> from mice import MICE
>>>
>>>
>>> def gradient(x, thts):
>>>     return x - thts
>>>
>>>
>>> def sampler(n):
>>>     return np.random.random((n, 1))
>>>
>>>
>>> df = MICE(gradient , sampler=sampler)
>>> x = 10
>>> for i in range(10):
...    grad = df(x)
...    x = x - grad

However, it is flexible enough to tackle more complex problems. For more information on how to use MICE and examples, check the documentation.

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