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author Olivier Delalleau <delallea@iro>
date Mon, 13 Sep 2010 09:15:25 -0400
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1 Optimization API
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2 ================
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3
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4 Members: Bergstra, Lamblin, Delalleau, Glorot, Breuleux, Bordes
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5 Leader: Bergstra
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6
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7
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8 Description
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9 -----------
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10
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11 This API is for iterative optimization algorithms, such as:
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12
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13 - stochastic gradient descent (incl. momentum, annealing)
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14 - delta bar delta
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15 - conjugate methods
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16 - L-BFGS
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17 - "Hessian Free"
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18 - SGD-QN
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19 - TONGA
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20
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21 The API includes an iterative interface based on Theano, and a one-shot
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22 interface similar to SciPy and MATLAB that is based on Python and Numpy, that
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23 only uses Theano for the implementation.
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24
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25
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26 Iterative Interface
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27 -------------------
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28
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29 def iterative_optimizer(parameters,
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30 cost=None,
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31 grads=None,
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32 stop=None,
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33 updates=None,
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34 **kwargs):
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35 """
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36 :param parameters: list or tuple of Theano variables (typically shared vars)
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37 that we want to optimize iteratively. If we're minimizing f(x), then
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38 together, these variables represent 'x'.
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39
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40 :param cost: scalar-valued Theano variable that computes an exact or noisy estimate of
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41 cost (what are the conditions on the noise?). Some algorithms might
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42 need an exact cost, some algorithms might ignore the cost if the grads
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43 are given.
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44
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45 :param grads: list or tuple of Theano variables representing the gradients on
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46 the corresponding parameters. These default to tensor.grad(cost,
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47 parameters).
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48
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49 :param stop: a shared variable (scalar integer) that (if provided) will be
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50 updated to say when the iterative minimization algorithm has finished
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51 (1) or requires more iterations (0).
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52
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53 :param updates: a dictionary to update with the (var, new_value) items
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54 associated with the iterative algorithm. The default is a new empty
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55 dictionary. A KeyError is raised in case of key collisions.
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56
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57 :param kwargs: algorithm-dependent arguments
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58
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59 :returns: a dictionary mapping each parameter to an expression that it
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60 should take in order to carry out the optimization procedure.
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61
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62 If all the parameters are shared variables, then this dictionary may be
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63 passed as the ``updates`` argument to theano.function.
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64
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65 There may be more key,value pairs in the dictionary corresponding to
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66 internal variables that are part of the optimization algorithm.
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67
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68 """
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69
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70
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71 One-shot Interface
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72 ------------------
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73
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74 def minimize(x0, f, df, opt_algo, **kwargs):
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75 """
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76 Return a point x_new that minimizes function `f` with derivative `df`.
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77
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78 This is supposed to provide an interface similar to scipy's minimize
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79 routines, or MATLAB's.
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80
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81 :type x0: numpy ndarray
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82 :param x0: starting point for minimization
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83
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84 :type f: python callable mapping something like x0 to a scalar
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85 :param f: function to minimize
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86
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87 :type df: python callable mapping something like x0 to the derivative of f at that point
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88 :param df: derivative of `f`
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89
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90 :param opt_algo: one of the functions that implements the
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91 `iterative_optimizer` interface.
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92
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93 :param kwargs: passed through to `opt_algo`
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94
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95 """
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96
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97 OD: Could it be more convenient for x0 to be a list?
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98
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99 OD: Why make a difference between iterative and one-shot versions? A one-shot
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100 algorithm can be seen as an iterative one that stops after its first
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101 iteration. The difference I see between the two interfaces proposed here
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102 is mostly that one relies on Theano while the other one does not, but
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103 hopefully a non-Theano one can be created by simply wrapping around the
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104 Theano one.
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105