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api_optimization: Edited comment - Unpacking is actually needed on each call to f/df
author Olivier Delalleau <delallea@iro>
date Mon, 13 Sep 2010 23:55:04 -0400
parents e7c52923f122
children 7c5dc11c850a
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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 Theano Interface
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27 -----------------
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28
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29 The theano interface to optimization algorithms is to ask for a dictionary of
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30 updates that can be used in theano.function. Implementations of iterative
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31 optimization algorithms should be global functions with a signature like
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32 'iterative_optimizer'.
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33
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34 def iterative_optimizer(parameters,
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35 cost=None,
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36 gradients=None,
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37 stop=None,
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38 updates=None,
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39 **kwargs):
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40 """
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41 :param parameters: list or tuple of Theano variables
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42 that we want to optimize iteratively. If we're minimizing f(x), then
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43 together, these variables represent 'x'. Typically these are shared
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44 variables and their values are the initial values for the minimization
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45 algorithm.
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46
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47 :param cost: scalar-valued Theano variable that computes an exact or noisy estimate of
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48 cost (what are the conditions on the noise?). Some algorithms might
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49 need an exact cost, some algorithms might ignore the cost if the
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50 gradients are given.
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51
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52 :param gradients: list or tuple of Theano variables representing the gradients on
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53 the corresponding parameters. These default to tensor.grad(cost,
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54 parameters).
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55
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56 :param stop: a shared variable (scalar integer) that (if provided) will be
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57 updated to say when the iterative minimization algorithm has finished
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58 (1) or requires more iterations (0).
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59
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60 :param updates: a dictionary to update with the (var, new_value) items
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61 associated with the iterative algorithm. The default is a new empty
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62 dictionary. A KeyError is raised in case of key collisions.
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63
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64 :param kwargs: algorithm-dependent arguments
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65
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66 :returns: a dictionary mapping each parameter to an expression that it
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67 should take in order to carry out the optimization procedure.
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68
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69 If all the parameters are shared variables, then this dictionary may be
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70 passed as the ``updates`` argument to theano.function.
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71
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72 There may be more key,value pairs in the dictionary corresponding to
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73 internal variables that are part of the optimization algorithm.
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74
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75 """
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76
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77
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78 Numpy Interface
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79 ---------------
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80
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81 The numpy interface to optimization algorithms is supposed to mimick
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82 scipy's. Its arguments are numpy arrays, and functions that manipulate numpy
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83 arrays.
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84
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85 TODO: There is also room for an iterative object (that doesn't hog program
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86 control) but which nonetheless works on numpy objects. Actually minimize() should
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87 use this iterative interface under the hood.
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88
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89 def minimize(x0, f, df, opt_algo, **kwargs):
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90 """
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91 Return a point x_new that minimizes function `f` with derivative `df`.
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92
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93 This is supposed to provide an interface similar to scipy's minimize
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94 routines, or MATLAB's.
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95
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96 :type x0: numpy ndarray
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97 :param x0: starting point for minimization
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98
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99 :type f: python callable mapping something like x0 to a scalar
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100 :param f: function to minimize
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101
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102 :type df: python callable mapping something like x0 to the derivative of f at that point
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103 :param df: derivative of `f`
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104
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105 :param opt_algo: one of the functions that implements the
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106 `iterative_optimizer` interface.
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107
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108 :param kwargs: passed through to `opt_algo`
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109
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110 """
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111
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112 OD asks: Could it be more convenient for x0 to be a list?
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113
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114 JB replies: Yes, but that's not the interface used by other minimize()
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115 routines (e.g. in scipy). Maybe another list-based interface is required?
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116
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117 OD replies: I think most people would prefer to use a list-based interface, so
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118 they don't have to manually pack / unpack multiple arrrays of parameters. So I
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119 would vote in favor or having both (where the main reason to also provide a
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120 non-list interface would be to allow one to easily switch e.g. to scipy's
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121 minimize).
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122 I would guess the reason scipy's interface is like this is because it makes
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123 it easier for the optimization algorithm. However, this does not really
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124 matter if we are just wrapping a theano-based algorithm (that already has
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125 to handle multiple parameters), and avoiding useless data copies on each call
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126 to f / df can only help speed-wise.
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127
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128 OD asks: Why make a difference between iterative and one-shot versions? A one-shot
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129 algorithm can be seen as an iterative one that stops after its first
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130 iteration. The difference I see between the two interfaces proposed here
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131 is mostly that one relies on Theano while the other one does not, but
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132 hopefully a non-Theano one can be created by simply wrapping around the
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133 Theano one.
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134
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135 JB replies: Right, it would make more sense to distinguish them by the fact that
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136 one works on Theano objects, and the other on general Python callable functions.
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137 There is room for an iterative numpy interface, but I didn't make it yet. Would
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138 that answer your question?
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139
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140 OD replies and asks: Partly. Do we really need a non-iterative interface?
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141
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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142 Examples
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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143 --------
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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144
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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145
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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146 Simple stochastic gradient descent with extra updates:
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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147
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
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148 sgd([p], gradients=[g], updates={a:b}, step_size=.1) will return {a:b, p:p-.1*g}