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small fix to make the API_optimization show on the web.
author Frederic Bastien <nouiz@nouiz.org>
date Fri, 17 Sep 2010 16:59:08 -0400
parents 14aa0a5bb661
children 073c2fab7bcd
rev   line source
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1 .. _v2planning_optimization:
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2
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3 Optimization API
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4 ================
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5
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6 Members: Bergstra, Lamblin, Delalleau, Glorot, Breuleux, Bordes
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7 Leader: Bergstra
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8
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9
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10 Description
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11 -----------
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12
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13 This API is for iterative optimization algorithms, such as:
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14
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15 - stochastic gradient descent (incl. momentum, annealing)
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16 - delta bar delta
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17 - conjugate methods
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18 - L-BFGS
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19 - "Hessian Free"
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20 - SGD-QN
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21 - TONGA
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22
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23 The API includes an iterative interface based on Theano, and a one-shot
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24 interface similar to SciPy and MATLAB that is based on Python and Numpy, that
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25 only uses Theano for the implementation.
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26
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27
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28 Theano Interface
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29 -----------------
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30
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31 The theano interface to optimization algorithms is to ask for a dictionary of
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32 updates that can be used in theano.function. Implementations of iterative
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33 optimization algorithms should be global functions with a signature like
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34 'iterative_optimizer'.
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35
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36 def iterative_optimizer(parameters,
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37 cost=None,
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38 gradients=None,
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39 stop=None,
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40 updates=None,
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41 **kwargs):
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42 """
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43 :param parameters: list or tuple of Theano variables
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44 that we want to optimize iteratively. If we're minimizing f(x), then
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45 together, these variables represent 'x'. Typically these are shared
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46 variables and their values are the initial values for the minimization
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47 algorithm.
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48
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49 :param cost: scalar-valued Theano variable that computes an exact or noisy estimate of
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50 cost (what are the conditions on the noise?). Some algorithms might
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51 need an exact cost, some algorithms might ignore the cost if the
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52 gradients are given.
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53
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54 :param gradients: list or tuple of Theano variables representing the gradients on
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55 the corresponding parameters. These default to tensor.grad(cost,
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56 parameters).
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57
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58 :param stop: a shared variable (scalar integer) that (if provided) will be
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59 updated to say when the iterative minimization algorithm has finished
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60 (1) or requires more iterations (0).
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61
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62 :param updates: a dictionary to update with the (var, new_value) items
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63 associated with the iterative algorithm. The default is a new empty
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64 dictionary. A KeyError is raised in case of key collisions.
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65
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66 :param kwargs: algorithm-dependent arguments
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67
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68 :returns: a dictionary mapping each parameter to an expression that it
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69 should take in order to carry out the optimization procedure.
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70
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71 If all the parameters are shared variables, then this dictionary may be
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72 passed as the ``updates`` argument to theano.function.
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73
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74 There may be more key,value pairs in the dictionary corresponding to
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75 internal variables that are part of the optimization algorithm.
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76
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77 """
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78
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79
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80 Numpy Interface
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81 ---------------
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82
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83 The numpy interface to optimization algorithms is supposed to mimick
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84 scipy's. Its arguments are numpy arrays, and functions that manipulate numpy
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85 arrays.
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86
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87 def minimize(x0, f, df, opt_algo, **kwargs):
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88 """
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89 Return a point x_new with the same type as x0 that minimizes function `f`
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90 with derivative `df`.
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91
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92 This is supposed to provide an interface similar to scipy's minimize
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93 routines, or MATLAB's.
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94
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95 :type x0: numpy ndarray or list of numpy ndarrays.
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96 :param x0: starting point for minimization
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97
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98 :type f: python callable mapping something like x0 to a scalar
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99 :param f: function to minimize
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100
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101 :type df: python callable mapping something like x0 to the derivative of f at that point
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102 :param df: derivative of `f`
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103
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104 :param opt_algo: one of the functions that implements the
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105 `iterative_optimizer` interface.
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106
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107 :param kwargs: passed through to `opt_algo`
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108
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109 """
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110
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111
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112 There is also a numpy-based wrapper to the iterative algorithms.
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113 This can be more useful than minimize() because it doesn't hog program
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114 control. Technically minimize() is probably implemented using this
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115 minimize_iterator interface.
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116
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117 class minimize_iterator(object):
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118 """
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119 Attributes
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120 - x - the current best estimate of the minimum
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121 - f - the function being minimized
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122 - df - f's derivative function
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123 - opt_algo - the optimization algorithm at work (a serializable, callable
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124 object with the signature of iterative_optimizer above).
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125
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126 """
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127 def __init__(self, x0, f, df, opt_algo, **kwargs):
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128 """Initialize state (arguments as in minimize())
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129 """
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130 def __iter__(self):
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131 return self
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132 def next(self):
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133 """Take a step of minimization and return self raises StopIteration when
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134 the algorithm is finished with minimization
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135
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136 """
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137
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138
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139 Examples
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140 --------
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141
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142 Simple stochastic gradient descent could be called like this:
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143
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diff changeset
144 sgd([p], gradients=[g], step_size=.1)
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
145
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
146 and this would return
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
147
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
148 {p:p-.1*g}
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
149
1100
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
diff changeset
150
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
diff changeset
151 Simple stochastic gradient descent with extra updates:
153cf820a975 v2planning - updates to api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1069
diff changeset
152
1149
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parents: 1108
diff changeset
153 sgd([p], gradients=[g], updates={a:b}, step_size=.1)
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
154
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
155 will return
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
156
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
157 {a:b, p:p-.1*g}
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
158
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
159
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
160 If the parameters collide with keys in a given updates dictionary an exception
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
161 will be raised:
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
162
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
163 sgd([p], gradients=[g], updates={p:b}, step_size=.1)
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
164
7c5dc11c850a cleaning up api_optimization
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1108
diff changeset
165 will raise a KeyError.