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annotate doc/v2_planning/api_optimization.txt @ 1165:42ddbefd1e03

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made the API_formulas.txt and removed duplicate stuff from the formulas.txt file
author Frederic Bastien <nouiz@nouiz.org>
date Fri, 17 Sep 2010 13:57:07 -0400
parents 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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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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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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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 def minimize(x0, f, df, opt_algo, **kwargs):
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86 """
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87 Return a point x_new with the same type as x0 that minimizes function `f`
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88 with derivative `df`.
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89
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90 This is supposed to provide an interface similar to scipy's minimize
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91 routines, or MATLAB's.
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92
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93 :type x0: numpy ndarray or list of numpy ndarrays.
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94 :param x0: starting point for minimization
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95
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96 :type f: python callable mapping something like x0 to a scalar
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97 :param f: function to minimize
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98
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99 :type df: python callable mapping something like x0 to the derivative of f at that point
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100 :param df: derivative of `f`
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101
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102 :param opt_algo: one of the functions that implements the
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103 `iterative_optimizer` interface.
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104
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105 :param kwargs: passed through to `opt_algo`
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106
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107 """
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108
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109
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110 There is also a numpy-based wrapper to the iterative algorithms.
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111 This can be more useful than minimize() because it doesn't hog program
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112 control. Technically minimize() is probably implemented using this
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113 minimize_iterator interface.
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114
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115 class minimize_iterator(object):
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116 """
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117 Attributes
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118 - x - the current best estimate of the minimum
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119 - f - the function being minimized
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120 - df - f's derivative function
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121 - opt_algo - the optimization algorithm at work (a serializable, callable
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122 object with the signature of iterative_optimizer above).
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123
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124 """
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125 def __init__(self, x0, f, df, opt_algo, **kwargs):
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126 """Initialize state (arguments as in minimize())
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127 """
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128 def __iter__(self):
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129 return self
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130 def next(self):
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131 """Take a step of minimization and return self raises StopIteration when
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132 the algorithm is finished with minimization
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133
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134 """
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135
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136
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137 Examples
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138 --------
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139
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140 Simple stochastic gradient descent could be called like this:
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141
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142 sgd([p], gradients=[g], step_size=.1)
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143
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144 and this would return
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parents: 1108
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145
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parents: 1108
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146 {p:p-.1*g}
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147
1100
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parents: 1069
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148
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parents: 1069
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149 Simple stochastic gradient descent with extra updates:
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150
1149
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151 sgd([p], gradients=[g], updates={a:b}, step_size=.1)
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152
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parents: 1108
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153 will return
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parents: 1108
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154
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parents: 1108
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155 {a:b, p:p-.1*g}
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parents: 1108
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156
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parents: 1108
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157
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parents: 1108
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158 If the parameters collide with keys in a given updates dictionary an exception
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parents: 1108
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159 will be raised:
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parents: 1108
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160
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161 sgd([p], gradients=[g], updates={p:b}, step_size=.1)
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parents: 1108
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162
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parents: 1108
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163 will raise a KeyError.