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added some wishlist items for gd module
author James Bergstra <bergstrj@iro.umontreal.ca>
date Fri, 03 Sep 2010 12:35:49 -0400
parents 4d7fdd04b66a
children
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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36 .. code-block:: python
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37
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38 def iterative_optimizer(parameters,
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39 cost=None,
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40 gradients=None,
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41 stop=None,
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42 updates=None,
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43 **kwargs):
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44 """
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45 :param parameters: list or tuple of Theano variables
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46 that we want to optimize iteratively. If we're minimizing f(x), then
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47 together, these variables represent 'x'. Typically these are shared
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48 variables and their values are the initial values for the minimization
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49 algorithm.
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50
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51 :param cost: scalar-valued Theano variable that computes an exact or noisy estimate of
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52 cost (what are the conditions on the noise?). Some algorithms might
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53 need an exact cost, some algorithms might ignore the cost if the
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54 gradients are given.
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55
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56 :param gradients: list or tuple of Theano variables representing the gradients on
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57 the corresponding parameters. These default to tensor.grad(cost,
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58 parameters).
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59
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60 :param stop: a shared variable (scalar integer) that (if provided) will be
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61 updated to say when the iterative minimization algorithm has finished
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62 (1) or requires more iterations (0).
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63
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64 :param updates: a dictionary to update with the (var, new_value) items
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65 associated with the iterative algorithm. The default is a new empty
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66 dictionary. A KeyError is raised in case of key collisions.
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67
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68 :param kwargs: algorithm-dependent arguments
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69
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70 :returns: a dictionary mapping each parameter to an expression that it
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71 should take in order to carry out the optimization procedure.
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72
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73 If all the parameters are shared variables, then this dictionary may be
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74 passed as the ``updates`` argument to theano.function.
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75
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76 There may be more key,value pairs in the dictionary corresponding to
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77 internal variables that are part of the optimization algorithm.
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78
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79 """
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80
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81
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82 Numpy Interface
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83 ---------------
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84
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85 The numpy interface to optimization algorithms is supposed to mimick
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86 scipy's. Its arguments are numpy arrays, and functions that manipulate numpy
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87 arrays.
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88
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89 .. code-block:: python
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90
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91 def minimize(x0, f, df, opt_algo, **kwargs):
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92 """
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93 Return a point x_new with the same type as x0 that minimizes function `f`
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94 with derivative `df`.
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95
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96 This is supposed to provide an interface similar to scipy's minimize
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97 routines, or MATLAB's.
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98
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99 :type x0: numpy ndarray or list of numpy ndarrays.
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100 :param x0: starting point for minimization
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101
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102 :type f: python callable mapping something like x0 to a scalar
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103 :param f: function to minimize
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104
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105 :type df: python callable mapping something like x0 to the derivative of f at that point
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106 :param df: derivative of `f`
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107
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108 :param opt_algo: one of the functions that implements the
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109 `iterative_optimizer` interface.
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110
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111 :param kwargs: passed through to `opt_algo`
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112
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113 """
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114
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115
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116 There is also a numpy-based wrapper to the iterative algorithms.
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117 This can be more useful than minimize() because it doesn't hog program
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118 control. Technically minimize() is probably implemented using this
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119 minimize_iterator interface.
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120
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121 .. code-block:: python
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122
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123 class minimize_iterator(object):
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124 """
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125 Attributes
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126 - x - the current best estimate of the minimum
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127 - f - the function being minimized
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128 - df - f's derivative function
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129 - opt_algo - the optimization algorithm at work (a serializable, callable
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130 object with the signature of iterative_optimizer above).
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131
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132 """
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133 def __init__(self, x0, f, df, opt_algo, **kwargs):
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134 """Initialize state (arguments as in minimize())
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135 """
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136 def __iter__(self):
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137 return self
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138 def next(self):
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139 """Take a step of minimization and return self raises StopIteration when
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140 the algorithm is finished with minimization
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141
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142 """
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143
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144
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145 JB replies: I don't think so, but for the few lines of code required, I think it would be nice to
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146 provide an function that matches scipy's API.
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147
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148 OD: Looks like the reply above was pasted in the wrong place... where was it
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149 supposed to go?
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150
1100
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151 Examples
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152 --------
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153
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154 Simple stochastic gradient descent could be called like this:
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155
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156 .. code-block:: python
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157
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158 sgd([p], gradients=[g], step_size=.1)
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159
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160 and this would return
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161
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162 .. code-block:: python
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163
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164 {p:p-.1*g}
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165
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166
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167 Simple stochastic gradient descent with extra updates:
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168
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169 .. code-block:: python
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170
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171 sgd([p], gradients=[g], updates={a:b}, step_size=.1)
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172
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173 will return
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174
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175 .. code-block:: python
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176
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177 {a:b, p:p-.1*g}
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178
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179
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180 If the parameters collide with keys in a given updates dictionary an exception
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181 will be raised:
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182
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183 .. code-block:: python
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184
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185 sgd([p], gradients=[g], updates={p:b}, step_size=.1)
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186
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187 will raise a ``KeyError``.