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author pascanur
date Fri, 17 Sep 2010 16:13:58 -0400
parents f2105a06201c
children 0e12ea6ba661
rev   line source
1064
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James Bergstra <bergstrj@iro.umontreal.ca>
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1 =========================
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2 Optimization for Learning
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3 =========================
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4
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5 Members: Bergstra, Lamblin, Delalleau, Glorot, Breuleux, Bordes
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6 Leader: Bergstra
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7
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8
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9
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10 Initial Writeup by James
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11 =========================================
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12
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13
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14
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15 Previous work - scikits, openopt, scipy provide function optimization
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16 algorithms. These are not currently GPU-enabled but may be in the future.
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17
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18
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19 IS PREVIOUS WORK SUFFICIENT?
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20 --------------------------------
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21
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22 In many cases it is (I used it for sparse coding, and it was ok).
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23
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24 These packages provide batch optimization, whereas we typically need online
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25 optimization.
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26
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27 It can be faster (to run) and more convenient (to implement) to have
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28 optimization algorithms as Theano update expressions.
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29
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30
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31 What optimization algorithms do we want/need?
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32 ---------------------------------------------
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33
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34 - sgd
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35 - sgd + momentum
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36 - sgd with annealing schedule
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37 - TONGA
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38 - James Marten's Hessian-free
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39 - Conjugate gradients, batch and (large) mini-batch [that is also what Marten's thing does]
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40
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41 Do we need anything to make batch algos work better with Pylearn things?
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42 - conjugate methods? yes
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43 - L-BFGS? maybe, when needed
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44
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45
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46
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47
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48
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49 Discussion
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50 ==========
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51
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52 OD asks: Could it be more convenient for x0 to be a list?
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53
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54 JB replies: Yes, but that's not the interface used by other minimize()
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55 routines (e.g. in scipy). Maybe another list-based interface is required?
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56
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57 OD replies: I think most people would prefer to use a list-based interface, so
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58 they don't have to manually pack / unpack multiple arrrays of parameters. So I
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59 would vote in favor or having both (where the main reason to also provide a
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60 non-list interface would be to allow one to easily switch e.g. to scipy's
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61 minimize).
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62 I would guess the reason scipy's interface is like this is because it makes
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63 it easier for the optimization algorithm. However, this does not really
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64 matter if we are just wrapping a theano-based algorithm (that already has
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65 to handle multiple parameters), and avoiding useless data copies on each call
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66 to f / df can only help speed-wise.
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67 JB replies: Done, I added possibility that x0 is list of ndarrays to the api
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68 doc.
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69
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70
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71
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72 OD asks: Why make a difference between iterative and one-shot versions? A one-shot
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73 algorithm can be seen as an iterative one that stops after its first
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74 iteration. The difference I see between the two interfaces proposed here
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75 is mostly that one relies on Theano while the other one does not, but
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76 hopefully a non-Theano one can be created by simply wrapping around the
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77 Theano one.
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78
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79 JB replies: Right, it would make more sense to distinguish them by the fact that
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80 one works on Theano objects, and the other on general Python callable functions.
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81 There is room for an iterative numpy interface, but I didn't make it yet. Would
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82 that answer your question?
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83
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84 OD replies and asks: Partly. Do we really need a non-iterative interface?
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85
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86 OD: I wish we could get closer to each other the Theano and Numpy interfaces.
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87 It would be nice if we could do something like:
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88
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89 # Theano version.
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90 updates = sgd([p], gradients=[g], stop=stop, step_size=.1)
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91 sgd_step = theano.function([input_var, target_var], [], updates=updates)
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92 while not stop.value:
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93 input, target = training_iter.next()
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94 sgd_step(input, target)
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95
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96 # Numpy version (you can replace *.value by regular numpy arrays).
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97 sgd_step = sgd([p.value], gradients=g_func, stop=stop.value, step_size=.1)
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98 while not stop.value:
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99 input, target = training_iter.next()
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100 sgd_step(input, target)
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101
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102 where sgd would look something like:
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103
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104 class sgd(...):
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105 def __init__(self, parameters, cost=None, gradients=None, stop=None,
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106 step_size=None):
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107 # Allow for extra arguments to be provided in self.__call__, that
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108 # are forwarded to the underlying gradients function.
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109 self.gradients = lambda *lst, **kw: gradients(*(parameters + lst),
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110 **kw)
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111 ...
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112
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113 def __call__(*lst, **kw):
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114 grads = self.gradients(*lst, **kw)
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115 for param, grad in izip(self.parameters, grads):
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116 param -= self.step_size * grad
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117
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118 Then a wrapper to provide a scipy-like interface could be:
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119
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120 def minimize(x0, f, df, algo, **kw):
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121 stop = numpy.array(0, dtype=numpy.int8)
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122 algo_step = eval(algo)([x0], cost=f, gradients=lambda x: (df(x), ),
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123 stop=stop, **kw)
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124 while not stop:
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125 algo_step()
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126
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127