Stochastic optimization routines for Theano
The downhill package provides algorithms for minimizing scalar loss functions that are defined using Theano.
Several optimization algorithms are included:
- Equilibrated SGD
- Nesterov’s Accelerated Gradient
- Resilient Backpropagation
- Stochastic Gradient Descent
All algorithms permit the use of regular or Nesterov-style momentum as well.
Quick Start: Matrix Factorization
Let’s say you have 100 samples of 1000-dimensional data, and you want to represent your data as 100 coefficients in a 10-dimensional basis. This is pretty straightforward to model using Theano: you can use a matrix multiplication as the data model, a squared-error term for optimization, and a sparse regularizer to encourage small coefficient values.
Once you have constructed an expression for the loss, you can optimize it with a single call to downhill.minimize:
import downhill import numpy as np import theano import theano.tensor as TT FLOAT = 'df'[theano.config.floatX == 'float32'] def rand(a, b): return np.random.randn(a, b).astype(FLOAT) A, B, K = 20, 5, 3 # Set up a matrix factorization problem to optimize. u = theano.shared(rand(A, K), name='u') v = theano.shared(rand(K, B), name='v') z = TT.matrix() err = TT.sqr(z - TT.dot(u, v)) loss = err.mean() + abs(u).mean() + (v * v).mean() # Minimize the regularized loss with respect to a data matrix. y = np.dot(rand(A, K), rand(K, B)) + rand(A, B) # Monitor during optimization. monitors = (('err', err.mean()), ('|u|<0.1', (abs(u) < 0.1).mean()), ('|v|<0.1', (abs(v) < 0.1).mean())) downhill.minimize( loss=loss, train=[y], patience=0, batch_size=A, # Process y as a single batch. max_gradient_norm=1, # Prevent gradient explosion! learning_rate=0.1, monitors=monitors, monitor_gradients=True) # Print out the optimized coefficients u and basis v. print('u =', u.get_value()) print('v =', v.get_value())
If you prefer to maintain more control over your model during optimization, downhill provides an iterative optimization interface:
opt = downhill.build(algo='rmsprop', loss=loss, monitors=monitors, monitor_gradients=True) for metrics, _ in opt.iterate(train=[[y]], patience=0, batch_size=A, max_gradient_norm=1, learning_rate=0.1): print(metrics)
If that’s still not enough, you can just plain ask downhill for the updates to your model variables and do everything else yourself:
updates = downhill.build('rmsprop', loss).get_updates( batch_size=A, max_gradient_norm=1, learning_rate=0.1) func = theano.function([z], loss, updates=list(updates)) for _ in range(100): print(func(y)) # Evaluate func and apply variable updates.
Mailing list: https://groups.google.com/forum/#!forum/downhill-users
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