Gradient-based hyperparameter optimization package with TensorFlow

This is the new package that implements the algorithms presented in the paper Forward and Reverse Gradient-Based Hyperparameter Optimization. For the older package see RFHO. FAR-HO features simplified interfaces, additional capabilities and a tighter integration with tensorflow.

• Reverse-HG, generalization of algorithms presented in Domke [2012] and MacLaurin et Al. [2015] (without reversable dynamics and "reversable dtype")
• Forward-HG
• Online versions of the two previous algorithms: Real-Time HO (RTHO) and Truncated-Reverse HO (TRHO)

The first two algorithms compute, with different procedures, the gradient of a validation error with respect to the hyperparameters - i.e. the hypergradient - while the last, based on Forward-HG, performs "real time" (i.e. at training time) hyperparameter updates.

These algorithms are useful also in a learning-to learn context where parameters of various meta-learners effectively play the role of hyperparamters, as explained here in the work A Bridge Between Hyperparameter Optimization and Learning-to-learn.

Clone the repository and run setup script.

git clone git clone https://github.com/lucfra/FAR-HO.git
cd FAR-HO
python setup.py install

Beside "usual" packages (numpy), FAR-HO is built upon tensorflow. Some examples depend on the package experimet_manager

Please note that required packages will not be installed automatically.

Aim of this package is to implement and develop gradient-based hyperparameter optimization (HO) techniques in TensorFlow, thus making them readily applicable to deep learning systems. This optimization techniques find also natural applications in the field of learning-to-learn. Feel free to issues comments, suggestions and feedbacks! You can email me at luca.franceschi@iit.it .

• Self contained example on MNIST with ReverseHG for the optimization of initial starting point (inital weights), weights of each example and learning rate.
• Coming soon: expamples of application of online HO algorithms.
• Hyper-representation and related notebook: an example in the context of learning-to-learn. In this case the hyperparameters are some of the weights of a convolutional neural network (plus the learning rate!). The idea is to learn a cross-episode shared representation by explicitly minimizing the mean generalization error over meta-training tasks. See A bridge between hyperparameter optimization and learning-to-Learn presentied at Workshop on meta-learning. Note: for the moment, for running the code for this experiment you need to install the package https://github.com/lucfra/ExperimentManager for data management and statistics recording.

• Create a model as you prefer¹ with TensorFlow
• Create the hyperparameters you wish to optimize² with the function get_hyperparameter (which could be also variables of your model)
• Define an inner objective (e.g. a training error) and an outer objective (e.g. a validation error) as scalar tensorflow.Tensor
• Create an instance of HyperOptimizer after choosing an hyper-gradient computation algorithm among ForwardHG and ReverseHG (see next section)
• Call the function HyperOptimizer.minimize specifying passing the outer and inner objectives, as well as an optimizer for the outer problem (which can be any optimizer form tensorflow) and an optimizer for the inner problem (which must be an optimizer contained in this package; at the moment gradient descent, gradient descent with momentum and Adam algorithms are available, but it is quite straightforward to implement other optimizers)
• Execute HyperOptimizer.run(T, ...) function inside a tensorflow.Session, optimize parameters and perform a step of optimization of hyperparameter optimization.

import far_ho as far
import tensorflow as tf

model = create_model(...)  

lambda1 = far.get_hyperparameter('lambda1', ...)
lambda1 = far.get_hyperparameter('lambda2', ...)
io, oo = create_objective(...)

inner_problem_optimizer = far.GradientDescentOptimizer(lr=far.get_hyperparameter('lr', 0.1))
outer_problem_optimizer = tf.train.AdamOptimizer()

farho = far.HyperOptimizer() 
ho_step = farho.minimize(oo, outer_problem_optimizer,
                     io, inner_problem_optimizer)

T = 100
with tf.Session().as_default():
  for _ in range(100):
    ho_step(T)    

¹ This is gradient-based optimization and for the computation of the hyper-gradients second order derivatives of the training error show up (even tough no Hessian matrix is explicitly computed at any time); therefore, all the ops used in the model should have a second order derivative registered in tensorflow.

² For the hyper-gradients to make sense, hyperparameters should be real-valued. Moreover, while ReverseHG should handle generic r-rank tensor hyperparameters, ForwardHGrequires scalars hyperparameters. Use the keyword argument scalar=True in get_hyperparameter for obtaining a scalr splitting of a general tensor.

Forward and Reverse-HG compute the same hypergradient, so the choice is a matter of time versus memory!

The online versions of the algorithms can dramatically speed-up the optimization.

The objective is to minimize some validation function E with respect to a vector of hyperparameters lambda. The validation error depends on the model output and thus on the model parameters w. w should be a minimizer of the training error and the hyperparameter optimization problem can be naturally formulated as a bilevel optimization problem.
Since these problems are rather hard to tackle, we
explicitly take into account the learning dynamics used to obtain the model
parameters (e.g. you can think about stochastic gradient descent with momentum), and we formulate HO as a constrained optimization problem. See the paper for details.

• Simplified interface: optimize paramters and hyperparamters with "just" a call of far.HyperOptimizer.minimize, create variables designed as hyperparameters with far.get_hyperparameter, no more need to vectorize the model weights, far.optimizers only need to specify the update as a list of pairs (v, v_{k+1})
• Additional capabilities: set an initalizaiton dynamics and optimize the (dsitribution) of initial weights, allowed explicit dependence of the outer objective w.r.t. hyperparameters, support for multiple outer objectives and multiple inner problems (episode batching, average the sampling from distributions, ...)
• Tighter integration: collections for hyperparameters and hypergradients (use far.GraphKeys), use out-of-the-box models (no need to vectorize the model), use any TensorFlow optimizer for the outer objective (validation error)
• Lighter package: only code for implementing the algorithms and running the examples
• Forward hypergradient methods have been reimplemented with a double reverse mode trick, thanks to Jamie Townsend.

@InProceedings{pmlr-v70-franceschi17a,
  title = 	 {Forward and Reverse Gradient-Based Hyperparameter Optimization},
  author = 	 {Luca Franceschi and Michele Donini and Paolo Frasconi and Massimiliano Pontil},
  booktitle = 	 {Proceedings of the 34th International Conference on Machine Learning},
  pages = 	 {1165--1173},
  year = 	 {2017},
  volume = 	 {70},
  series = 	 {Proceedings of Machine Learning Research},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v70/franceschi17a/franceschi17a.pdf},
}

For the work on learning-to-learn

@article{franceschi2017bridge,
  title={A Bridge Between Hyperparameter Optimization and Larning-to-learn},
  author={Franceschi, Luca and Frasconi, Paolo and Donini, Michele and Pontil, Massimiliano},
  journal={arXiv preprint arXiv:1712.06283},
  year={2017}
}