Gradient-based hyperparameter optimization package with TensorFlow

The package implements the three algorithms presented in the paper Forward and Reverse Gradient-Based Hyperparameter Optimization [2017] (https://arxiv.org/abs/1703.01785):

• Reverse-HO, generalization of algorithms presented in Domke [2012] and MacLaurin et Al. [2015] (without reversable dynamics and "reversable dtype")
• Forward-HO
• Real-Time Hyperparameter Optimization (RTHO)

Clone the repository and run setup script.

git clone https://github.com/lucfra/RFHO.git
cd rfho
python setup.py install

Beside "usual" packages (numpy, pickle, gzip), RFHO depends on tensorflow. Some secondary module depends also on cvxopt (projections) and intervaltree. The core code works without this packages, so feel free to ignore these requirements.

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. The package is under development and at the moment the code is not particularly optimized; please feel free to issues comments, suggestions and feedbacks! You can also email me at luca.franceschi@iit.it .

• Self contained example on MNIST (!) with Reverse-HO (Forward-HO and RTHO coming very soon..)
• A module with a more complete set of examples showing all algorithms an various models (still on MNIST...)

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 natuarlly 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.

• All the hyperparameter optimization algorithms are implemented in the module hyper_gradients. The classes ReverseHyperGradient and ForwardHyperGradient are responsible of the computation of the hyper-gradients while RealTimeHO is an helper class that implements RTHO algorithm (based on ForwardHyperGradient).
• The module optimizers contains classes that implement gradient descent based iterative optimizers. Since the HO methods need to access to the optimizer dynamics (which is seen as a dynamical system) we haven't been able to employ TensorFlow optimizers. At the moment the following optimizers are implemented
  • GradientDescentOptimizer
  • MomentumOptimizer
  • AdamOptimizer (not compatible yet with Forward-HO)
• models module contains some helper function to build up models. It also contains the core function vectorize_model which transform the computational graph so that all the parameters of the model are conveniently collected into a single vector (rank-1 tensor) of the appropriate dimension (see method doc for further details)
• utils method contains some use useful functions. Most notably cross_entropy_loss re-implements the cross entropy with softmax output. This was necessary since tensorflow function has zero Hessian.