This code implements an adapted version of the safe, Bayesian optimization algorithm, SafeOpt [1,2]. It also provides an implementation for the original algorithm in [3]. The code can be used to automatically optimize a performance measures subject to a safety constraint by adapting parameters. The prefered way of citing this code is by referring to [1, 2].
[1] F. Berkenkamp, A. P. Schoellig, A. Krause, "Safe Controller Optimization for Quadrotors with Gaussian Processes" in Proc. of the IEEE International Conference on Robotics and Automation (ICRA), 2016, pp. 491-496, arXiv:1509.01066 [cs.RO]
[2] F. Berkenkamp, A. Krause, A. P. Schoellig, "Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics", ArXiv, 2016, arXiv:1602.04450 [cs.RO]
[3] Y. Sui, A. Gotovos, J. W. Burdick, and A. Krause, “Safe exploration for optimization with Gaussian processes” in Proc. of the International Conference on Machine Learning (ICML), 2015, pp. 997–1005. [PDF]
The easiest way to install the necessary python libraries is by installing pip (e.g. sudo apt-get install python-pip on Ubuntu) and running
sudo pip install -r requirements.txt
The easiest way to get familiar with the library is to run the interactive example ipython notebooks!
Make sure that the ipywidgets module is installed.
All functions and classes are documented on Read The Docs.
The algorithm is implemented in the gp_opt.py file. Next to some helper
functions, the class SafeOpt implements the core algorithm. It can be
initialized as
SafeOpt(gp, parameter_set, fmin, lipschitz=None, beta=3.0, num_contexts=0, threshold=0, scaling=None)
gpis a Gaussian process from theGPytoolbox in https://github.com/SheffieldML/GPy. This Gaussian process should already include the points of the initial, safe set. For multiple constraints, this is a list of independent GPs instead.- The
parameter_setis a 2d-array of sampling locations for the GP, which is used to compute new evaluation points. It can, for example, be create with thelinearly_spaced_combinationsfunction in the safeopt library. - Lastly, fmin defines the safe lower bounds on the function values.
The class several optional arguments:
- The
lipschitzargument can be used to specify the Lipschitz constant to determine the set of expanders. If it is not None, the algorithm in [1] is used to determine expanders directly with the confidence itnervals. - The confidence interval that is used can be specified by
beta, which can be a constant or a function of the iteration number. num_contextscan be used to specify which of the parameters are contexts that we do not optimize over, see [2].- Potential expanders that have confidence intervals smaller than the
thresholdvalue are not considered by the algorithm. This is useful to avoid unecessary exploration (Typical values are the noise standard deviation). scalingis used when multiple constraints are specified, in order to account for different magnitudes of functions.
Once the class is initialized, its optimize method can be used to determine the next parameters at which to evaluate the objective function. The resulting data point can be added with the add_new_data_point method. The plot method illustrates the Gaussian process intervals in 1 or 2 dimensions.
For a more detailed documentation see the class/method docstrings within the source code.
The code is licenced under the MIT license and free to use by anyone without any restrictions.