gp.hpp 14.9 KB
Newer Older
1
2
3
4
//| Copyright Inria May 2015
//| This project has received funding from the European Research Council (ERC) under
//| the European Union's Horizon 2020 research and innovation programme (grant
//| agreement No 637972) - see http://www.resibots.eu
5
//|
6
7
8
9
10
11
//| Contributor(s):
//|   - Jean-Baptiste Mouret (jean-baptiste.mouret@inria.fr)
//|   - Antoine Cully (antoinecully@gmail.com)
//|   - Kontantinos Chatzilygeroudis (konstantinos.chatzilygeroudis@inria.fr)
//|   - Federico Allocati (fede.allocati@gmail.com)
//|   - Vaios Papaspyros (b.papaspyros@gmail.com)
12
//|
13
14
15
16
17
//| This software is a computer library whose purpose is to optimize continuous,
//| black-box functions. It mainly implements Gaussian processes and Bayesian
//| optimization.
//| Main repository: http://github.com/resibots/limbo
//| Documentation: http://www.resibots.eu/limbo
18
//|
19
20
21
22
23
//| This software is governed by the CeCILL-C license under French law and
//| abiding by the rules of distribution of free software.  You can  use,
//| modify and/ or redistribute the software under the terms of the CeCILL-C
//| license as circulated by CEA, CNRS and INRIA at the following URL
//| "http://www.cecill.info".
24
//|
25
26
27
28
29
//| As a counterpart to the access to the source code and  rights to copy,
//| modify and redistribute granted by the license, users are provided only
//| with a limited warranty  and the software's author,  the holder of the
//| economic rights,  and the successive licensors  have only  limited
//| liability.
30
//|
31
32
33
34
35
36
37
38
39
40
//| In this respect, the user's attention is drawn to the risks associated
//| with loading,  using,  modifying and/or developing or reproducing the
//| software by the user in light of its specific status of free software,
//| that may mean  that it is complicated to manipulate,  and  that  also
//| therefore means  that it is reserved for developers  and  experienced
//| professionals having in-depth computer knowledge. Users are therefore
//| encouraged to load and test the software's suitability as regards their
//| requirements in conditions enabling the security of their systems and/or
//| data to be ensured and,  more generally, to use and operate it in the
//| same conditions as regards security.
41
//|
42
43
//| The fact that you are presently reading this means that you have had
//| knowledge of the CeCILL-C license and that you accept its terms.
44
//|
45
46
#ifndef LIMBO_MODEL_GP_HPP
#define LIMBO_MODEL_GP_HPP
47
48

#include <cassert>
49
#include <iostream>
50
#include <limits>
51
#include <vector>
52

53
#include <Eigen/Cholesky>
54
55
56
#include <Eigen/Core>
#include <Eigen/LU>

57
#include <limbo/model/gp/no_lf_opt.hpp>
58
#include <limbo/tools.hpp>
59

60
namespace limbo {
61
    namespace model {
Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
62
63
64
65
66
        /// @ingroup model
        /// A classic Gaussian process.
        /// It is parametrized by:
        /// - a mean function
        /// - [optionnal] an optimizer for the hyper-parameters
67
        template <typename Params, typename KernelFunction, typename MeanFunction, class HyperParamsOptimizer = gp::NoLFOpt<Params>>
68
        class GP {
69
        public:
70
            /// useful because the model might be created before knowing anything about the process
71
            GP() : _dim_in(-1), _dim_out(-1) {}
72
73
74

            /// useful because the model might be created  before having samples
            GP(int dim_in, int dim_out)
75
                : _dim_in(dim_in), _dim_out(dim_out), _kernel_function(dim_in), _mean_function(dim_out) {}
76

77
            /// Compute the GP from samples, observation, noise. This call needs to be explicit!
78
            void compute(const std::vector<Eigen::VectorXd>& samples,
Antoine Cully's avatar
Antoine Cully committed
79
                const std::vector<Eigen::VectorXd>& observations,
80
                const Eigen::VectorXd& noises, bool compute_kernel = true)
81
82
83
84
85
            {
                assert(samples.size() != 0);
                assert(observations.size() != 0);
                assert(samples.size() == observations.size());

86
87
88
89
		if (_dim_in != samples[0].size()) {
		    _dim_in = samples[0].size();
		    _kernel_function = KernelFunction(_dim_in); // the cost of building a functor should be relatively low
		}
90

91
92
93
94
                if (_dim_out != observations[0].size()) {
                    _dim_out = observations[0].size();
                    _mean_function = MeanFunction(_dim_out); // the cost of building a functor should be relatively low
                }
95

96
97
98
99
100
101
102
                _samples = samples;

                _observations.resize(observations.size(), _dim_out);
                for (int i = 0; i < _observations.rows(); ++i)
                    _observations.row(i) = observations[i];

                _mean_observation = _observations.colwise().mean();
103

Antoine Cully's avatar
Antoine Cully committed
104
                _noises = noises;
105
106

                this->_compute_obs_mean();
107
108
                if (compute_kernel)
                    this->_compute_full_kernel();
109
            }
110

111
            /// Do not forget to call this if you use hyper-prameters optimization!!
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
112
113
            void optimize_hyperparams()
            {
114
                _hp_optimize(*this);
115
            }
116

117
118
            /// add sample and update the GP. This code uses an incremental implementation of the Cholesky
            /// decomposition. It is therefore much faster than a call to compute()
119
120
121
            void add_sample(const Eigen::VectorXd& sample, const Eigen::VectorXd& observation, double noise)
            {
                if (_samples.empty()) {
122
		  if (_dim_in != sample.size()) {
123
124
                    _dim_in = sample.size();
                    _kernel_function = KernelFunction(_dim_in); // the cost of building a functor should be relatively low
125
126
127
128
129
		  }
		  if (_dim_out != observation.size()) {
		    _dim_out = observation.size();
		    _mean_function = MeanFunction(_dim_out); // the cost of building a functor should be relatively low
		  }
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
130
131
                }
                else {
132
133
                    assert(sample.size() == _dim_in);
                    assert(observation.size() == _dim_out);
134
135
                }

136
137
138
139
140
141
142
                _samples.push_back(sample);

                _observations.conservativeResize(_observations.rows() + 1, _dim_out);
                _observations.bottomRows<1>() = observation.transpose();

                _mean_observation = _observations.colwise().mean();

Antoine Cully's avatar
Antoine Cully committed
143
144
145
                _noises.conservativeResize(_noises.size() + 1);
                _noises[_noises.size() - 1] = noise;
                //_noise = noise;
146
147

                this->_compute_obs_mean();
148
                this->_compute_incremental_kernel();
149
150
            }

151
            /**
152
             \\rst
153
             return :math:`\mu`, :math:`\sigma^2` (unormalized). If there is no sample, return the value according to the mean function. Using this method instead of separate calls to mu() and sigma() is more efficient because some computations are shared between mu() and sigma().
154
155
             \\endrst
	  		*/
156
157
158
159
            std::tuple<Eigen::VectorXd, double> query(const Eigen::VectorXd& v) const
            {
                if (_samples.size() == 0)
                    return std::make_tuple(_mean_function(v, *this),
160
                        _kernel_function(v, v));
161
162

                Eigen::VectorXd k = _compute_k(v);
163
                return std::make_tuple(_mu(v, k), _sigma(v, k));
164
165
166
            }

            /**
167
             \\rst
168
             return :math:`\mu` (unormalized). If there is no sample, return the value according to the mean function.
169
170
             \\endrst
	  		*/
171
172
173
174
175
176
177
178
            Eigen::VectorXd mu(const Eigen::VectorXd& v) const
            {
                if (_samples.size() == 0)
                    return _mean_function(v, *this);
                return _mu(v, _compute_k(v));
            }

            /**
179
             \\rst
180
             return :math:`\sigma^2` (unormalized). If there is no sample, return the max :math:`\sigma^2`.
181
182
             \\endrst
	  		*/
183
184
            double sigma(const Eigen::VectorXd& v) const
            {
185
                if (_samples.size() == 0)
186
                    return _kernel_function(v, v);
187
                return _sigma(v, _compute_k(v));
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
            }

            /// return the number of dimensions of the input
            int dim_in() const
            {
                assert(_dim_in != -1); // need to compute first !
                return _dim_in;
            }

            /// return the number of dimensions of the output
            int dim_out() const
            {
                assert(_dim_out != -1); // need to compute first !
                return _dim_out;
            }

            const KernelFunction& kernel_function() const { return _kernel_function; }

206
            KernelFunction& kernel_function() { return _kernel_function; }
207
208
209
210
211

            const MeanFunction& mean_function() const { return _mean_function; }

            MeanFunction& mean_function() { return _mean_function; }

Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
212
            /// return the maximum observation (only call this if the output of the GP is of dimension 1)
213
214
215
216
217
218
            Eigen::VectorXd max_observation() const
            {
                if (_observations.cols() > 1)
                    std::cout << "WARNING max_observation with multi dimensional "
                                 "observations doesn't make sense"
                              << std::endl;
219
                return tools::make_vector(_observations.maxCoeff());
220
221
222
223
224
            }

            /// return the mean observation (only call this if the output of the GP is of dimension 1)
            Eigen::VectorXd mean_observation() const
            {
225
                // TODO: Check if _dim_out is correct?!
226
227
228
229
230
231
232
233
234
235
236
                return _samples.size() > 0 ? _mean_observation
                                           : Eigen::VectorXd::Zero(_dim_out);
            }

            const Eigen::MatrixXd& mean_vector() const { return _mean_vector; }

            const Eigen::MatrixXd& obs_mean() const { return _obs_mean; }

            /// return the number of samples used to compute the GP
            int nb_samples() const { return _samples.size(); }

237
            ///  recomputes the GP
Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
238
            void recompute(bool update_obs_mean = true)
239
            {
240
241
242
                assert(!_samples.empty());

                if (update_obs_mean)
243
                    this->_compute_obs_mean();
244

245
                this->_compute_full_kernel();
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
            }

            /// return the likelihood (do not compute it!)
            double get_lik() const { return _lik; }

            /// set the likelihood (you need to compute it from outside!)
            void set_lik(const double& lik) { _lik = lik; }

            /// LLT matrix (from Cholesky decomposition)
            //const Eigen::LLT<Eigen::MatrixXd>& llt() const { return _llt; }
            const Eigen::MatrixXd& matrixL() const { return _matrixL; }

            const Eigen::MatrixXd& alpha() const { return _alpha; }

            /// return the list of samples that have been tested so far
            const std::vector<Eigen::VectorXd>& samples() const { return _samples; }

        protected:
            int _dim_in;
            int _dim_out;

            KernelFunction _kernel_function;
            MeanFunction _mean_function;

            std::vector<Eigen::VectorXd> _samples;
            Eigen::MatrixXd _observations;
            Eigen::MatrixXd _mean_vector;
            Eigen::MatrixXd _obs_mean;

Antoine Cully's avatar
Antoine Cully committed
275
276
277
            Eigen::VectorXd _noises;
            Eigen::VectorXd _noises_bl;

278
279
280
281
282
283
284
285
286
            Eigen::MatrixXd _alpha;
            Eigen::VectorXd _mean_observation;

            Eigen::MatrixXd _kernel;

            Eigen::MatrixXd _matrixL;

            double _lik;

287
288
            HyperParamsOptimizer _hp_optimize;

289
290
291
292
293
294
295
296
            void _compute_obs_mean()
            {
                _mean_vector.resize(_samples.size(), _dim_out);
                for (int i = 0; i < _mean_vector.rows(); i++)
                    _mean_vector.row(i) = _mean_function(_samples[i], *this);
                _obs_mean = _observations - _mean_vector;
            }

297
            void _compute_full_kernel()
298
            {
299
300
301
302
303
304
                size_t n = _samples.size();
                _kernel.resize(n, n);

                // O(n^2) [should be negligible]
                for (size_t i = 0; i < n; i++)
                    for (size_t j = 0; j <= i; ++j)
Antoine Cully's avatar
Antoine Cully committed
305
                        _kernel(i, j) = _kernel_function(_samples[i], _samples[j]) + ((i == j) ? _noises[i] : 0); // noise only on the diagonal
306
307
308
309
310
311
312
313

                for (size_t i = 0; i < n; i++)
                    for (size_t j = 0; j < i; ++j)
                        _kernel(j, i) = _kernel(i, j);

                // O(n^3)
                _matrixL = Eigen::LLT<Eigen::MatrixXd>(_kernel).matrixL();

314
                this->_compute_alpha();
315
316
317
            }

            void _compute_incremental_kernel()
318
            {
319
                // Incremental LLT
320
                // This part of the code is inpired from the Bayesopt Library (cholesky_add_row function).
321
322
                // However, the mathematical fundations can be easily retrieved by detailling the equations of the
                // extended L matrix that produces the desired kernel.
323

324
325
                size_t n = _samples.size();
                _kernel.conservativeResize(n, n);
326

327
                for (size_t i = 0; i < n; ++i) {
Antoine Cully's avatar
Antoine Cully committed
328
                    _kernel(i, n - 1) = _kernel_function(_samples[i], _samples[n - 1]) + ((i == n - 1) ? _noises[i] : 0); // noise only on the diagonal
329
                    _kernel(n - 1, i) = _kernel(i, n - 1);
330
331
                }

332
333
334
335
336
337
                _matrixL.conservativeResizeLike(Eigen::MatrixXd::Zero(n, n));

                double L_j;
                for (size_t j = 0; j < n - 1; ++j) {
                    L_j = _kernel(n - 1, j) - (_matrixL.block(j, 0, 1, j) * _matrixL.block(n - 1, 0, 1, j).transpose())(0, 0);
                    _matrixL(n - 1, j) = (L_j) / _matrixL(j, j);
338
339
                }

340
341
                L_j = _kernel(n - 1, n - 1) - (_matrixL.block(n - 1, 0, 1, n - 1) * _matrixL.block(n - 1, 0, 1, n - 1).transpose())(0, 0);
                _matrixL(n - 1, n - 1) = sqrt(L_j);
Antoine Cully's avatar
Antoine Cully committed
342

343
                this->_compute_alpha();
344
345
            }

346
            void _compute_alpha()
347
            {
348
                // alpha = K^{-1} * this->_obs_mean;
349
                Eigen::TriangularView<Eigen::MatrixXd, Eigen::Lower> triang = _matrixL.template triangularView<Eigen::Lower>();
350
351
                _alpha = triang.solve(_obs_mean);
                triang.adjoint().solveInPlace(_alpha);
352
353
354
355
356
357
358
359
360
            }

            Eigen::VectorXd _mu(const Eigen::VectorXd& v, const Eigen::VectorXd& k) const
            {
                return (k.transpose() * _alpha) + _mean_function(v, *this).transpose();
            }

            double _sigma(const Eigen::VectorXd& v, const Eigen::VectorXd& k) const
            {
361
362
                Eigen::VectorXd z = _matrixL.triangularView<Eigen::Lower>().solve(k);
                double res = _kernel_function(v, v) - z.dot(z);
363
364
365
366
367
368
369
370
371
372
373
374
375
376

                return (res <= std::numeric_limits<double>::epsilon()) ? 0 : res;
            }

            Eigen::VectorXd _compute_k(const Eigen::VectorXd& v) const
            {
                Eigen::VectorXd k(_samples.size());
                for (int i = 0; i < k.size(); i++)
                    k[i] = _kernel_function(_samples[i], v);
                return k;
            }
        };
    }
}
377

378
#endif