PopulationBasedStepSizeAdaptation.h
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1 /*!
2  * \brief Implements the tep size adaptation based on the success of the new population compared to the old
3  *
4  * \author O.Krause
5  * \date 2014
6  *
7  * \par Copyright 1995-2017 Shark Development Team
8  *
9  * <BR><HR>
10  * This file is part of Shark.
11  * <http://shark-ml.org/>
12  *
13  * Shark is free software: you can redistribute it and/or modify
14  * it under the terms of the GNU Lesser General Public License as published
15  * by the Free Software Foundation, either version 3 of the License, or
16  * (at your option) any later version.
17  *
18  * Shark is distributed in the hope that it will be useful,
19  * but WITHOUT ANY WARRANTY; without even the implied warranty of
20  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21  * GNU Lesser General Public License for more details.
22  *
23  * You should have received a copy of the GNU Lesser General Public License
24  * along with Shark. If not, see <http://www.gnu.org/licenses/>.
25  *
26  */
27 #ifndef SHARK_ALGORITHMS_DIRECTSEARCH_OPERATORS_POPULATION_BASED_STEP_SIZE_ADAPTATION_H
28 #define SHARK_ALGORITHMS_DIRECTSEARCH_OPERATORS_POPULATION_BASED_STEP_SIZE_ADAPTATION_H
29 
30 #include <shark/LinAlg/Base.h>
31 #include <cmath>
32 
33 namespace shark {
34 
35 /// \brief Step size adaptation based on the success of the new population compared to the old
36 ///
37 /// This is the step size adaptation algorithm as proposed in
38 /// Ilya Loshchilov, "A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization"
39 ///
40 /// It ranks the old and new population together and checks whether the mean rank of the new population
41 /// is lower than the old one in this combined population. If this is true, the step size is increased
42 /// in an exponential fashion. More formally, let \f$ r_t(i) \f$ be the rank of the i-th individual in the
43 /// current population in the combined ranking and \f$ r_{t-1}(i) \f$ the rank of the i-th previous
44 /// individual. Then we have
45 /// \f[ z_t \leftarrow \frac 1 {\lamba^2} \sum_i^{\lambda} r_{t-1}(i) - r_t(i) - z*\f]
46 /// where \f$ z* \f$ is a target success value, which defaults to 0.25
47 /// this statistic is stabilised using an exponential average:
48 /// \f[ s_t \leftarrow (1-c)*s_{t-1} + c*z_t \f]
49 /// where the learning rate c defaults to 0.3
50 /// finally we adapt the step size sigma by
51 /// \f[ \sigma_t = \sigma_{t-1} exp(s_t/d) \f]
52 /// where the damping factor d defaults to 1
53 class PopulationBasedStepSizeAdaptation{
54 public:
55  PopulationBasedStepSizeAdaptation():m_targetSuccessRate(0.25), m_c(0.3), m_d(1.0){}
56 
57  /////Getter and Setter functions/////////
58 
59  double targetSuccessRate()const{
60  return m_targetSuccessRate;
61  }
62 
63  double& targetSuccessRate(){
64  return m_targetSuccessRate;
65  }
66 
67  double learningRate()const{
68  return m_c;
69  }
70 
71  double& learningRate(){
72  return m_c;
73  }
74 
75  double dampingFactor()const{
76  return m_d;
77  }
78 
79  double& dampingFactor(){
80  return m_d;
81  }
82 
83  double stepSize()const{
84  return m_stepSize;
85  }
86 
87  ///\brief Initializes a new trial by setting the initial learning rate and resetting the internal values.
88  void init(double initialStepSize){
89  m_stepSize = initialStepSize;
90  m_s = 0;
91  m_prevFitness.resize(0);
92  }
93 
94  /// \brief updates the step size using the newly sampled population
95  ///
96  /// The offspring is assumed to be ordered in ascending order by their penalizedFitness
97  /// (this is the same as ordering by the unpenalized fitness in an unconstrained setting)
98  template<class Population>
99  void update(Population const& offspring){
100  std::size_t lambda = offspring.size();
101  if (m_prevFitness.size() == lambda){
102  //get estimate of z
103  std::size_t indexOld = 0;
104  std::size_t indexNew = 0;
105  std::size_t rank = 1;
106  double z = 0;
107  while(indexOld < lambda && indexNew < lambda){
108  if (offspring[indexNew].penalizedFitness() <= m_prevFitness[indexOld]){
109  z-=rank;
110  ++indexNew;
111  }
112  else{
113  z+=rank;
114  ++indexOld;
115  }
116  ++rank;
117  }
118  //case 1: the worst elements in the old population are better than the worst in the new
119  while(indexNew < lambda){
120  z-=rank;
121  ++indexNew;
122  ++rank;
123  }
124  //case 2: the opposite
125  while(indexOld< lambda){
126  z += rank;
127  ++indexOld;
128  ++rank;
129  }
130  z /= lambda*lambda;
131  z -= m_targetSuccessRate;
132  m_s = (1-m_c)*m_s +m_c*z;
133  m_stepSize *= std::exp(m_s/m_d);
134  }
135 
136  //store fitness values of last iteration
137  m_prevFitness.resize(lambda);
138  for(std::size_t i = 0; i != lambda; ++i)
139  m_prevFitness(i) = offspring[i].penalizedFitness();
140  }
141 protected:
142  double m_stepSize;///< current value for the step size
143  RealVector m_prevFitness;///< fitness values of the previous iteration for ranking
144  double m_s; ///< The time average of the population success
145 
146  //hyper parameters
147  double m_targetSuccessRate;
148  double m_c;
149  double m_d;
150 };
151 
152 }
153 
154 #endif