example.py 8.99 KB
 Steven Cordwell committed Aug 18, 2013 1 2 3 4 5 6 7 8 ``````# -*- coding: utf-8 -*- """ Created on Sun Aug 18 14:32:25 2013 @author: steve """ from numpy import diag, ones, where, zeros `````` Steven Cordwell committed Aug 24, 2013 9 ``````from numpy.random import randint, random `````` Steven Cordwell committed Aug 18, 2013 10 11 ``````from scipy.sparse import coo_matrix, dok_matrix `````` Steven Cordwell committed Aug 24, 2013 12 ``````def forest(S=3, r1=4, r2=2, p=0.1, is_sparse=False): `````` Steven Cordwell committed Aug 18, 2013 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 `````` """Generate a MDP example based on a simple forest management scenario. This function is used to generate a transition probability (``A`` × ``S`` × ``S``) array ``P`` and a reward (``S`` × ``A``) matrix ``R`` that model the following problem. A forest is managed by two actions: 'Wait' and 'Cut'. An action is decided each year with first the objective to maintain an old forest for wildlife and second to make money selling cut wood. Each year there is a probability ``p`` that a fire burns the forest. Here is how the problem is modelled. Let {1, 2 . . . ``S`` } be the states of the forest, with ``S`` being the oldest. Let 'Wait' be action 1 and 'Cut' action 2. After a fire, the forest is in the youngest state, that is state 1. The transition matrix P of the problem can then be defined as follows:: | p 1-p 0.......0 | | . 0 1-p 0....0 | P[1,:,:] = | . . 0 . | | . . . | | . . 1-p | | p 0 0....0 1-p | | 1 0..........0 | | . . . | P[2,:,:] = | . . . | | . . . | | . . . | | 1 0..........0 | The reward matrix R is defined as follows:: | 0 | | . | R[:,1] = | . | | . | | 0 | | r1 | | 0 | | 1 | R[:,2] = | . | | . | | 1 | | r2 | Parameters --------- S : int, optional The number of states, which should be an integer greater than 0. By default it is 3. r1 : float, optional The reward when the forest is in its oldest state and action 'Wait' is performed. By default it is 4. r2 : float, optional The reward when the forest is in its oldest state and action 'Cut' is performed. By default it is 2. p : float, optional The probability of wild fire occurence, in the range ]0, 1[. By default it is 0.1. Returns ------- out : tuple ``out[1]`` contains the transition probability matrix P with a shape of (A, S, S). ``out[2]`` contains the reward matrix R with a shape of (S, A). Examples -------- >>> import mdp >>> P, R = mdp.exampleForest() >>> P array([[[ 0.1, 0.9, 0. ], [ 0.1, 0. , 0.9], [ 0.1, 0. , 0.9]], [[ 1. , 0. , 0. ], [ 1. , 0. , 0. ], [ 1. , 0. , 0. ]]]) >>> R array([[ 0., 0.], [ 0., 1.], [ 4., 2.]]) """ if S <= 1: `````` 99 `````` raise ValueError("The number of states 'S' must be greater than 1.") `````` Steven Cordwell committed Aug 18, 2013 100 `````` if (r1 <= 0) or (r2 <= 0): `````` 101 `````` raise ValueError("The rewards must be greater than non-negative.") `````` Steven Cordwell committed Aug 18, 2013 102 `````` if (p < 0) or (p > 1): `````` 103 `````` raise ValueError("The probability 'p' must be in [0; 1].") `````` Steven Cordwell committed Aug 18, 2013 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 `````` # Definition of Transition matrix P(:,:,1) associated to action Wait # (action 1) and P(:,:,2) associated to action Cut (action 2) # | p 1-p 0.......0 | | 1 0..........0 | # | . 0 1-p 0....0 | | . . . | # P(:,:,1) = | . . 0 . | and P(:,:,2) = | . . . | # | . . . | | . . . | # | . . 1-p | | . . . | # | p 0 0....0 1-p | | 1 0..........0 | if is_sparse: P = [] rows = range(S) * 2 cols = [0] * S + range(1, S) + [S - 1] vals = [p] * S + [1-p] * S P.append(coo_matrix((vals, (rows, cols)), shape=(S,S)).tocsr()) rows = range(S) cols = [0] * S vals = [1] * S P.append(coo_matrix((vals, (rows, cols)), shape=(S,S)).tocsr()) else: P = zeros((2, S, S)) P[0, :, :] = (1 - p) * diag(ones(S - 1), 1) P[0, :, 0] = p P[0, S - 1, S - 1] = (1 - p) P[1, :, :] = zeros((S, S)) P[1, :, 0] = 1 # Definition of Reward matrix R1 associated to action Wait and # R2 associated to action Cut # | 0 | | 0 | # | . | | 1 | # R(:,1) = | . | and R(:,2) = | . | # | . | | . | # | 0 | | 1 | # | r1 | | r2 | R = zeros((S, 2)) R[S - 1, 0] = r1 R[:, 1] = ones(S) R[0, 1] = 0 R[S - 1, 1] = r2 # we want to return the generated transition and reward matrices return (P, R) `````` Steven Cordwell committed Aug 24, 2013 145 ``````def rand(S, A, is_sparse=False, mask=None): `````` Steven Cordwell committed Aug 18, 2013 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 `````` """Generate a random Markov Decision Process. Parameters ---------- S : int number of states (> 0) A : int number of actions (> 0) is_sparse : logical, optional false to have matrices in dense format, true to have sparse matrices (default false). mask : array or None, optional matrix with 0 and 1 (0 indicates a place for a zero probability), (SxS) (default, random) Returns ------- out : tuple ``out[1]`` contains the transition probability matrix P with a shape of (A, S, S). ``out[2]`` contains the reward matrix R with a shape of (S, A). Examples -------- >>> import mdp >>> P, R = mdp.exampleRand(5, 3) """ # making sure the states and actions are more than one if (S < 1) or (A < 1): `````` 176 177 `````` raise ValueError("The number of states S and the number of actions A " "must be greater than 1.") `````` Steven Cordwell committed Aug 18, 2013 178 179 180 181 182 `````` # if the user hasn't specified a mask, then we will make a random one now if mask is not None: # the mask needs to be SxS or AxSxS try: if mask.shape not in ((S, S), (A, S, S)): `````` 183 `````` raise ValueError("'mask' must have dimensions S×S or A×S×S.") `````` Steven Cordwell committed Aug 18, 2013 184 `````` except AttributeError: `````` 185 `````` raise TypeError("'mask' must be a numpy array or matrix.") `````` Steven Cordwell committed Aug 18, 2013 186 187 188 189 190 191 192 193 194 195 196 197 198 199 `````` # generate the transition and reward matrices based on S, A and mask if is_sparse: # definition of transition matrix : square stochastic matrix P = [None] * A # definition of reward matrix (values between -1 and +1) R = [None] * A for a in xrange(A): # it may be more efficient to implement this by constructing lists # of rows, columns and values then creating a coo_matrix, but this # works for now PP = dok_matrix((S, S)) RR = dok_matrix((S, S)) for s in xrange(S): if mask is None: `````` Steven Cordwell committed Aug 24, 2013 200 `````` m = random(S) `````` Steven Cordwell committed Aug 18, 2013 201 202 203 204 205 206 207 208 209 210 211 `````` m[m <= 2/3.0] = 0 m[m > 2/3.0] = 1 elif mask.shape == (A, S, S): m = mask[a][s] # mask[a, s, :] else: m = mask[s] n = int(m.sum()) # m[s, :] if n == 0: m[randint(0, S)] = 1 n = 1 cols = where(m)[0] # m[s, :] `````` Steven Cordwell committed Aug 24, 2013 212 `````` vals = random(n) `````` Steven Cordwell committed Aug 18, 2013 213 `````` vals = vals / vals.sum() `````` Steven Cordwell committed Aug 24, 2013 214 `````` reward = 2*random(n) - ones(n) `````` Steven Cordwell committed Aug 18, 2013 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 `````` PP[s, cols] = vals RR[s, cols] = reward # PP.tocsr() takes the same amount of time as PP.tocoo().tocsr() # so constructing PP and RR as coo_matrix in the first place is # probably "better" P[a] = PP.tocsr() R[a] = RR.tocsr() else: # definition of transition matrix : square stochastic matrix P = zeros((A, S, S)) # definition of reward matrix (values between -1 and +1) R = zeros((A, S, S)) for a in range(A): for s in range(S): # create our own random mask if there is no user supplied one if mask is None: `````` Steven Cordwell committed Aug 24, 2013 231 `````` m = random(S) `````` Steven Cordwell committed Aug 18, 2013 232 233 234 235 236 237 238 239 240 241 242 `````` r = random() m[m <= r] = 0 m[m > r] = 1 elif mask.shape == (A, S, S): m = mask[a][s] # mask[a, s, :] else: m = mask[s] # Make sure that there is atleast one transition in each state if m.sum() == 0: m[randint(0, S)] = 1 n = 1 `````` Steven Cordwell committed Aug 24, 2013 243 `````` P[a][s] = m * random(S) `````` Steven Cordwell committed Aug 18, 2013 244 `````` P[a][s] = P[a][s] / P[a][s].sum() `````` Steven Cordwell committed Aug 24, 2013 245 `````` R[a][s] = (m * (2*random(S) - ones(S, dtype=int))) `````` Steven Cordwell committed Aug 18, 2013 246 247 `````` # we want to return the generated transition and reward matrices return (P, R)``````