def __init__(self, policy):
# world object, (starting state is trivial)
world = World((0,0),(1,1))
value = {}
for state in world.allStates():
value[state] = 0
discount = 0.9
delta = 1
while abs(delta) > 0.00001:
delta = 0
for state in world.allStates():
world.setState(state)
old = value[state]
# we can set the minimum to 0 since we know every value will be 0 or positive
curMax = 0
for move in world.moveList():
if world.posAfterMove(move) == (0,0):
probSum = 10
else:
probSum = 0
for nextState,prob in world.nextPreyStates():
probSum += prob*discount*value[nextState]
curMax = max(curMax,probSum)
value[state] = curMax
delta = max(delta,abs(old - curMax))
value[(0,0)] = 10
self.value = value
self.actionList = []
self.allList = []
self.bottomPolicy = policy
self.discount = discount
def MCon(episodes, initValue=15,epsilon=0.1, alpha=0.5,discount=0.9):
# world object, (starting state is trivial)
world = World((0,0),(1,1))
# initialize Q value table and Return list for every (s,a)-pair
Q = {}
R = {}
for state in world.allStates():
for move in world.moveList():
Q[state,move] = initValue # some value
R[state,move] = [] # empty list; return = cummulative discounted reward
steps = [0]*episodes # list counting number of iterations
for i in range(episodes):
iterations = 0
# initialize world
world.setState((-5,-5))
stateActionPairs = {}
# generate an episode using current policy
while True:
state = world.position
# move the predator according to policy
action = epsGreedyPolicy(state, world, Q, epsilon)
world.move(action)
if not (state,action) in stateActionPairs: # store first occurence
stateActionPairs[(state,action)] = iterations # will be used for discounting
iterations += 1
# check if predator caught the prey
if world.stopState():
break
# move the prey (stochasticly)
world.performPreyMove()
newState = world.position
steps[i] = iterations # save amount of iterations needed to catch the prey
# update Q and R
for pair in stateActionPairs.keys():
firstReturn = 10.0*discount**(iterations-stateActionPairs[pair]) # always zero but 10 when episode ends
R[pair].append(firstReturn)
Q[pair] = np.mean(np.array(R[pair]))
# update policy done in epsilon greedy policy code
return steps
def Qlearning(episodes, policy, startState=(-5,-5), initValue=15,policyParam=0.1, alpha=0.4,discount=0.9):
# world object, (starting state is trivial)
world = World((0,0),(1,1))
# Q value table
Q = {}
for state in world.allStates():
for move in world.moveList():
Q[state,move] = initValue
steps = [0]*episodes
for i in range(episodes):
iterations = 0
# initialize world
world.setState(startState)
while True:
state = world.position
# move the predator according to policy with one parameter (epsilon for E-greedy or Tua for softmax)
action = policy(state, world, Q, policyParam)
world.move(action)
iterations += 1
# check if predator caught the prey
if world.stopState():
# the Q(s,a) update rule (note that the next state is the absorbing state)
Q[state,action] = Q[state,action] + alpha * (10 - Q[state,action])
break
# move the prey (stochasticly)
world.performPreyMove()
newState = world.position
# the maximum value the agent can have after another move
maxQ = max([Q[newState,nextAction] for nextAction in world.moveList()])
# the Q(s,a) update rule (note that the immediate reward is zero)
Q[state,action] = Q[state,action] + alpha * ( discount*maxQ - Q[state,action])
# print the number of steps the predator took
steps[i] = iterations
return steps
def minimax(episodes,initial_state,epsilon, decay, gamma, alpha_pred=1.0, alpha_prey=1.0):
# initialization might be too expansive
Q_pred = dict()
Q_prey = dict()
V_pred = dict()
V_prey = dict()
pi_pred = dict()
pi_prey = dict()
initValue = 1.0
# initialisation
world = World((5,5),initial_state)
for state in world.allStates():
V_pred[state] = 1.0
V_prey[state] = 1.0
for action in world.allMoveList():
pi_pred[(state,action)]=1.0/len(world.allMoveList())
for prey_move in world.singleMoveList():
Q_pred[(state, action, prey_move)]=1.0
Q_prey[(state, action, prey_move)]=1.0
for action in world.singleMoveList():
pi_prey[(state,action)]=1.0/len(world.singleMoveList())
# absorbing states
terminal_state = tuple([(0,0)] * len(initial_state))
V_pred[terminal_state] = 0.0
V_prey[terminal_state] = 0.0
steps = [0]*episodes
rewards = [0]*episodes
for epi in range(episodes):
# initialize world
world = World((5,5),initial_state)
# print "Begin Pred", V_pred[world.position]
# print "End Prey", V_prey[world.position]
# for s in world.singleMoveList():
# print s, "Pred", V_pred[(s,)]
# print s, "Prey", V_pred[(s,)]
# for a in world.allMoveList():
# for a2 in world.singleMoveList():
# print s, "Q", a, a2, Q_pred[(state,a,a2)]
iterations =0
while not world.stopState():
state = world.position
# choose action
action_pred = minimax_policy(epsilon, pi_pred, state, world.allMoveList())
action_prey = minimax_policy(epsilon, pi_prey, state, world.singleMoveList())
reward = world.move(action_prey,action_pred)
iterations +=1
new_state = world.position
# update Q
# if (state,action_prey) not in Q_prey:
# Q_prey[state,action_prey] = initValue
# if (state,action_pred) not in Q_pred:
# Q_pred[state,action_pred] = initValue
Q_pred[(state,action_pred,action_prey)] = (1.0-alpha_pred)*Q_pred[(state,action_pred,action_prey)] + alpha_pred*(reward[1]+ gamma* V_pred[new_state])
Q_prey[(state,action_pred,action_prey)] = (1.0-alpha_prey)*Q_prey[(state,action_pred,action_prey)] + alpha_prey*(reward[0]+ gamma* V_prey[new_state])
# update pi
# adapted from example: http://abel.ee.ucla.edu/cvxopt/examples/tutorial/lp.html
## PREDATOR update
# constraint to minimize w.r.t. prey action
minConstr = [[1.0] + [-Q_pred[(state,a_pred,a_prey)] for a_pred in world.allMoveList()] for a_prey in world.singleMoveList()]
# constrinat to keep every pi(a) positive
posConstr = []
for i in range(1,len(world.allMoveList())+1):
new_row = [0.0] * (len(world.allMoveList())+1)
new_row[i] = -1.0
posConstr.append(new_row)
normGreater = [0.0] + [1.0] * len(world.allMoveList())
normSmaller = [0.0] + [-1.0] * len(world.allMoveList())
A = matrix([normGreater, normSmaller] + minConstr + posConstr).trans()
b = matrix([ 1.0, -1.0] + [0.0] * (len(world.singleMoveList()) + len(world.allMoveList())) )
# -1 V and 0 for all pi(s,a)
c = matrix([ -1.0 ] + [0.0] * len(world.allMoveList()))
sol=solvers.lp(c,A,b)
V_pred[state] = sol['x'][0]
for a_pred, x in zip(world.allMoveList(),sol['x'][1:]):
pi_pred[(state,a_pred)] = x
# ## PREY update
# constraint to minimize w.r.t. prey action
minConstr = [[1.0] + [-Q_prey[(state,a_pred,a_prey)] for a_prey in world.singleMoveList()] for a_pred in world.allMoveList()]
# # constriant to keep every pi(a) positive
posConstr = []
for i in range(1,len(world.singleMoveList())+1):
new_row = [0.0] * (len(world.singleMoveList())+1)
new_row[i] = -1.0
posConstr.append(new_row)
normGreater = [0.0] + [ 1.0] * len(world.singleMoveList())
normSmaller = [0.0] + [-1.0] * len(world.singleMoveList())
A = matrix([normGreater, normSmaller] + minConstr + posConstr).trans()
b = matrix([ 1.0, -1.0] + [0.0] * (len(world.allMoveList()) + len(world.singleMoveList())) )
# -1 V and 0 for all pi(s,a)
c = matrix([ -1.0 ] + [0.0] * len(world.singleMoveList()))
sol=solvers.lp(c,A,b)
V_prey[state] = sol['x'][0]
for a_prey, x in zip(world.singleMoveList(),sol['x'][1:]):
pi_prey[(state,a_prey)] = x
alpha_pred *= decay
alpha_prey *= decay
if epi > 0 and epi % 50 == 0:
print "Episode",epi
steps[epi] = iterations
if reward[1] > 0:
rewards[epi] = 1
return steps, rewards
def MCoff(episodes, behaPolicy, matches=[], initValue=15,discount=0.9):
# behaPolicy = dictionary with keys (state,action) and value P(action|state)
world = World((0,0),(1,1))
movelist = world.moveList()
def policy(world):
return world.pickElementWithProbs([(move,behaPolicy[(world.position,move)]) for move in movelist])
# initialize Q value table and Return list for every (s,a)-pair
Q = {}
R = {}
num = {}
denum = {}
for state in world.allStates():
for move in world.moveList():
num[state,move] = 0.0
denum[state,move] = 0.0
Q[state,move] = float(initValue) # some value
R[state,move] = [] # empty list; return = cummulative discounted reward
steps = [0]*episodes # list counting number of iterations
for epi in range(episodes):
time = 0
totalTime =0
# initialize world
world.setState((-5,-5))
episode = []
while True:
action = policy(world)
episode.append((world.position, action))
if action == None:
print action, state
world.move(action)
if world.stopState():
break
world.performPreyMove()
# save the pairs that match, and their first occurence
matchingHistory = {}
# last time move was equal to policy
last = 0
for i, (state, action) in enumerate(episode[::-1]):
actionValues = [(Q[state,maction],maction) for maction in world.moveList()]
bestActions = [actionValues[j][1] for j in maxIndices(actionValues)]
matchingHistory[(state, action)] = len(episode)-i - 1
if action not in bestActions:
last = len(episode)-i
break
matches.append(len(episode)-last)
for (state, action) in matchingHistory:
if matchingHistory[(state, action)] >= last-1:
w = np.prod([ 1.0/behaPolicy[episode[j]] for j in range(matchingHistory[(state, action)],len(episode))])
num[(state,move)] += w * (10.0*discount**matchingHistory[(state, action)]) # return is gamma^{T-t}*10
denum[(state,move)] += w
Q[(state,move)]= num[(state,move)]/float(denum[(state,move)])
world.setState((-5,-5))
iterations = 0
while True:
iterations += 1
actionValues = [(maction, Q[state,maction]) for maction in world.moveList()]
bestAction = random.choice([actionValues[j][0] for j in maxIndices(actionValues)])
world.move(bestAction)
if world.stopState() or iterations > 2000:
break
world.performPreyMove()
steps[epi] = iterations
return steps
