reinforcement learning homework

1 files changed, 341 insertions, 0 deletions

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+from random import random
+from itertools import product
+from collections import defaultdict
+from sys import argv
+
+maze = [ [0, 0, 0, 0, 0, 0, 0],
+         [0, 0, 1, 0, 0, 0, 0],
+         [0, 1, 1, 0, 0, 0, 0],
+         [0, 0, 1, 0, 0, 1, 0],
+         [0, 0, 0, 0, 0, 1, 2] ]
+
+start=(1,1)
+theta = None
+theta_1 = 0.00001
+theta_2 = 0.01
+gamma=0.9 # discount
+epsilon = 0.1
+epsilon_reduction = 1
+alpha = 0.4
+alpha_reduction = 0.9998
+friendlyness = 0.7  # probability that the model actually performs the action we've requested.
+                    # the model will perform a random other actions with probability of (1-friendlyness)/3.
+                    # putting 0.25 here will make it just random.
+frameskip = 99
+visu = True
+
+
+def cursor_up(n):
+        print("\033[%dA" % n)
+
+def args(argv):
+    result=defaultdict(lambda:None)
+    ss=None
+    for s in argv[1:]+["-"]:
+        if s[0]=='-':
+            if ss!=None:
+                result[ss]=True
+            ss=s
+        else:
+            if ss!=None:
+                result[ss]=s
+                ss=None
+            else:
+                explode
+    return result
+
+arg=args(argv)
+print(arg)
+
+mode = None
+if arg['-1'] or arg['--policy-evaluation']:
+    mode = 1
+elif arg['-2'] or arg['--q-learning']:
+    mode = 2
+else:
+    print("Usage: %s MODE [OPTIONS]" % argv[0])
+    print("       MODE:  -1 / --policy-evaluation or\n" +
+          "              -2 / --q-learning\n" +
+          "       OPTIONS: --theta NUM     # convergence threshold\n" +
+          "                                # default: %f / %f for -1 / -2\n" % (theta_1, thetha_2) +
+          "                --gamma NUM     # learning discount for value iteration\n" +
+          "                                # default: %f\n" % gamma +
+          "                --alpha NUM     # learning rate for q-learning\n" +
+          "                                # default: %f\n" % alpha +
+          "                --alphared NUM  # reduction of alpha per episode\n" +
+          "                                # default: %f\n" % alpha_reduction +
+          "                --friendly NUM  # friendlyness of the system (probability\n" +
+          "                                  that the requested action is really done)\n" +
+          "                                # default: %f\n" % friendlyness +
+          "                --epsilon NUM   # value for the epsilon-policy used in q-learning\n" +
+          "                                # default: %f\n" % epsilon +
+          "                --epsred NUM    # reduction of epsilon per episode\n" +
+          "                                # default: %f\n\n" % epsilon_reduction +
+          "                --frameskip NUM # frameskip for visualisation\n" +
+          "                                # default: %f\n" % frameskip +
+          "                --quiet         # disable visualisation" +
+          "                --file FILE     # output file for q learning")
+    exit()
+
+
+if arg['-q'] or arg['--quiet']:
+    visu = False
+
+if arg['--theta']:
+    theta = theta_1 = theta_2 = float(arg['--theta'])
+
+if arg['--gamma']:
+    gamma = float(arg['--gamma'])
+
+if arg['--epsilon']:
+    epsilon = float(arg['--epsilon'])
+
+if arg['--epsred']:
+    epsilon_reduction = float(arg['--epsred'])
+
+if arg['--alpha']:
+    alpha = float(arg['--alpha'])
+
+if arg['--alphared']:
+    alpha_reduction = float(arg['--alphared'])
+
+if arg['--friendly']:
+    friendlyness = float(arg['--friendly'])
+
+logfile = None
+if arg['--file']:
+    logfile = open(arg['--file'], "w")
+
+NORTH=0
+EAST=1
+SOUTH=2
+WEST=3
+
+directions = [NORTH, EAST, SOUTH, WEST]
+dir_coords = [(0,-1), (1,0), (0,1), (-1,0)]
+
+def argmax(l):
+    return max(range(len(l)), key=lambda i:l[i])
+
+def merge_dicts(dicts):
+    result = defaultdict(lambda:0.)
+    for factor, d in dicts:
+        for k in d:
+            result[k] += factor * d[k]
+    return result
+
+def draw_randomly(d):
+    c = 0.
+    rnd = random()
+    for k in d:
+        c += d[k]
+        if rnd < c:
+            return k
+
+def visualize(maze, P):
+    n=0
+    for y in range(len(maze)):
+        line1=""
+        line2=""
+        line3=""
+        for x in range(len(maze[0])):
+            if maze[y][x] == 1:
+                line1 += "@" * (2+7)
+                line3 += "@" * (2+7)
+                line2 += "@@@%03.1f@@@" % P[y][x]
+            elif maze[y][x] == 2:
+                line1 += "." * (2+7)
+                line3 += "." * (2+7)
+                line2 += ".%07.5f." % P[y][x]
+            else:
+                line1 += "'" + " " * (7) + " "
+                line3 += " " + " " * (7) + " "
+                line2 += " %07.5f " % P[y][x]
+        print(line1)
+        print(line3)
+        print(line2)
+        print(line3)
+        print(line3)
+        n+=5
+    return n
+
+def visualize2(maze, Q):
+    n=0
+    for y in range(len(maze)):
+        line1=""
+        line2=""
+        line3=""
+        line4=""
+        line5=""
+        for x in range(len(maze[0])):
+            if maze[y][x] == 1:
+                f = lambda s : s.replace(" ","@")
+            elif maze[y][x] == 2:
+                f = lambda s : s.replace(" ","+")
+            else:
+                f = lambda s : s
+
+            maxdir = argmax(Q[y][x])
+            line3 += f("'     " + ("^" if maxdir == NORTH else " ") + "     ")
+            line5 += f("      " + ("v" if maxdir == SOUTH else " ") + "     ")
+            line1 += f("    %04.2f    " % Q[y][x][NORTH])
+            line2 += f("%s%04.2f  %04.2f%s" % ("<" if maxdir == WEST else " ",Q[y][x][WEST], Q[y][x][EAST], ">" if maxdir == EAST else " "))
+            line4 += f("    %04.2f    " % Q[y][x][SOUTH])
+        print(line3)
+        print(line1)
+        print(line2)
+        print(line4)
+        print(line5)
+        n+=5
+    return n
+
+class World:
+    def __init__(self, maze, pos):
+        self.x,self.y = pos
+        self.maze = maze
+        self.xlen = len(maze[0])
+        self.ylen = len(maze)
+
+    def possible_next_states(self, s):
+        # must return at least all possible states.
+        # must only return valid states.
+        x,y = s
+        return filter(lambda s : s[0]>=0 and s[1]>=0 and s[0] < self.xlen and s[1] < self.ylen, [(x,y),(x+1,y),(x-1,y),(x,y-1),(x,y+1)])
+
+
+    # definitely walks from (x,y) into direction.
+    # returns the neighboring coordinate on success,
+    # or the old one if there was a wall
+    def walk(self, x,y, direction):
+        dx,dy=dir_coords[direction]
+        nx,ny = x+dx, y+dy
+
+        if 0 <= nx and nx < self.xlen and \
+           0 <= ny and ny < self.ylen and \
+           self.maze[y][x] == 0 and \
+           self.maze[ny][nx] != 1:
+            return nx,ny
+        else:
+            return x,y
+
+
+    # gives probabilities for new states, given
+    # the command "direction".
+    def action(self, x,y , direction):
+        newstates = defaultdict(lambda:0.)
+        for i in range(4):
+            newstates[ self.walk(x,y, (direction+i)%4 ) ] += friendlyness if i == 0 else (1-friendlyness)/3. #[1.0,0.,0.,0.][i] # [0.7,0.1,0.1,0.1][i]
+        return newstates
+
+    def take_action(self, x,y, direction):
+        newstates = self.action(x,y,direction)
+        ss = draw_randomly(newstates)
+        return self.R((x,y),ss, None), ss
+
+
+    def P(self, s, ss, pi):
+        return merge_dicts([(pi[d], self.action(s[0],s[1], d)) for d in directions])[ss]
+
+
+    def R(self, s, ss, pi):
+        if s!=ss and self.maze[ss[1]][ss[0]] == 2: # goal
+            return 10.0
+        else:
+            return 0.
+
+    def is_final(self,s):
+        return self.maze[s[1]][s[0]] == 2
+
+if mode == 1:  # policy evaluation
+    theta = theta_1
+    a = World(maze, start)
+
+    V = [ [0.0] * a.xlen for i in range(a.ylen) ]
+    pi = [ [ [0.25] * 4 for i in range(a.xlen) ] for j in range(a.ylen) ]
+
+    i=0
+    while True:
+        i = i + 1
+        delta = 0
+        for x,y in product(range(a.xlen), range(a.ylen)):
+            v = V[y][x]
+            V[y][x] = sum( a.P((x,y),(xx,yy), pi[y][x]) * (  a.R((x,y),(xx,yy), pi[y][x]) + gamma * V[yy][xx]  ) for xx,yy in product(range(a.xlen), range(a.ylen)) )
+            delta = max(delta, abs(v - V[y][x]))
+
+        print("iteration %.3d, delta=%.7f"%(i,delta))
+        n = 0
+        if visu:
+            n = visualize(maze,V)
+        cursor_up(n+2)
+
+        if (delta < theta):
+            break
+    print("finished after %d iterations" % i)
+    visualize(maze,V)
+
+elif True:  # q-learning
+    theta = theta_2
+
+    a = World(maze, start)
+    Q = [ [ [0. for k in range(4)] for i in range(a.xlen) ] for j in range(a.ylen) ]
+
+    i=0
+    stopstate = -1
+    total_reward = 0.
+    for i in range(1000000):
+        s = start
+        maxdiff=0.
+        for j in range(100):
+            # epsilon-greedy
+            greedy = argmax(Q[s[1]][s[0]])
+            rnd = random()
+            action = None
+            if rnd < epsilon:
+                action = ( greedy + int(1 + 3 * rnd / epsilon) ) % 4
+            else:
+                action = greedy
+
+            r,ss = a.take_action(s[0],s[1], action)
+            #print ((r,ss))
+            diff = alpha * (r + gamma * max( [ Q[ss[1]][ss[0]][aa] for aa in directions ] ) - Q[s[1]][s[0]][action])
+            Q[s[1]][s[0]][action] += diff
+            maxdiff = max(abs(diff),maxdiff)
+            total_reward += r
+            s = ss
+            if a.is_final(ss):
+                break
+
+        if (i % (frameskip+1) == 0):
+            print("iteration %.3d, alpha=%.3e, epsilon=%.3e maxdiff=%.7f"%(i,alpha,epsilon,maxdiff))
+            n = 0
+            if visu:
+                n = visualize2(maze,Q)
+            cursor_up(n+2)
+
+        if (logfile != None):
+            print("%d\t%f" % (i, total_reward), file=logfile)
+
+        # Wikipedia says on this: "When the problem is stochastic [which it is!],
+        # the algorithm still converges under some technical conditions on the
+        # learning rate, that require it to decrease to zero.
+        # So let's sloooowly decrease our learning rate here. Otherwise it won't
+        # converge, but instead oscillate plus/minus 0.5.
+        # However, if we set the friendlyness of our system to 1.0, then it would
+        # also converge without this learning rate reduction, because we have a
+        # non-stochastic but a deterministic system now.
+        alpha *= alpha_reduction
+        epsilon *= epsilon_reduction
+
+        
+        # stop once we're below theta for at least 100 episodes. But not before we went above theta at least once.
+        if maxdiff < theta:
+            stopstate -= 1
+            if stopstate == 0:
+                break
+        else:
+            stopstate = 100
+    
+    print("finished after %.3d iterations, alpha=%.3e, epsilon=%.3e"%(i,alpha,epsilon))
+    visualize2(maze,Q)
+    if logfile != None:
+        logfile.close()