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calendar_problem_RL_probabilistic_greedy.py
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import numpy as np
from matplotlib import pyplot as plt
from matplotlib.gridspec import GridSpec
from matplotlib.animation import FuncAnimation
import time
from IPython.display import clear_output
from matplotlib import transforms, animation
import imageio
from IPython.display import HTML
import matplotlib
matplotlib.rcParams['animation.embed_limit'] = 2**128
def softmax_probabilities(vals):
t = np.exp(vals)
return np.exp(vals) / np.sum(t)
def softmax_sample(vals):
probs = softmax_probabilities(vals)
return np.random.choice([0, 1], size=1, p=probs)[0], probs
def rainbow_text(x, y, ls, lc, ax, fig,**kw):
t = ax.transData
for s,c in zip(ls,lc):
text = ax.text(x, y, s, color=c, transform=t, **kw)
text.draw(fig.canvas.get_renderer())
ex = text.get_window_extent()
t = transforms.offset_copy(text._transform, x=ex.width, units='dots')
global state_locations, actions, state_rewards, state_q_values, state_actions, current_algorithm_step, previous_state_action, current_state_action, is_first_iteration, alpha, new_previous_q_val_memory, current_state_color, previous_state_color, random_action_choice
def reset():
global state_locations, actions, state_rewards, state_q_values, state_actions, current_algorithm_step, previous_state_action, current_state_action, is_first_iteration, alpha, new_previous_q_val_memory, current_state_color, previous_state_color, random_action_choice
state_q_values = {0: [0.1, 0],
1: [0, 0.1],
2: [0, 0.1],
3: [0, 0],
4: [0, 0.1],
5: [0, 0],
6: [0, 0],
7: [0, 0],
8: [0, 0]}
state_actions = {0: [1, 2],
1: [3, 4],
2: [5, 6],
4: [7, 8]}
state_locations = [(0.15, 0.5),
(0.4, 0.775), (0.4, 0.225),
(0.65, 0.9), (0.65, 0.65), (0.65, 0.35), (0.65, 0.1),
(0.9, 0.8), (0.9, 0.525)]
actions = [(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6), (4, 7), (4, 8)]
state_rewards = {1: 4,
2: 1,
3: 10,
4: 1,
5: 2,
6: -3,
7: -3,
8: -4}
current_algorithm_step = -1
random_action_choice = softmax_sample(state_q_values[0]) # softmax_sample([0, 0])
current_state_action = [0, random_action_choice[0]]
previous_state_action = None
previous_state_color = 'C5'
current_state_color = 'C1'
is_first_iteration = True
alpha = 1
new_previous_q_val_memory = None
return ()
def get_current_rl_step():
if current_algorithm_step == -1:
return "initialize Q values"
if current_algorithm_step == 0:
return "start"
if current_algorithm_step == 1:
return "action selection rule"
if current_algorithm_step == 2:
return "take action from previous state"
if current_algorithm_step == 3:
return "update Q values"
if current_algorithm_step == 4:
return "update previous/current state-actions"
def draw_calendar_problem(ax, fig):
global state_q_values, state_locations, actions, state_rewards, previous_state_action, current_state_action, is_first_iteration, alpha, new_previous_q_val_memory
ax.cla()
ax.axis('off')
state_radius = 0.09
for state, state_location in enumerate(state_locations):
edgecolor = current_state_color if state == current_state_action[0] and (current_algorithm_step >= 1 or current_state_action[0] != 0) else 'k'
lw = 5 if state == current_state_action[0] and (current_algorithm_step >= 1 or current_state_action[0] != 0) else 1
if previous_state_action is not None:
if state == previous_state_action[0]:
edgecolor = previous_state_color
lw = 5
circle = plt.Circle(state_location, state_radius, edgecolor=edgecolor, linewidth=lw,
facecolor='white', zorder=2, alpha=1)
ax.add_patch(circle)
if state in state_actions:
for action in state_actions[state]:
#textcolor = current_state_color if state == current_state_action[0] and max(state_q_values[state]) == state_q_values[state][state_actions[state].index(action)] and current_algorithm_step >= 2 else 'k'
textcolor = current_state_color if state == current_state_action[0] and state_actions[state].index(action) == current_state_action[1] and current_algorithm_step >= 2 else 'k'
if previous_state_action is not None:
#if state == previous_state_action[0] and max(state_q_values[previous_state_action[0]]) == state_q_values[previous_state_action[0]][state_actions[previous_state_action[0]].index(action)]:
if state == previous_state_action[0] and state_actions[state].index(action) == previous_state_action[1]:
textcolor = previous_state_color
if textcolor == 'k':
actioncolor = 'gray'
else:
actioncolor = textcolor
xs = [state_locations[state][0], state_locations[action][0]]
ys = [state_locations[state][1], state_locations[action][1]]
ax.plot(xs, ys, zorder=1, color=actioncolor, linewidth=10)
if current_algorithm_step != -1:
offset_multiplier = 1
for action in [0, 1]:
textcolor = current_state_color if state == current_state_action[0] and action == current_state_action[1] and current_algorithm_step >= 2 else 'k'
if previous_state_action is not None:
if state == previous_state_action[0] and action == previous_state_action[1]:
textcolor = previous_state_color
if previous_state_action is not None and new_previous_q_val_memory is not None:
if state == previous_state_action[0] and action == previous_state_action[1]:
ax.text(state_location[0], state_location[1] + (offset_multiplier*0.035),
f'{state_q_values[state][action]}→{new_previous_q_val_memory:.1f}',
ha='center', va='center', fontsize=10, color=textcolor, fontweight='bold')
else:
ax.text(state_location[0], state_location[1] + (offset_multiplier*0.035),
f'{state_q_values[state][action]}',
ha='center', va='center', fontsize=15, color=textcolor)
else:
ax.text(state_location[0], state_location[1] + (offset_multiplier*0.035),
f'{state_q_values[state][action]}',
ha='center', va='center', fontsize=15, color=textcolor)
offset_multiplier *= -1
else:
ax.text(state_location[0], state_location[1], f"State {state}",
ha='center', va='center', fontsize=15, color='k')
for state in state_rewards:
reward = state_rewards[state]
state_location = state_locations[state]
ax.text(state_location[0], state_location[1] + state_radius + 0.035, reward, color='r',
ha='center', va='center', fontsize=15, fontweight='bold')
if current_algorithm_step >= 0:
ax.text(state_locations[0][0] - 0.01, state_locations[0][1] + 0.125, "start", color='k',
fontsize=15, fontweight='bold', ha='center', va='center')
if current_algorithm_step == -1:
ax.annotate("state", xy=(state_locations[0][0],
state_locations[0][1] + state_radius + 0.01),
xytext=[0.1, 0.75],
arrowprops=dict(facecolor='black', shrink=0),
ha='right', va='center', fontsize=15)
ax.annotate("action", xy=(state_locations[0][0] + state_radius,
state_locations[0][1] + state_radius + state_radius - 0.01),
xytext=[0.1, 0.85],
arrowprops=dict(facecolor='black', shrink=0),
ha='right', va='center', fontsize=15)
ax.annotate("reward", xy=(state_locations[1][0] - 0.025,
state_locations[1][1] + state_radius + 0.04),
xytext=[0.15, 0.95],
arrowprops=dict(facecolor='black', shrink=0),
ha='right', va='center', fontsize=15)
ax.annotate("terminal state", xy=(state_locations[8][0],
state_locations[8][1] - state_radius - 0.02),
xytext=[1.05, 0.25],
arrowprops=dict(facecolor='black', shrink=0),
ha='right', va='center', fontsize=15)
def draw_current_step(ax, fig):
global is_first_iteration, current_state_action, previous_state_action, alpha, new_previous_q_val_memory, random_action_choice
ax.cla()
ax.axis('off')
ax.set_title('Next Step:', fontsize=20, y=0.8)
current_step = get_current_rl_step()
if current_step == "initialize Q values":
current_step_text = "assign initial\nQ values to\neach state-action pair\n\nterminal states are assigned\nQ values of 0"
ax.text(0.5, 0.4, current_step_text, ha='center', va='center',
fontsize=20, color='k')
if current_step == "start":
if is_first_iteration:
current_step_text = "begin at\nthe start state"
else:
current_step_text = 'restart at the\nstart state because\ntermimal state\nreached and set the\n"previous state-action"\nto None'
random_action_choice = softmax_sample(state_q_values[0]) #softmax_sample([0, 0])
current_state_action = [0, random_action_choice[0]]
previous_state_action = None
is_first_iteration = True
ax.set_title('Next Step:', fontsize=20, y=0.9)
ax.text(0.5, 0.5, current_step_text, ha='center', va='center',
fontsize=20, color='k')
if current_step == "action selection rule":
if not is_first_iteration:
#random_action_choice = softmax_sample(state_q_values[current_state_action[0]])
ax.text(0.5, 0.95, "action selection rule", fontsize=20, color='k', va='center', ha='center')
current_step_text = "use softmax function to\nconvert current state's q-values\nto probabilities"
ax.text(0.5, 0.65, current_step_text, ha='center', va='center',
fontsize=20, color='k')
q_up = state_q_values[current_state_action[0]][0]
q_down = state_q_values[current_state_action[0]][1]
p_up = random_action_choice[1][0]
p_down = random_action_choice[1][1]
q_up = f'{q_up:.2f}'
q_down = f'{q_down:.2f}'
p_up = f'{round(p_up, 2)*100:.0f}%'
p_down = f'{round(p_down, 2)*100:.0f}%'
current_step_text = r"prob_up = $ e^{{{{{0}}}}} / (e^{{{{{0}}}}} + e^{{{{{1}}}}})$ = {2}".format(q_up, q_down, p_up)
ax.text(0.5, 0.45, current_step_text, ha='center', va='center',
fontsize=20, color='k')
current_step_text = r"prob_down = $ e^{{{{{0}}}}} / (e^{{{{{0}}}}} + e^{{{{{1}}}}})$ = {2}".format(q_down, q_up, p_down)
ax.text(0.5, 0.35, current_step_text, ha='center', va='center',
fontsize=20, color='k')
tmp_random_action = 'up' if random_action_choice[0] == 0 else 'down'
current_step_text = f'flipping a weighed coin\n with the probabilties above\nyielded random action: go {tmp_random_action}'
ax.text(0.5, 0.1, current_step_text, ha='center', va='center',
fontsize=20, color='k')
ax.set_title('Next Step:', fontsize=20, y=1.15)
else:
ax.text(0.5, 0.95, "action selection rule", fontsize=20, color='k', va='center', ha='center')
current_step_text = "use softmax function to\nconvert current state's q-values\nto probabilities"
ax.text(0.5, 0.65, current_step_text, ha='center', va='center',
fontsize=20, color='k')
q_up = state_q_values[current_state_action[0]][0]
q_down = state_q_values[current_state_action[0]][1]
p_up = random_action_choice[1][0]
p_down = random_action_choice[1][1]
q_up = f'{q_up:.2f}'
q_down = f'{q_down:.2f}'
p_up = f'{round(p_up, 2)*100:.0f}%'
p_down = f'{round(p_down, 2)*100:.0f}%'
current_step_text = r"prob_up = $ e^{{{{{0}}}}} / (e^{{{{{0}}}}} + e^{{{{{1}}}}})$ = {2}".format(q_up, q_down, p_up)
ax.text(0.5, 0.45, current_step_text, ha='center', va='center',
fontsize=20, color='k')
current_step_text = r"prob_down = $ e^{{{{{0}}}}} / (e^{{{{{0}}}}} + e^{{{{{1}}}}})$ = {2}".format(q_down, q_up, p_down)
ax.text(0.5, 0.35, current_step_text, ha='center', va='center',
fontsize=20, color='k')
tmp_random_action = 'up' if random_action_choice[0] == 0 else 'down'
current_step_text = f'flipping a weighed coin\n with the probabilties above\nyielded random action: go {tmp_random_action}'
ax.text(0.5, 0.1, current_step_text, ha='center', va='center',
fontsize=20, color='k')
ax.set_title('Next Step:', fontsize=20, y=1.15)
if current_step == "take action from previous state":
ax.text(0.5, 0.8, f"current state-action\n Q(s', a') = " + f'{state_q_values[current_state_action[0]][current_state_action[1]]}',
ha='center', va='center',
fontsize=20, color=current_state_color)
current_state_reward = state_rewards[current_state_action[0]] if current_state_action[0] in state_rewards else 0
ax.text(0.5, 0.55, f"current state-reward\n R(s') = " + f'{current_state_reward:.2f}',
ha='center', va='center',
fontsize=20, color=current_state_color)
if previous_state_action is not None:
ax.text(0.5, 0.25, f"previous state-action\n Q(s', a') = " + f'{state_q_values[previous_state_action[0]][previous_state_action[1]]}',
ha='center', va='center',
fontsize=20, color=previous_state_color)
else:
ax.text(0.5, 0.15, f"previous state-action\n Q(s, a) = None",
ha='center', va='center',
fontsize=20, color=previous_state_color)
ax.set_title('')
if current_step == "update previous/current state-actions":
if is_first_iteration:
current_step_text = 'since presently no\n"previous state-action" exists,\nskip Q-value update step'
ax.text(0.5, 0.75, current_step_text, ha='center', va='center',
fontsize=15, color='k')
ax.text(0.5, 0.25, 'follow current Q value action\nfrom current state to\nget the next "current state",\nand set the next\n"previous state-action"\nto current state-action', ha='center', va='center',
fontsize=15, color='k')
is_first_iteration = False
ax.set_title('Next Step:', fontsize=20, y=1)
else:
ax.text(0.5, 0.8, 'update previous state-action Q value', ha='center', va='center',
fontsize=18, color='k')
ax.text(0.5, 0.3, 'follow current Q value action\nfrom current state to\nget the next "current state",\nand set the next\n"previous state-action"\nto current state-action', ha='center', va='center',
fontsize=18, color='k')
ax.set_title('Next Step:', fontsize=20, y=1)
if new_previous_q_val_memory is not None:
state_q_values[previous_state_action[0]][previous_state_action[1]] = new_previous_q_val_memory
new_previous_q_val_memory = None
if current_step == "update Q values":
current_step_text = "update previous state-action's\nQ value"
ax.text(0.5, 0.8, current_step_text,
ha='center', va='center', fontsize=20, color='k')
#ax.text(0.5, 0.5, "prediction error =\nR(s') + Q(s', a') - Q(s, a)",
# ha='center', va='center', fontsize=15, color='k')
rainbow_text(-0.1, 0.55,
ls=["prediction error", " = ", "R(s')", " + ", "Q(s', a')", " - ", "Q(s, a)"],
lc=['C0', 'k', 'red', 'k', current_state_color, 'k', previous_state_color],
ha='left', va='center', fontsize=15, ax=ax, fig=fig, fontweight='bold')
r_s = 0 if current_state_action[0] not in state_rewards else state_rewards[current_state_action[0]]
current_q_val = state_q_values[current_state_action[0]][current_state_action[1]]
previous_q_val = state_q_values[previous_state_action[0]][previous_state_action[1]]
pred_err = r_s + current_q_val - previous_q_val
ax.text(0.5, 0.4, f"{pred_err:.2f} = {r_s:.2f} + {current_q_val:.2f} - {previous_q_val:.2f}",
ha='center', va='center', fontsize=20, color='k')
#ax.text(0.5, 0.2, r"Q(s, a) = Q(s, a) + ($\alpha$ * prediction error)",
# ha='center', va='center', fontsize=15, color='k')
rainbow_text(-0.1, 0.15,
ls=["Q(s, a)", " = ", "Q(s, a)", " + (", r"$\alpha$", " * ", "prediction error", ")"],
lc=[previous_state_color, 'k', previous_state_color, 'k', 'C0', 'k', 'C0', 'k'],
ha='left', va='center', fontsize=15, ax=ax, fig=fig, fontweight='bold')
new_previous_q_val = previous_q_val + (alpha * pred_err)
ax.text(0.5, 0.0, f"{new_previous_q_val:.2f} = {previous_q_val:.2f} + ({alpha:.2f} * {pred_err:.2f})",
ha='center', va='center', fontsize=20, color='k')
new_previous_q_val_memory = round(new_previous_q_val, 2)
ax.set_title('Next Step:', fontsize=20, y=1)
def update_algorithm():
global current_algorithm_step, previous_state_action, current_state_action, is_first_iteration, random_action_choice
if current_algorithm_step == 2 and previous_state_action is None:
current_algorithm_step += 2
else:
current_algorithm_step += 1
if current_algorithm_step == 5:
if previous_state_action is None:
previous_state_action = current_state_action
current_state = state_actions[previous_state_action[0]][previous_state_action[1]]
random_action_choice = softmax_sample(state_q_values[current_state]) #softmax_sample([0, 0])
current_action = random_action_choice[0] #np.argmax(state_q_values[current_state])
current_state_action = [current_state, current_action]
elif current_state_action[0] in state_actions:
previous_state_action = current_state_action
current_state = state_actions[previous_state_action[0]][previous_state_action[1]]
random_action_choice = softmax_sample(state_q_values[current_state]) # softmax_sample([0, 0])
current_action = random_action_choice[0] #np.argmax(state_q_values[current_state])
current_state_action = [current_state, current_action]
else:
current_algorithm_step = 0
if current_algorithm_step >= 5:
current_algorithm_step = 1