OpenAI Frozen Lake v0

We are attempting to solve the openai frozen lake environment using reinforcement learning. Openai provides many environments for simulation.

Let us understand what reinforcement learning is and compare it with other available methodologies. The frozen lake problem involves a grid maze with a starting point and a goal. Along the way there are a few fatal pitfalls. Solving the frozen lake requires us to build an agent/bot who can traverse the maze and reach the goal without falling into the pitfalls. The duration of the travel is not a constraint but it is better if the bot can reach it quicker.

SFFF (S: starting point, safe)
FHFH (F: frozen surface, safe)
FFFH (H: hole, fall to your doom)
HFFG (G: goal, where the frisbee is located)

The frozen lake can be solved using a multitude of ways with standard graph search algos to optimization algorithms. There is one caveat though, the environment adds a small complexity to the mix. If our bot wanted to move right, there is a slight chance the bot may move in a random direction. Apparently a gust of wind pushes us away This complexity tends to break our algos like graph search etc which may not handle random probabilities. One worthy method to solve this dynamic environment is Reinforcement Learning.

Framework

we will use the openai gym module to train our bot. Our bot will be a neural network and we will use keras and tensorflow for implementation. We will use Q learning which is a technique of RL(Reinforcement Learning).



In [20]:

    
import gym
import tensorflow as tf
from collections import deque
import numpy as np
from keras.models import Sequential
from keras.layers import Dense
from keras.optimizers import Adam
from gym import wrappers
import shutil



In [21]:

    
shutil.rmtree('./monitor')
env = gym.make('FrozenLake-v0')
env = wrappers.Monitor(env,'./monitor')









    



[2017-07-16 15:00:00,373] Making new env: FrozenLake-v0
[2017-07-16 15:00:00,373] Creating monitor directory ./monitor



In [22]:

    
print(env.observation_space.n)
print(env.action_space.n)

Sample Simulation

The frozen lake environment has the following important entities;

State: A state denotes the current nature of the environment. For frozen lake there are 16 states, each corresponding to a single step.
Action: An action denotes a decision that can be taken by an agent in any state. For frozen lake there are 4 possible actions that can be take in any state; up, down, left and right provided there is a possibility
Reward: A reward signifies the result of an action at a particular state. In frozen lake the reward is 1 if we reach the goal and 0 if we fail. The openai doesn't provide any reward for each action or falling into a hole.
Done: Done signifies the end state of a simulation. For frozen lake, if a bot reaches the goal or falls into a hole, Done returns a value of True, else False.

Below is an example of a single simulation episode.



In [31]:

    
state = env.reset()
for i in range(10):
    env.render()
    action = env.action_space.sample()
    next_state, reward, done, prob = env.step(action)
    print('state:{} action:{} next_state:{} reward:{} done:{}'.format(state, action, next_state, reward, done))
    state = next_state
    if done:
        break









    



SFFF
FHFH
FFFH
HFFG
state:0 action:3 next_state:1 reward:0.0 done:False
  (Up)
SFFF
FHFH
FFFH
HFFG
state:1 action:2 next_state:1 reward:0.0 done:False
  (Right)
SFFF
FHFH
FFFH
HFFG
state:1 action:0 next_state:0 reward:0.0 done:False
  (Left)
SFFF
FHFH
FFFH
HFFG
state:0 action:1 next_state:1 reward:0.0 done:False
  (Down)
SFFF
FHFH
FFFH
HFFG
state:1 action:3 next_state:2 reward:0.0 done:False
  (Up)
SFFF
FHFH
FFFH
HFFG
state:2 action:0 next_state:2 reward:0.0 done:False
  (Left)
SFFF
FHFH
FFFH
HFFG
state:2 action:1 next_state:3 reward:0.0 done:False
  (Down)
SFFF
FHFH
FFFH
HFFG
state:3 action:3 next_state:2 reward:0.0 done:False
  (Up)
SFFF
FHFH
FFFH
HFFG
state:2 action:2 next_state:2 reward:0.0 done:False
  (Right)
SFFF
FHFH
FFFH
HFFG
state:2 action:2 next_state:3 reward:0.0 done:False

Q Learning

Q-learning is one of the techniques used to implement RL. Q-learning relies on the Bellman's equation.

$$ Q(s, a) = r + \gamma \max{Q(s', a')} $$

The Bellman equation provides a way to incorporate future rewards of an action to a current state. This is a core component of Q Learning. In a nutshell Q-learning is finding the function Q = f(state, action) which can be used to derive the action needed for a given state to traverse an environment.

The pseudo code for Q-learning is below

Initialize the memory $D$
Initialize the action-value network $Q$ with random weights
For episode = 1, $M$ do
- For $t$, $T$ do
  - With probability $\epsilon$ select a random action $a_t$, otherwise select $a_t = \mathrm{argmax}_a Q(s,a)$
  - Execute action $a_t$ in simulator and observe reward $r_{t+1}$ and new state $s_{t+1}$
  - Store transition $<s_t, a_t, r_{t+1}, s_{t+1}>$ in memory $D$
  - Sample random mini-batch from $D$: $<s_j, a_j, r_j, s'_j>$
  - Set $\hat{Q}_j = r_j$ if the episode ends at $j+1$, otherwise set $\hat{Q}_j = r_j + \gamma \max_{a'}{Q(s'_j, a')}$
  - Make a gradient descent step with loss $(\hat{Q}_j - Q(s_j, a_j))^2$
- endfor
endfor



In [23]:

    
learning_rate = 0.001
memory_size = 2000

episodes = 5000
steps = 100
# changed from 0.95
gamma = 0.99

epsilon = 1
epsilon_stop = 0.01
epsilon_decay = 0.995
batch_size = 32

The Learner

Our agent is a simple neural network with a rectified linear hidden layer and a linear output layer. We are using Adam optimizer. The neural network will be having a memory to store past experiences. This is known as Temporal Difference Learning.



In [24]:

    
bot = Sequential()
bot.add(Dense(10, input_dim=16, activation='relu'))
bot.add(Dense(4, activation='linear'))
bot.compile(loss='mse', optimizer = Adam(learning_rate))
memory = deque(maxlen=memory_size)



In [25]:

    
state_lkup = np.eye(env.observation_space.n)
action_lkup = np.eye(env.action_space.n)



In [26]:

    
reward_list=[]
state = env.reset()
for episode in range(episodes):
    total_reward = 0
    state = env.reset()
    for step in range(steps):
        if epsilon > np.random.rand():
            action = env.action_space.sample()
        else:
            action = np.argmax(bot.predict(np.reshape(state_lkup[state], (-1, env.observation_space.n))))
        next_state, reward, done, prob = env.step(action)
        if done and reward==0:
            reward = -1
        if not done and reward==0:
            reward = -0.02
        memory.append((state, action, reward, next_state, done))
        state = next_state
        total_reward = total_reward + reward
        if done:
            print('episode:{} steps:{} total reward:{} epsilon:{}'.format(episode + 1, step + 1, total_reward, epsilon))
            reward_list.append(total_reward)
            break
        
        minibatch = [memory[ii] for ii in np.random.choice(range(len(memory)), batch_size)]
        states = [each[0] for each in minibatch]
        actions = [each[1] for each in minibatch]
        rewards = [each[2] for each in minibatch]
        next_states = [each[3] for each in minibatch]
        dones = [each[4] for each in minibatch]
        
        next_states = np.reshape([state_lkup[state] for state in next_states], [-1,env.observation_space.n])
        states = np.reshape([state_lkup[state] for state in states], [-1,env.observation_space.n])
        actions = np.reshape(actions, (batch_size, 1))
        targetQs = bot.predict(next_states)
        episode_ends = (next_states == np.zeros(states[0].shape)).all(axis=1)
        targetQs[episode_ends] = (0, 0, 0, 0)
        
        targets = rewards + gamma * np.max(targetQs, axis=1)
        targets_f = bot.predict(states)
        
        for pos in range(len(actions)):
            targets_f[pos,actions[pos]] = targets[pos]
        
        bot.fit(states, targets_f, epochs=1, verbose=0)
    if epsilon > epsilon_stop:
        epsilon = epsilon * epsilon_decay









    



[2017-07-16 15:00:26,036] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000000.json
[2017-07-16 15:00:26,036] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000001.json






    



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[2017-07-16 15:00:27,069] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000008.json






    



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[2017-07-16 15:00:27,934] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000027.json






    



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[2017-07-16 15:00:31,606] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000125.json






    



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[2017-07-16 15:00:38,638] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000216.json






    



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[2017-07-16 15:00:50,977] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000343.json






    



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[2017-07-16 15:01:12,240] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000512.json






    



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[2017-07-16 15:01:42,927] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video000729.json






    



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[2017-07-16 15:02:30,121] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video001000.json






    



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[2017-07-16 15:06:31,041] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video002000.json






    



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[2017-07-16 15:10:48,683] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video003000.json






    



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[2017-07-16 15:15:05,725] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video004000.json






    



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episode:4996 steps:63 total reward:-0.24000000000000066 epsilon:0.00998645168764533
episode:4997 steps:100 total reward:-2.9800000000000013 epsilon:0.00998645168764533






    



[2017-07-16 15:19:37,935] Starting new video recorder writing to C:\Users\Abdul\Documents\My Projects\Deep learning nano degree\my-experiments\reinforcement learning\monitor\openaigym.video.2.12772.video005000.json






    



episode:4998 steps:36 total reward:0.2999999999999997 epsilon:0.00998645168764533
episode:4999 steps:23 total reward:0.5599999999999998 epsilon:0.00998645168764533
episode:5000 steps:37 total reward:0.2799999999999997 epsilon:0.00998645168764533

Performance

After running the simulation for around 5000 episodes and plotting the rewards per iteration, we can notice that the rewards increase over time.



In [30]:

    
import matplotlib.pyplot as plt
%matplotlib inline 

def running_mean(x, N):
    cumsum = np.cumsum(np.insert(x, 0, 0)) 
    return (cumsum[N:] - cumsum[:-N]) / N 

smoothed_rews = running_mean(reward_list, 10)

plt.plot(reward_list, color='grey', alpha=0.3)
plt.plot(smoothed_rews)









    Out[30]:





[<matplotlib.lines.Line2D at 0x27268a2d198>]

Submission to OpenAI

This submission solves the environment around the 2.3K episodes.



In [29]:

    
env.close()
gym.upload('./monitor', api_key='')









    



[2017-07-16 15:20:32,132] [FrozenLake-v0] Uploading 5000 episodes of training data
[2017-07-16 15:20:35,422] [FrozenLake-v0] Uploading videos of 15 training episodes (1706 bytes)
[2017-07-16 15:20:36,031] [FrozenLake-v0] Creating evaluation object from ./monitor with learning curve and training video
[2017-07-16 15:20:36,641] 
****************************************************
You successfully uploaded your evaluation on FrozenLake-v0 to
OpenAI Gym! You can find it at:

    https://gym.openai.com/evaluations/eval_i7IBk5tTPOFM0a714aFrg

****************************************************