This tutorial is about so-called Reinforcement Learning in which an agent is learning how to navigate some environment, in this case Atari games from the 1970-80's. The agent does not know anything about the game and must learn how to play it from trial and error. The only information that is available to the agent is the screen output of the game, and whether the previous action resulted in a reward or penalty.
This is a very difficult problem in Machine Learning / Artificial Intelligence, because the agent must both learn to distinguish features in the game-images, and then connect the occurence of certain features in the game-images with its own actions and a reward or penalty that may be deferred many steps into the future.
This problem was first solved by the researchers from Google DeepMind. This tutorial is based on the main ideas from their early research papers (especially this and this), although we make several changes because the original DeepMind algorithm was awkward and over-complicated in some ways. But it turns out that you still need several tricks in order to stabilize the training of the agent, so the implementation in this tutorial is unfortunately also somewhat complicated.
The basic idea is to have the agent estimate so-called Q-values whenever it sees an image from the game-environment. The Q-values tell the agent which action is most likely to lead to the highest cumulative reward in the future. The problem is then reduced to finding these Q-values and storing them for later retrieval using a function approximator.
This builds on some of the previous tutorials. You should be familiar with TensorFlow and Convolutional Neural Networks from Tutorial #01 and #02. It will also be helpful if you are familiar with one of the builder APIs in Tutorials #03 or #03-B.
This tutorial uses the Atari game Breakout, where the player or agent is supposed to hit a ball with a paddle, thus avoiding death while scoring points when the ball smashes pieces of a wall.
When a human learns to play a game like this, the first thing to figure out is what part of the game environment you are controlling - in this case the paddle at the bottom. If you move right on the joystick then the paddle moves right and vice versa. The next thing is to figure out what the goal of the game is - in this case to smash as many bricks in the wall as possible so as to maximize the score. Finally you need to learn what to avoid - in this case you must avoid dying by letting the ball pass beside the paddle.
Below are shown 3 images from the game that demonstrate what we need our agent to learn. In the image to the left, the ball is going downwards and the agent must learn to move the paddle so as to hit the ball and avoid death. The image in the middle shows the paddle hitting the ball, which eventually leads to the image on the right where the ball smashes some bricks and scores points. The ball then continues downwards and the process repeats.
The problem is that there are 10 states between the ball going downwards and the paddle hitting the ball, and there are an additional 18 states before the reward is obtained when the ball hits the wall and smashes some bricks. How can we teach an agent to connect these three situations and generalize to similar situations? The answer is to use so-called Reinforcement Learning with a Neural Network, as shown in this tutorial.
One of the simplest ways of doing Reinforcement Learning is called Q-learning. Here we want to estimate so-called Q-values which are also called action-values, because they map a state of the game-environment to a numerical value for each possible action that the agent may take. The Q-values indicate which action is expected to result in the highest future reward, thus telling the agent which action to take.
Unfortunately we do not know what the Q-values are supposed to be, so we have to estimate them somehow. The Q-values are all initialized to zero and then updated repeatedly as new information is collected from the agent playing the game. When the agent scores a point then the Q-value must be updated with the new information.
There are different formulas for updating Q-values, but the simplest is to set the new Q-value to the reward that was observed, plus the maximum Q-value for the following state of the game. This gives the total reward that the agent can expect from the current game-state and onwards. Typically we also multiply the max Q-value for the following state by a so-called discount-factor slightly below 1. This causes more distant rewards to contribute less to the Q-value, thus making the agent favour rewards that are closer in time.
The formula for updating the Q-value is:
Q-value for state and action = reward + discount * max Q-value for next state
In academic papers, this is typically written with mathematical symbols like this:
$$ Q(s_{t},a_{t}) \leftarrow \underbrace{r_{t}}_{\rm reward} + \underbrace{\gamma}_{\rm discount} \cdot \underbrace{\max_{a}Q(s_{t+1}, a)}_{\rm estimate~of~future~rewards} $$Furthermore, when the agent loses a life, then we know that the future reward is zero because the agent is dead, so we set the Q-value for that state to zero.
The images below demonstrate how Q-values are updated in a backwards sweep through the game-states that have previously been visited. In this simple example we assume all Q-values have been initialized to zero. The agent gets a reward of 1 point in the right-most image. This reward is then propagated backwards to the previous game-states, so when we see similar game-states in the future, we know that the given actions resulted in that reward.
The discounting is an exponentially decreasing function. This example uses a discount-factor of 0.97 so the Q-value for the 3rd image is about $0.885 \simeq 0.97^4$ because it is 4 states prior to the state that actually received the reward. Similarly for the other states. This example only shows one Q-value per state, but in reality there is one Q-value for each possible action in the state, and the Q-values are updated in a backwards-sweep using the formula above. This is shown in the next section.
The Q-values for the possible actions have been estimated by a Neural Network. For the action NOOP in state t the Q-value is estimated to be 2.900, which is the highest Q-value for that state so the agent takes that action, i.e. the agent does not do anything between state t and t+1 because NOOP means "No Operation".
In state t+1 the agent scores 4 points, but this is limited to 1 point in this implementation so as to stabilize the training. The maximum Q-value for state t+1 is 1.830 for the action RIGHTFIRE. So if we select that action and continue to select the actions proposed by the Q-values estimated by the Neural Network, then the discounted sum of all the future rewards is expected to be 1.830.
Now that we know the reward of taking the NOOP action from state t to t+1, we can update the Q-value to incorporate this new information. This uses the formula above:
$$ Q(state_{t},NOOP) \leftarrow \underbrace{r_{t}}_{\rm reward} + \underbrace{\gamma}_{\rm discount} \cdot \underbrace{\max_{a}Q(state_{t+1}, a)}_{\rm estimate~of~future~rewards} = 1.0 + 0.97 \cdot 1.830 \simeq 2.775 $$The new Q-value is 2.775 which is slightly lower than the previous estimate of 2.900. This Neural Network has already been trained for 150 hours so it is quite good at estimating Q-values, but earlier during the training, the estimated Q-values would be more different.
The idea is to have the agent play many, many games and repeatedly update the estimates of the Q-values as more information about rewards and penalties becomes available. This will eventually lead to good estimates of the Q-values, provided the training is numerically stable, as discussed further below. By doing this, we create a connection between rewards and prior actions.
If we only use a single image from the game-environment then we cannot tell which direction the ball is moving. The typical solution is to use multiple consecutive images to represent the state of the game-environment.
This implementation uses another approach by processing the images from the game-environment in a motion-tracer that outputs two images as shown below. The left image is from the game-environment and the right image is the processed image, which shows traces of recent movements in the game-environment. In this case we can see that the ball is going downwards and has bounced off the right wall, and that the paddle has moved from the left to the right side of the screen.
Note that the motion-tracer has only been tested for Breakout and partially tested for Space Invaders, so it may not work for games with more complicated graphics such as Doom.
We need a function approximator that can take a state of the game-environment as input and produce as output an estimate of the Q-values for that state. We will use a Convolutional Neural Network for this. Although they have achieved great fame in recent years, they are actually a quite old technologies with many problems - one of which is training stability. A significant part of the research for this tutorial was spent on tuning and stabilizing the training of the Neural Network.
To understand why training stability is a problem, consider the 3 images below which show the game-environment in 3 consecutive states. At state $t$ the agent is about to score a point, which happens in the following state $t+1$. Assuming all Q-values were zero prior to this, we should now set the Q-value for state $t+1$ to be 1.0 and it should be 0.97 for state $t$ if the discount-value is 0.97, according to the formula above for updating Q-values.
If we were to train a Neural Network to estimate the Q-values for the two states $t$ and $t+1$ with Q-values 0.97 and 1.0, respectively, then the Neural Network will most likely be unable to distinguish properly between the images of these two states. As a result the Neural Network will also estimate a Q-value near 1.0 for state $t+2$ because the images are so similar. But this is clearly wrong because the Q-values for state $t+2$ should be zero as we do not know anything about future rewards at this point, and that is what the Q-values are supposed to estimate.
If this is continued and the Neural Network is trained after every new game-state is observed, then it will quickly cause the estimated Q-values to explode. This is an artifact of training Neural Networks which must have sufficiently large and diverse training-sets. For this reason we will use a so-called Replay Memory so we can gather a large number of game-states and shuffle them during training of the Neural Network.
This flowchart shows roughly how Reinforcement Learning is implemented in this tutorial. There are two main loops which are run sequentially until the Neural Network is sufficiently accurate at estimating Q-values.
The first loop is for playing the game and recording data. This uses the Neural Network to estimate Q-values from a game-state. It then stores the game-state along with the corresponding Q-values and reward/penalty in the Replay Memory for later use.
The other loop is activated when the Replay Memory is sufficiently full. First it makes a full backwards sweep through the Replay Memory to update the Q-values with the new rewards and penalties that have been observed. Then it performs an optimization run so as to train the Neural Network to better estimate these updated Q-values.
There are many more details in the implementation, such as decreasing the learning-rate and increasing the fraction of the Replay Memory being used during training, but this flowchart shows the main ideas.
The Neural Network used in this implementation has 3 convolutional layers, all of which have filter-size 3x3. The layers have 16, 32, and 64 output channels, respectively. The stride is 2 in the first two convolutional layers and 1 in the last layer.
Following the 3 convolutional layers there are 4 fully-connected layers each with 1024 units and ReLU-activation. Then there is a single fully-connected layer with linear activation used as the output of the Neural Network.
This architecture is different from those typically used in research papers from DeepMind and others. They often have large convolutional filter-sizes of 8x8 and 4x4 with high stride-values. This causes more aggressive down-sampling of the game-state images. They also typically have only a single fully-connected layer with 256 or 512 ReLU units.
During the research for this tutorial, it was found that smaller filter-sizes and strides in the convolutional layers, combined with several fully-connected layers having more units, were necessary in order to have sufficiently accurate Q-values. The Neural Network architectures originally used by DeepMind appear to distort the Q-values quite significantly. A reason that their approach still worked, is possibly due to their use of a very large Replay Memory with 1 million states, and that the Neural Network did one mini-batch of training for each step of the game-environment, and some other tricks.
The architecture used here is probably excessive but it takes several days of training to test each architecture, so it is left as an exercise for the reader to try and find a smaller Neural Network architecture that still performs well.
The documentation for OpenAI Gym currently suggests that you need to build it in order to install it. But if you just want to install the Atari games, then you only need to install a single pip-package by typing the following commands in a terminal.
This assumes you already have an Anaconda environment named tf which has TensorFlow installed, it will then be cloned to another environment named tf-gym where OpenAI Gym is also installed. This allows you to easily switch between your normal TensorFlow environment and another one which also contains OpenAI Gym.
You can also have two environments named tf-gpu and tf-gpu-gym for the GPU versions of TensorFlow.
In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import tensorflow as tf
import gym
import numpy as np
import math
The main source-code for Reinforcement Learning is located in the following module:
In [2]:
import reinforcement_learning as rl
This was developed using Python 3.6.0 (Anaconda) with package versions:
In [3]:
# TensorFlow
tf.__version__
Out[3]:
In [4]:
# OpenAI Gym
gym.__version__
Out[4]:
In [5]:
env_name = 'Breakout-v0'
# env_name = 'SpaceInvaders-v0'
This is the base-directory for the TensorFlow checkpoints as well as various log-files.
In [6]:
rl.checkpoint_base_dir = 'checkpoints_tutorial16/'
Once the base-dir has been set, you need to call this function to set all the paths that will be used. This will also create the checkpoint-dir if it does not already exist.
In [7]:
rl.update_paths(env_name=env_name)
You can download a TensorFlow checkpoint which holds all the pre-trained variables for the Neural Network. Two checkpoints are provided, one for Breakout and one for Space Invaders. They were both trained for about 150 hours on a laptop with 2.6 GHz CPU and a GTX 1070 GPU.
These TensorFlow checkpoints were developed with OpenAI gym v. 0.8.1 and atari-py v. 0.0.19 which had unused / redundant actions as noted above. There appears to have been a change in the gym API since then, as the unused actions are no longer present. This means the vectors with actions and Q-values now only contain 4 elements instead of the 6 shown here. This also means that the TensorFlow checkpoints cannot be used with newer versions of gym and atari-py, so in order to use these pre-trained checkpoints you need to install the older versions of gym and atari-py - or you can just train a new model yourself so you get a new TensorFlow checkpoint.
These checkpoints are 280-360 MB each. They are currently hosted on the webserver I use for www.hvass-labs.org because it is awkward to automatically download large files on Google Drive. To lower the traffic on my webserver, this line has been commented out, so you have to activate it manually. You are welcome to download it, I just don't want it to download automatically for everyone who only wants to run this Notebook briefly.
In [8]:
# rl.maybe_download_checkpoint(env_name=env_name)
I believe the webserver is located in Denmark. If you are having problems downloading the files using the automatic function above, then you can try and download the files manually in a webbrowser or using wget or curl. Or you can download from Google Drive, where you will get an anti-virus warning that is awkward to bypass automatically:
You can use the checksum to ensure the downloaded files are complete:
The Agent-class implements the main loop for playing the game, recording data and optimizing the Neural Network. We create an object-instance and need to set training=True because we want to use the replay-memory to record states and Q-values for plotting further below. We disable logging so this does not corrupt the logs from the actual training that was done previously. We can also set render=True but it will have no effect as long as training==True.
In [9]:
agent = rl.Agent(env_name=env_name,
training=True,
render=True,
use_logging=False)
The Neural Network is automatically instantiated by the Agent-class. We will create a direct reference for convenience.
In [10]:
model = agent.model
Similarly, the Agent-class also allocates the replay-memory when training==True. The replay-memory will require more than 3 GB of RAM, so it should only be allocated when needed. We will need the replay-memory in this Notebook to record the states and Q-values we observe, so they can be plotted further below.
In [11]:
replay_memory = agent.replay_memory
The agent's run() function is used to play the game. This uses the Neural Network to estimate Q-values and hence determine the agent's actions. If training==True then it will also gather states and Q-values in the replay-memory and train the Neural Network when the replay-memory is sufficiently full. You can set num_episodes=None if you want an infinite loop that you would stop manually with ctrl-c. In this case we just set num_episodes=1 because we are not actually interested in training the Neural Network any further, we merely want to collect some states and Q-values in the replay-memory so we can plot them below.
In [12]:
agent.run(num_episodes=1)
In training-mode, this function will output a line for each episode. The first counter is for the number of episodes that have been processed. The second counter is for the number of states that have been processed. These two counters are stored in the TensorFlow checkpoint along with the weights of the Neural Network, so you can restart the training e.g. if you only have one computer and need to train during the night.
Note that the number of episodes is almost 90k. It is impractical to print that many lines in this Notebook, so the training is better done in a terminal window by running the following commands:
source activate tf-gpu-gym # Activate your Python environment with TF and Gym.
python reinforcement-learning.py --env Breakout-v0 --trainingData is being logged during training so we can plot the progress afterwards. The reward for each episode and a running mean of the last 30 episodes are logged to file. Basic statistics for the Q-values in the replay-memory are also logged to file before each optimization run.
This could be logged using TensorFlow and TensorBoard, but they were designed for logging variables of the TensorFlow graph and data that flows through the graph. In this case the data we want logged does not reside in the graph, so it becomes a bit awkward to use TensorFlow to log this data.
We have therefore implemented a few small classes that can write and read these logs.
In [13]:
log_q_values = rl.LogQValues()
log_reward = rl.LogReward()
We can now read the logs from file:
In [14]:
log_q_values.read()
log_reward.read()
This plot shows the reward for each episode during training, as well as the running mean of the last 30 episodes. Note how the reward varies greatly from one episode to the next, so it is difficult to say from this plot alone whether the agent is really improving during the training, although the running mean does appear to trend upwards slightly.
In [15]:
plt.plot(log_reward.count_states, log_reward.episode, label='Episode Reward')
plt.plot(log_reward.count_states, log_reward.mean, label='Mean of 30 episodes')
plt.xlabel('State-Count for Game Environment')
plt.legend()
plt.show()
The following plot shows the mean Q-values from the replay-memory prior to each run of the optimizer for the Neural Network. Note how the mean Q-values increase rapidly in the beginning and then they increase fairly steadily for 40 million states, after which they still trend upwards but somewhat more irregularly.
The fast improvement in the beginning is probably due to (1) the use of a smaller replay-memory early in training so the Neural Network is optimized more often and the new information is used faster, (2) the backwards-sweeping of the replay-memory so the rewards are used to update the Q-values for many of the states, instead of just updating the Q-values for a single state, and (3) the replay-memory is balanced so at least half of each mini-batch contains states whose Q-values have high estimation-errors for the Neural Network.
The original paper from DeepMind showed much slower progress in the first phase of training, see Figure 2 in that paper but note that the Q-values are not directly comparable, possibly because they used a higher discount factor of 0.99 while we only used 0.97 here.
In [16]:
plt.plot(log_q_values.count_states, log_q_values.mean, label='Q-Value Mean')
plt.xlabel('State-Count for Game Environment')
plt.legend()
plt.show()
When the agent and Neural Network is being trained, the so-called epsilon-probability is typically decreased from 1.0 to 0.1 over a large number of steps, after which the probability is held fixed at 0.1. This means the probability is 0.1 or 10% that the agent will select a random action in each step, otherwise it will select the action that has the highest Q-value. This is known as the epsilon-greedy policy. The choice of 0.1 for the epsilon-probability is a compromise between taking the actions that are already known to be good, versus exploring new actions that might lead to even higher rewards or might lead to death of the agent.
During testing it is common to lower the epsilon-probability even further. We have set it to 0.01 as shown here:
In [17]:
agent.epsilon_greedy.epsilon_testing
Out[17]:
We will now instruct the agent that it should no longer perform training by setting this boolean:
In [18]:
agent.training = False
We also reset the previous episode rewards.
In [19]:
agent.reset_episode_rewards()
We can render the game-environment to screen so we can see the agent playing the game, by setting this boolean:
In [20]:
agent.render = True
We can now run a single episode by calling the run() function again. This should open a new window that shows the game being played by the agent. At the time of this writing, it was not possible to resize this tiny window, and the developers at OpenAI did not seem to care about this feature which should obviously be there.
In [21]:
agent.run(num_episodes=1)
The game-play is slightly random, both with regard to selecting actions using the epsilon-greedy policy, but also because the OpenAI Gym environment will repeat any action between 2-4 times, with the number chosen at random. So the reward of one episode is not an accurate estimate of the reward that can be expected in general from this agent.
We need to run 30 or even 50 episodes to get a more accurate estimate of the reward that can be expected.
We will first reset the previous episode rewards.
In [22]:
agent.reset_episode_rewards()
We disable the screen-rendering so the game-environment runs much faster.
In [23]:
agent.render = False
We can now run 30 episodes. This records the rewards for each episode. It might have been a good idea to disable the output so it does not print all these lines - you can do this as an exercise.
In [24]:
agent.run(num_episodes=30)
We can now print some statistics for the episode rewards, which vary greatly from one episode to the next.
In [25]:
rewards = agent.episode_rewards
print("Rewards for {0} episodes:".format(len(rewards)))
print("- Min: ", np.min(rewards))
print("- Mean: ", np.mean(rewards))
print("- Max: ", np.max(rewards))
print("- Stdev: ", np.std(rewards))
We can also plot a histogram with the episode rewards.
In [26]:
_ = plt.hist(rewards, bins=30)
In [27]:
def print_q_values(idx):
"""Print Q-values and actions from the replay-memory at the given index."""
# Get the Q-values and action from the replay-memory.
q_values = replay_memory.q_values[idx]
action = replay_memory.actions[idx]
print("Action: Q-Value:")
print("====================")
# Print all the actions and their Q-values.
for i, q_value in enumerate(q_values):
# Used to display which action was taken.
if i == action:
action_taken = "(Action Taken)"
else:
action_taken = ""
# Text-name of the action.
action_name = agent.get_action_name(i)
print("{0:12}{1:.3f} {2}".format(action_name, q_value,
action_taken))
# Newline.
print()
This helper-function plots a state from the replay-memory and optionally prints the Q-values.
In [28]:
def plot_state(idx, print_q=True):
"""Plot the state in the replay-memory with the given index."""
# Get the state from the replay-memory.
state = replay_memory.states[idx]
# Create figure with a grid of sub-plots.
fig, axes = plt.subplots(1, 2)
# Plot the image from the game-environment.
ax = axes.flat[0]
ax.imshow(state[:, :, 0], vmin=0, vmax=255,
interpolation='lanczos', cmap='gray')
# Plot the motion-trace.
ax = axes.flat[1]
ax.imshow(state[:, :, 1], vmin=0, vmax=255,
interpolation='lanczos', cmap='gray')
# This is necessary if we show more than one plot in a single Notebook cell.
plt.show()
# Print the Q-values.
if print_q:
print_q_values(idx=idx)
The replay-memory has room for 200k states but it is only partially full from the above call to agent.run(num_episodes=1). This is how many states are actually used.
In [29]:
num_used = replay_memory.num_used
num_used
Out[29]:
Get the Q-values from the replay-memory that are actually used.
In [30]:
q_values = replay_memory.q_values[0:num_used, :]
For each state, calculate the min / max Q-values and their difference. This will be used to lookup interesting states in the following sections.
In [31]:
q_values_min = q_values.min(axis=1)
q_values_max = q_values.max(axis=1)
q_values_dif = q_values_max - q_values_min
In [32]:
idx = np.argmax(replay_memory.rewards)
idx
Out[32]:
This state is where the ball hits the wall so the agent scores a point.
We can show the surrounding states leading up to and following this state. Note how the Q-values are very close for the different actions, because at this point it really does not matter what the agent does as the reward is already guaranteed. But note how the Q-values decrease significantly after the ball has hit the wall and a point has been scored.
Also note that the agent uses the Epsilon-greedy policy for taking actions, so there is a small probability that a random action is taken instead of the action with the highest Q-value.
In [33]:
for i in range(-5, 3):
plot_state(idx=idx+i)
In [34]:
idx = np.argmax(q_values_max)
idx
Out[34]:
In [35]:
for i in range(0, 5):
plot_state(idx=idx+i)
In [36]:
idx = np.argmax(replay_memory.end_life)
idx
Out[36]:
In [37]:
for i in range(-10, 0):
plot_state(idx=idx+i)
This example shows the state where there is the greatest difference in Q-values, which means that the agent believes one action will be much more beneficial than another. But because the agent uses the Epsilon-greedy policy, it sometimes selects a random action instead.
In [38]:
idx = np.argmax(q_values_dif)
idx
Out[38]:
In [39]:
for i in range(0, 5):
plot_state(idx=idx+i)
This example shows the state where there is the smallest difference in Q-values, which means that the agent believes it does not really matter which action it selects, as they all have roughly the same expectations for future rewards.
The Neural Network estimates these Q-values and they are not precise. The differences in Q-values may be so small that they fall within the error-range of the estimates.
In [40]:
idx = np.argmin(q_values_dif)
idx
Out[40]:
In [41]:
for i in range(0, 5):
plot_state(idx=idx+i)
The outputs of the convolutional layers can be plotted so we can see how the images from the game-environment are being processed by the Neural Network.
This is the helper-function for plotting the output of the convolutional layer with the given name, when inputting the given state from the replay-memory.
In [42]:
def plot_layer_output(model, layer_name, state_index, inverse_cmap=False):
"""
Plot the output of a convolutional layer.
:param model: An instance of the NeuralNetwork-class.
:param layer_name: Name of the convolutional layer.
:param state_index: Index into the replay-memory for a state that
will be input to the Neural Network.
:param inverse_cmap: Boolean whether to inverse the color-map.
"""
# Get the given state-array from the replay-memory.
state = replay_memory.states[state_index]
# Get the output tensor for the given layer inside the TensorFlow graph.
# This is not the value-contents but merely a reference to the tensor.
layer_tensor = model.get_layer_tensor(layer_name=layer_name)
# Get the actual value of the tensor by feeding the state-data
# to the TensorFlow graph and calculating the value of the tensor.
values = model.get_tensor_value(tensor=layer_tensor, state=state)
# Number of image channels output by the convolutional layer.
num_images = values.shape[3]
# Number of grid-cells to plot.
# Rounded-up, square-root of the number of filters.
num_grids = math.ceil(math.sqrt(num_images))
# Create figure with a grid of sub-plots.
fig, axes = plt.subplots(num_grids, num_grids, figsize=(10, 10))
print("Dim. of each image:", values.shape)
if inverse_cmap:
cmap = 'gray_r'
else:
cmap = 'gray'
# Plot the outputs of all the channels in the conv-layer.
for i, ax in enumerate(axes.flat):
# Only plot the valid image-channels.
if i < num_images:
# Get the image for the i'th output channel.
img = values[0, :, :, i]
# Plot image.
ax.imshow(img, interpolation='nearest', cmap=cmap)
# Remove ticks from the plot.
ax.set_xticks([])
ax.set_yticks([])
# Ensure the plot is shown correctly with multiple plots
# in a single Notebook cell.
plt.show()
In [43]:
idx = np.argmax(q_values_max)
plot_state(idx=idx, print_q=False)
This shows the images that are output by the 1st convolutional layer, when inputting the above state to the Neural Network. There are 16 output channels of this convolutional layer.
Note that you can invert the colors by setting inverse_cmap=True in the parameters to this function.
In [44]:
plot_layer_output(model=model, layer_name='layer_conv1', state_index=idx, inverse_cmap=False)
In [45]:
plot_layer_output(model=model, layer_name='layer_conv2', state_index=idx, inverse_cmap=False)
These are the images output by the 3rd convolutional layer, when inputting the above state to the Neural Network. There are 64 output channels of this convolutional layer.
All these images are flattened to a one-dimensional array (or tensor) which is then used as the input to a fully-connected layer in the Neural Network.
During the training-process, the Neural Network has learnt what convolutional filters to apply to the images from the game-environment so as to produce these images, because they have proven to be useful when estimating Q-values.
Can you see what it is that the Neural Network has learned to detect in these images?
In [46]:
plot_layer_output(model=model, layer_name='layer_conv3', state_index=idx, inverse_cmap=False)
We can also plot the weights of the convolutional layers in the Neural Network. These are the weights that are being optimized so as to improve the ability of the Neural Network to estimate Q-values. Tutorial #02 explains in greater detail what convolutional weights are. There are also weights for the fully-connected layers but they are not shown here.
This is the helper-function for plotting the weights of a convoluational layer.
In [47]:
def plot_conv_weights(model, layer_name, input_channel=0):
"""
Plot the weights for a convolutional layer.
:param model: An instance of the NeuralNetwork-class.
:param layer_name: Name of the convolutional layer.
:param input_channel: Plot the weights for this input-channel.
"""
# Get the variable for the weights of the given layer.
# This is a reference to the variable inside TensorFlow,
# not its actual value.
weights_variable = model.get_weights_variable(layer_name=layer_name)
# Retrieve the values of the weight-variable from TensorFlow.
# The format of this 4-dim tensor is determined by the
# TensorFlow API. See Tutorial #02 for more details.
w = model.get_variable_value(variable=weights_variable)
# Get the weights for the given input-channel.
w_channel = w[:, :, input_channel, :]
# Number of output-channels for the conv. layer.
num_output_channels = w_channel.shape[2]
# Get the lowest and highest values for the weights.
# This is used to correct the colour intensity across
# the images so they can be compared with each other.
w_min = np.min(w_channel)
w_max = np.max(w_channel)
# This is used to center the colour intensity at zero.
abs_max = max(abs(w_min), abs(w_max))
# Print statistics for the weights.
print("Min: {0:.5f}, Max: {1:.5f}".format(w_min, w_max))
print("Mean: {0:.5f}, Stdev: {1:.5f}".format(w_channel.mean(),
w_channel.std()))
# Number of grids to plot.
# Rounded-up, square-root of the number of output-channels.
num_grids = math.ceil(math.sqrt(num_output_channels))
# Create figure with a grid of sub-plots.
fig, axes = plt.subplots(num_grids, num_grids)
# Plot all the filter-weights.
for i, ax in enumerate(axes.flat):
# Only plot the valid filter-weights.
if i < num_output_channels:
# Get the weights for the i'th filter of this input-channel.
img = w_channel[:, :, i]
# Plot image.
ax.imshow(img, vmin=-abs_max, vmax=abs_max,
interpolation='nearest', cmap='seismic')
# Remove ticks from the plot.
ax.set_xticks([])
ax.set_yticks([])
# Ensure the plot is shown correctly with multiple plots
# in a single Notebook cell.
plt.show()
These are the weights of the first convolutional layer of the Neural Network, with respect to the first input channel of the state. That is, these are the weights that are used on the image from the game-environment. Some basic statistics are also shown.
Note how the weights are more negative (blue) than positive (red). It is unclear why this happens as these weights are found through optimization. It is apparently beneficial for the following layers to have this processing with more negative weights in the first convolutional layer.
In [48]:
plot_conv_weights(model=model, layer_name='layer_conv1', input_channel=0)
We can also plot the convolutional weights for the second input channel, that is, the motion-trace of the game-environment. Once again we see that the negative weights (blue) have a much greater magnitude than the positive weights (red).
In [49]:
plot_conv_weights(model=model, layer_name='layer_conv1', input_channel=1)
These are the weights of the 2nd convolutional layer in the Neural Network. There are 16 input channels and 32 output channels of this layer. You can change the number for the input-channel to see the associated weights.
Note how the weights are more balanced between positive (red) and negative (blue) compared to the weights for the 1st convolutional layer above.
In [50]:
plot_conv_weights(model=model, layer_name='layer_conv2', input_channel=0)
These are the weights of the 3rd convolutional layer in the Neural Network. There are 32 input channels and 64 output channels of this layer. You can change the number for the input-channel to see the associated weights.
Note again how the weights are more balanced between positive (red) and negative (blue) compared to the weights for the 1st convolutional layer above.
In [51]:
plot_conv_weights(model=model, layer_name='layer_conv3', input_channel=0)
We trained an agent to play old Atari games quite well using Reinforcement Learning. Recent improvements to the training algorithm have improved the performance significantly. But is this true human-like intelligence? The answer is clearly NO!
Reinforcement Learning in its current form is a crude numerical algorithm for connecting visual images, actions, rewards and penalties when there is a time-lag between the signals. The learning is based on trial-and-error and cannot do logical reasoning like a human. The agent has no sense of "self" while a human has an understanding of what part of the game-environment it is controlling, so a human can reason logically like this: "(A) I control the paddle, and (B) I must avoid dying which happens when the ball flies past the paddle, so (C) I must move the paddle to hit the ball, and (D) this automatically scores points when the ball smashes bricks in the wall". A human would first learn these basic logical rules of the game - and then try and refine the eye-hand coordination to play the game better. Reinforcement Learning has no real comprehension of what is going on in the game and merely works on improving the eye-hand coordination until it gets lucky and does the right thing to score more points.
Furthermore, the training of the Reinforcement Learning algorithm required almost 150 hours of computation which played the game at high speeds. If the game was played at normal real-time speeds then it would have taken more than 1700 hours to train the agent, which is more than 70 days and nights.
Logical reasoning would allow for much faster learning than Reinforcement Learning, and it would be able to solve much more complicated problems than simple eye-hand coordination. I am skeptical if someone will be able to create true human-like intelligence from Reinforcement Learning algorithms.
Does that mean Reinforcement Learning is completely worthless? No, it has real-world applications that currently cannot be solved by other methods.
Another point of criticism is the use of Neural Networks. The majority of the research in Reinforcement Learning is actually spent on trying to stabilize the training of the Neural Network using various tricks. This is a waste of research time and strongly indicates that Neural Networks may not be a very good Machine Learning model compared to the human brain.
Below are suggestions for exercises and experiments that may help improve your skills with TensorFlow and Reinforcement Learning. Some of these ideas can easily be extended into full research problems that would help the community if you can solve them.
You should keep a log of your experiments, describing for each experiment the settings you tried and the results. You should also save the source-code and checkpoints / log-files.
It takes so much time to run these experiments, so please share your results with the rest of the community. Even if an experiment failed to produce anything useful, it will be helpful to others so they know not to redo the same experiment.
Thread on GitHub for discussing these experiments
You may want to backup this Notebook and the other files before making any changes.
You may find it helpful to add more command-line parameters to reinforcement_learning.py so you don't have to edit the source-code for testing other parameters.
estimate_all_q_values() which may be helpful.ReplayMemory.add() so as to stabilize the training. This means the agent cannot distinguish between small and large rewards. Can you use batch normalization to fix this problem, so you can use the actual reward values?Copyright (c) 2017 by Magnus Erik Hvass Pedersen
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