In this project, I build a reinforcement learning (RL) agent that controls a robotic arm within Unity's Reacher environment. The goal is to get 20 different robotic arms to maintain contact with the green spheres.
A reward of +0.1 is provided for each time-step that the agent's hand is in the goal location. Thus, the goal of your agent is to maintain its position at the target location for as many time steps as possible.
In order to solve the environment, our agent must achieve a score of +30 averaged across all 20 agents for 100 consecutive episodes.
- Set-up: Double-jointed arm which can move to target locations.
- Goal: Each agent must move its hand to the goal location, and keep it there.
- Agents: The environment contains 20 agents linked to a single Brain.
- Agent Reward Function (independent):
- +0.1 for each timestep agent's hand is in goal location.
- Brains: One Brain with the following observation/action space.
- Vector Observation space: 33 variables corresponding to position,rotation, velocity, and angular velocities of the two arm Rigidbodies.
- Vector Action space: (Continuous) Each action is a vector with four numbers, corresponding to torque applicable to two joints. Every entry in the action vector should be a number between -1 and 1.
- Visual Observations: None.
- Reset Parameters: Two, corresponding to goal size, and goal movement speed.
- Benchmark Mean Reward: 30### Solving the Environment
To get started, there are a few high-level architecture decisions we need to make. First, we need to determine which types of algorithms are most suitable for the Reacher environment. Second, we need to determine how many "brains" we want controlling the actions of our agents.
There are two key differences in the Reacher environment compared to the previous 'Navigation' project:
1- **_Multiple agents_** — The version of the environment I'm tackling in this project has 20 different agents, whereas the Navigation project had only a single agent. To keep things simple, I decided to use a single brain to control all 20 agents, rather than training 20 individual brains. Training multiple brains seemed unnecessary since all of the agents are essentially performing the same task under the same conditions. Also, training 20 brains would take a really long time!
2- **_Continuous action space_** — The action space is now continuous, which allows each agent to execute more complex and precise movements. Essentially, there's an unlimited range of possible action values to control the robotic arm, whereas the agent in the Navigation project was limited to four discrete actions: left, right, forward, backward.
Given the additional complexity of this environment, the value-based method we used for the last project is not suitable — i.e., the Deep Q-Network (DQN) algorithm. Most importantly, we need an algorithm that allows the robotic arm to utilise its full range of movement. For this, we'll need to explore a different class of algorithms called policy-based methods.
Here are some advantages of policy-based methods:
- Continuous action spaces — Policy-based methods are well-suited for continuous action spaces.
- Stochastic policies — Both value-based and policy-based methods can learn deterministic policies. However, policy-based methods can also learn true stochastic policies.
- Simplicity — Policy-based methods directly learn the optimal policy, without having to maintain a separate value function estimate. With value-based methods, the agent uses its experience with the environment to maintain an estimate of the optimal action-value function, from which an optimal policy is derived. This intermediate step requires the storage of lots of additional data since you need to account for all possible action values. Even if you discretize the action space, the number of possible actions can be quite high. For example, if we assumed only 10 degrees of freedom for both joints of our robotic arm, we'd have 1024 unique actions (210). Using DQN to determine the action that maximizes the action-value function within a continuous or high-dimensional space requires a complex optimization process at every timestep.
The algorithm I chose to model my project on is outlined in this paper, Continuous Control with Deep Reinforcement Learning, by researchers at Google Deepmind. In this paper, the authors present "a model-free, off-policy actor-critic algorithm using deep function approximators that can learn policies in high-dimensional, continuous action spaces." They highlight that DDPG can be viewed as an extension of Deep Q-learning to continuous tasks.
I used this vanilla, single-agent DDPG as a template. I further experimented with the DDPG algorithm based on other concepts covered in Udacity's classroom and lessons. My understanding and implementation of this algorithm (including various customizations) are discussed below.
Actor-critic methods leverage the strengths of both policy-based and value-based methods.
Using a policy-based approach, the agent (actor) learns how to act by directly estimating the optimal policy and maximizing reward through gradient ascent. Meanwhile, employing a value-based approach, the agent (critic) learns how to estimate the value (i.e., the future cumulative reward) of different state-action pairs. Actor-critic methods combine these two approaches in order to accelerate the learning process. Actor-critic agents are also more stable than value-based agents, while requiring fewer training samples than policy-based agents.
You can find the actor-critic logic implemented as part of the Agent() class here in ddpg_agent.py of the source code. The actor-critic models can be found via their respective Actor() and Critic() classes here in models.py.
Note: As we did with Double Q-Learning in the last project, we're again leveraging local and target networks to improve stability. This is where one set of parameters w is used to select the best action, and another set of parameters w' is used to evaluate that action. In this project, local and target networks are implemented separately for both the actor and the critic.
# Actor Network (w/ Target Network)
self.actor_local = Actor(state_size, action_size, random_seed).to(device)
self.actor_target = Actor(state_size, action_size, random_seed).to(device)
self.actor_optimizer = optim.Adam(self.actor_local.parameters(), lr=LR_ACTOR)
# Critic Network (w/ Target Network)
self.critic_local = Critic(state_size, action_size, random_seed).to(device)
self.critic_target = Critic(state_size, action_size, random_seed).to(device)
self.critic_optimizer = optim.Adam(self.critic_local.parameters(), lr=LR_CRITIC, weight_decay=WEIGHT_DECAY)One challenge is choosing which action to take while the agent is still learning the optimal policy. Should the agent choose an action based on the rewards observed thus far? Or, should the agent try a new action in hopes of earning a higher reward? This is known as the exploration vs. exploitation dilemma.
In the Navigation project, I addressed this by implementing an 𝛆-greedy algorithm. This algorithm allows the agent to systematically manage the exploration vs. exploitation trade-off. The agent "explores" by picking a random action with some probability epsilon 𝛜. Meanwhile, the agent continues to "exploit" its knowledge of the environment by choosing actions based on the deterministic policy with probability (1-𝛜).
However, this approach won't work for controlling a robotic arm. The reason is that the actions are no longer a discrete set of simple directions (i.e., up, down, left, right). The actions driving the movement of the arm are forces with different magnitudes and directions. If we base our exploration mechanism on random uniform sampling, the direction actions would have a mean of zero, in turn cancelling each other out. This can cause the system to oscillate without making much progress.
Instead, we'll use the Ornstein-Uhlenbeck process, as suggested in the previously mentioned paper by Google DeepMind (see bottom of page 4). The Ornstein-Uhlenbeck process adds a certain amount of noise to the action values at each timestep. This noise is correlated to previous noise, and therefore tends to stay in the same direction for longer durations without canceling itself out. This allows the arm to maintain velocity and explore the action space with more continuity.
You can find the Ornstein-Uhlenbeck process implemented here in the OUNoise class in ddpg_agent.py of the source code.
In total, there are five hyperparameters related to this noise process.
The Ornstein-Uhlenbeck process itself has three hyperparameters that determine the noise characteristics and magnitude:
- mu: the long-running mean
- theta: the speed of mean reversion
- sigma: the volatility parameter
Of these, I only tuned sigma. After running a few experiments, I reduced sigma from 0.3 to 0.2. The reduced noise volatility seemed to help the model converge faster.
Notice also there's an epsilon parameter used to decay the noise level over time. This decay mechanism ensures that more noise is introduced earlier in the training process (i.e., higher exploration), and the noise decreases over time as the agent gains more experience (i.e., higher exploitation). The starting value for epsilon and its decay rate are two hyperparameters that were tuned during experimentation.
You can find the epsilon process implemented here in the Agent.act() method in ddpg_agent.py of the source code. While the epsilon decay is performed here as part of the learning step.
The final noise parameters were set as follows:
OU_SIGMA = 0.2 # Ornstein-Uhlenbeck noise parameter
OU_THETA = 0.15 # Ornstein-Uhlenbeck noise parameter
EPSILON = 1.0 # explore->exploit noise process added to act step
EPSILON_DECAY = 1e-6 # decay rate for noise processIn the first few versions of my implementation, the agent performed the learning step at every timestep. This made training very slow, and there was no apparent benefit to the agent's performance. So, I implemented an interval in which the learning step is only performed every 20 timesteps. As part of each learning step, the algorithm samples experiences from the buffer and runs the Agent.learn() method 10 times.
LEARN_EVERY = 20 # learning timestep interval
LEARN_NUM = 10 # number of learning passesYou can find the learning interval implemented here in the Agent.step() method in ddpg_agent.py of the source code.
In early versions of my implementation, I had trouble getting my agent to learn. Or, rather, it would start to learn but then become very unstable and either plateau or collapse.
I suspect that one of the causes was outsized gradients. Unfortunately, I couldn't find an easy way to investigate this, although I'm sure there's some way of doing this in PyTorch. Absent this investigation, I hypothesize that many of the weights from my critic model were becoming quite large after just 5-10 episodes of training. (Note that at this point, I was running the learning process at every timestep, which made the problem worse.)
The issue of exploding gradients is described in layman's terms in this post by Jason Brownlee. Essentially, each layer of your net amplifies the gradient it receives. This becomes a problem when the lower layers of the network accumulate huge gradients, making their respective weight updates too large to allow the model to learn anything.
To combat this, I implemented gradient clipping using the torch.nn.utils.clip_grad_norm_ function. I set the function to "clip" the norm of the gradients at 1, therefore placing an upper limit on the size of the parameter updates, and preventing them from growing exponentially. Once this change was implemented, along with batch normalization (discussed in the next section), my model became much more stable and my agent started learning at a much faster rate.
You can find gradient clipping implemented here in the "update critic" section of the Agent.learn() method, within ddpg_agent.py of the source code.
Note that this function is applied after the backward pass, but before the optimization step.
# Compute critic loss
Q_expected = self.critic_local(states, actions)
critic_loss = F.mse_loss(Q_expected, Q_targets)
# Minimize the loss
self.critic_optimizer.zero_grad()
critic_loss.backward()
torch.nn.utils.clip_grad_norm_(self.critic_local.parameters(), 1)
self.critic_optimizer.step()I've used batch normalization many times in the past when building convolutional neural networks (CNN), in order to squash pixel values. But, it didn't occur to me how important it would be to this project. This was another aspect of the Google DeepMind paper that proved tremendously useful in my implementation of this project.
Similar to the exploding gradient issue mentioned above, running computations on large input values and model parameters can inhibit learning. Batch normalization addresses this problem by scaling the features to be within the same range throughout the model and across different environments and units. In additional to normalizing each dimension to have unit mean and variance, the range of values is often much smaller, typically between 0 and 1.
Initially, I added batch normalization between every layer in both the actor and critic models. However, this may have been overkill, and seemed to prolong training time. I eventually reduced the use of batch normalization to just the outputs of the first fully-connected layers of both the actor and critic models.
You can find batch normalization implemented here for the actor, and here for the critic, within model.py of the source code.
# actor forward pass
def forward(self, state):
"""Build an actor (policy) network that maps states -> actions."""
x = F.relu(self.bn1(self.fc1(state)))
x = F.relu(self.fc2(x))
return F.tanh(self.fc3(x))# critic forward pass
def forward(self, state, action):
"""Build a critic (value) network that maps (state, action) pairs -> Q-values."""
xs = F.relu(self.bn1(self.fcs1(state)))
x = torch.cat((xs, action), dim=1)
x = F.relu(self.fc2(x))
return self.fc3(x)Experience replay allows the RL agent to learn from past experience.
As with DQN in the previous project, DDPG also utilizes a replay buffer to gather experiences from each agent. Each experience is stored in a replay buffer as the agent interacts with the environment. In this project, there is one central replay buffer utilized by all 20 agents, therefore allowing agents to learn from each others' experiences.
The replay buffer contains a collection of experience tuples with the state, action, reward, and next state (s, a, r, s'). Each agent samples from this buffer as part of the learning step. Experiences are sampled randomly, so that the data is uncorrelated. This prevents action values from oscillating or diverging catastrophically, since a naive algorithm could otherwise become biased by correlations between sequential experience tuples.
Also, experience replay improves learning through repetition. By doing multiple passes over the data, our agents have multiple opportunities to learn from a single experience tuple. This is particularly useful for state-action pairs that occur infrequently within the environment.
The implementation of the replay buffer can be found here in the ddpg_agent.py file of the source code.
Once all of the various components of the algorithm were in place, my agent was able to solve the 20 agent Reacher environment. Again, the performance goal is an average reward of at least +30 over 100 episodes, and over all 20 agents.
The graph below shows the final results. The best performing agent was able to solve the environment starting with the 12th episode, with a top mean score of 39.3 in the 79th episode. The complete set of results and steps can be found in this notebook.
- Experiment with other algorithms — Tuning the DDPG algorithm required a lot of trial and error. Perhaps another algorithm such as Trust Region Policy Optimization (TRPO), [Proximal Policy Optimization (PPO)](Proximal Policy Optimization Algorithms), or Distributed Distributional Deterministic Policy Gradients (D4PG) would be more robust.
- Add prioritized experience replay — Rather than selecting experience tuples randomly, prioritized replay selects experiences based on a priority value that is correlated with the magnitude of error. This can improve learning by increasing the probability that rare and important experience vectors are sampled.