Deep Q-Learning (DQN)

Overview

As an extension of the Q-learning, DQN's main technical contribution is the use of replay buffer and target network, both of which would help improve the stability of the algorithm.

Original papers:

Human-level control through deep reinforcement learning

Implemented Variants

Variants Implemented	Description
`dqn_atari.py`, docs	For playing Atari games. It uses convolutional layers and common atari-based pre-processing techniques.
`dqn.py`, docs	For classic control tasks like `CartPole-v1`.

Below are our single-file implementations of DQN:

`dqn_atari.py`

The dqn_atari.py has the following features:

For playing Atari games. It uses convolutional layers and common atari-based pre-processing techniques.
Works with the Atari's pixel Box observation space of shape (210, 160, 3)
Works with the Discrete action space

Usage

poetry install -E atari
python cleanrl/dqn_atari.py --env-id BreakoutNoFrameskip-v4
python cleanrl/dqn_atari.py --env-id PongNoFrameskip-v4

Explanation of the logged metrics

Running python cleanrl/dqn_atari.py will automatically record various metrics such as actor or value losses in Tensorboard. Below is the documentation for these metrics:

charts/episodic_return: episodic return of the game
charts/SPS: number of steps per second
losses/td_loss: the mean squared error (MSE) between the Q values at timestep $t$ and the Bellman update target estimated using the reward $r_t$ and the Q values at timestep $t+1$, thus minimizing the one-step temporal difference. Formally, it can be expressed by the equation below. $$ J(\theta^{Q}) = \mathbb{E}_{(s,a,r,s') \sim \mathcal{D}} \big[ (Q(s, a) - y)^2 \big], $$ with the Bellman update target is $y = r + \gamma \, Q^{'}(s', a')$ and the replay buffer is $\mathcal{D}$.
losses/q_values: implemented as qf1(data.observations, data.actions).view(-1), it is the average Q values of the sampled data in the replay buffer; useful when gauging if under or over estimation happens.

Implementation details

dqn_atari.py is based on (Mnih et al., 2015)¹ but presents a few implementation differences:

dqn_atari.py use slightly different hyperparameters. Specifically,
- dqn_atari.py uses the more popular Adam Optimizer with the --learning-rate=1e-4 as follows:
```
optim.Adam(q_network.parameters(), lr=1e-4)
```
  whereas (Mnih et al., 2015)¹ (Exntended Data Table 1) uses the RMSProp optimizer with --learning-rate=2.5e-4, gradient momentum 0.95, squared gradient momentum 0.95, and min squared gradient 0.01 as follows:
```
optim.RMSprop(
    q_network.parameters(),
    lr=2.5e-4,
    momentum=0.95,
    # ... PyTorch's RMSprop does not directly support
    # squared gradient momentum and min squared gradient
    # so we are not sure what to put here.
)
```
- dqn_atari.py uses --learning-starts=80000 whereas (Mnih et al., 2015)¹ (Exntended Data Table 1) uses --learning-starts=50000.
- dqn_atari.py uses --target-network-frequency=1000 whereas (Mnih et al., 2015)¹ (Exntended Data Table 1) uses --learning-starts=10000.
- dqn_atari.py uses --total-timesteps=10000000 (i.e., 10M timesteps = 40M frames because of frame-skipping) whereas (Mnih et al., 2015)¹ uses --total-timesteps=50000000 (i.e., 50M timesteps = 200M frames) (See "Training details" under "METHODS" on page 6 and the related source code run_gpu#L32, dqn/train_agent.lua#L81-L82, and dqn/train_agent.lua#L165-L169).
- dqn_atari.py uses --end-e=0.01 (the final exploration epsilon) whereas (Mnih et al., 2015)¹ (Exntended Data Table 1) uses --end-e=0.1.
- dqn_atari.py uses --exploration-fraction=0.1 whereas (Mnih et al., 2015)¹ (Exntended Data Table 1) uses --exploration-fraction=0.02 (all corresponds to 250000 steps or 1M frames being the frame that epsilon is annealed to --end-e=0.1 ).
- dqn_atari.py handles truncation and termination properly like (Mnih et al., 2015)¹ by using SB3's replay buffer's handle_timeout_termination=True.
dqn_atari.py use a self-contained evaluation scheme: dqn_atari.py reports the episodic returns obtained throughout training, whereas (Mnih et al., 2015)¹ is trained with --end-e=0.1 but reported episodic returns using a separate evaluation process with --end-e=0.01 (See "Evaluation procedure" under "METHODS" on page 6).

Experiment results

To run benchmark experiments, see benchmark/c51.sh. Specifically, execute the following command:

Below are the average episodic returns for dqn_atari.py.

Environment	`dqn_atari.py` 10M steps	(Mnih et al., 2015)¹ 50M steps	(Hessel et al., 2017, Figure 5)³
BreakoutNoFrameskip-v4	366.928 ± 39.89	401.2 ± 26.9	~230 at 10M steps, ~300 at 50M steps
PongNoFrameskip-v4	20.25 ± 0.41	18.9 ± 1.3	~20 10M steps, ~20 at 50M steps
BeamRiderNoFrameskip-v4	6673.24 ± 1434.37	6846 ± 1619	~6000 10M steps, ~7000 at 50M steps

Note that we save computational time by reducing timesteps from 50M to 10M, but our dqn_atari.py scores the same or higher than (Mnih et al., 2015)¹ in 10M steps.

Learning curves:

Tracked experiments and game play videos:

`dqn.py`

The dqn.py has the following features:

Works with the Box observation space of low-level features
Works with the Discrete action space
Works with envs like CartPole-v1

Usage

python cleanrl/dqn.py --env-id CartPole-v1

Explanation of the logged metrics

See related docs for dqn_atari.py.

Implementation details

The dqn.py shares the same implementation details as dqn_atari.py except the dqn.py runs with different hyperparameters and neural network architecture. Specifically,

dqn.py uses a simpler neural network as follows:

self.network = nn.Sequential(
    nn.Linear(np.array(env.single_observation_space.shape).prod(), 120),
    nn.ReLU(),
    nn.Linear(120, 84),
    nn.ReLU(),
    nn.Linear(84, env.single_action_space.n),
)

dqn.py runs with different hyperparameters:

python dqn.py --total-timesteps 500000 \
    --learning-rate 2.5e-4 \
    --buffer-size 10000 \
    --gamma 0.99 \
    --target-network-frequency 500 \
    --max-grad-norm 0.5 \
    --batch-size 128 \
    --start-e 1 \
    --end-e 0.05 \
    --exploration-fraction 0.5 \
    --learning-starts 10000 \
    --train-frequency 10

Experiment results

To run benchmark experiments, see benchmark/c51.sh. Specifically, execute the following command:

Below are the average episodic returns for dqn.py.

Environment	`dqn.py`
CartPole-v1	488.69 ± 16.11
Acrobot-v1	-91.54 ± 7.20
MountainCar-v0	-194.95 ± 8.48

Note that the DQN has no official benchmark on classic control environments, so we did not include a comparison. That said, our dqn.py was able to achieve near perfect scores in CartPole-v1 and Acrobot-v1; further, it can obtain successful runs in the sparse environment MountainCar-v0.

Learning curves:

Tracked experiments and game play videos:

Mnih, V., Kavukcuoglu, K., Silver, D. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015). https://doi.org/10.1038/nature14236 ↩↩↩↩↩↩↩↩↩↩↩
[Proposal] Formal API handling of truncation vs termination. https://github.com/openai/gym/issues/2510 ↩
Hessel, M., Modayil, J., Hasselt, H.V., Schaul, T., Ostrovski, G., Dabney, W., Horgan, D., Piot, B., Azar, M.G., & Silver, D. (2018). Rainbow: Combining Improvements in Deep Reinforcement Learning. AAAI. ↩