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Categorical DQN (C51)

Overview

C51 introduces a distributional perspective for DQN: instead of learning a single value for an action, C51 learns to predict a distribution of values for the action. Empirically, C51 demonstrates impressive performance in ALE.

Original papers:

Implemented Variants

Variants Implemented Description
c51_atari.py, docs For playing Atari games. It uses convolutional layers and common atari-based pre-processing techniques.
c51.py, docs For classic control tasks like CartPole-v1.

Below are our single-file implementations of C51:

c51_atari.py

The c51_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/c51_atari.py --env-id BreakoutNoFrameskip-v4
python cleanrl/c51_atari.py --env-id PongNoFrameskip-v4

Explanation of the logged metrics

Running python cleanrl/c51_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/loss: the cross entropy loss between the \(t\) step state value distribution and the projected \(t+1\) step state value distribution
  • losses/q_values: implemented as (old_pmfs * q_network.atoms).sum(1), which is the sum of the probability of getting returns \(x\) (old_pmfs) multiplied by \(x\) (q_network.atoms), averaged over the sample obtained from the replay buffer; useful when gauging if under or over estimation happens

Implementation details

c51_atari.py is based on (Bellemare et al., 2017)1 but presents a few implementation differences:

  1. (Bellemare et al., 2017)1 injects stochaticity by doing "on each frame the environment rejects the agent’s selected action with probability \(p = 0.25\)", but c51_atari.py does not do this
  2. c51_atari.py use a self-contained evaluation scheme: c51_atari.py reports the episodic returns obtained throughout training, whereas (Bellemare et al., 2017)1 is trained with --end-e=0.01 but reported episodic returns using a separate evaluation process with --end-e=0.001 (See "5.2. State-of-the-Art Results" on page 7).
  3. c51_atari.py rescales the gradient so that the norm of the parameters does not exceed 0.5 like done in PPO ( ppo2/model.py#L102-L108).

Experiment results

PR vwxyzjn/cleanrl#159 tracks our effort to conduct experiments, and the reprodudction instructions can be found at vwxyzjn/cleanrl/benchmark/c51.

Below are the average episodic returns for c51_atari.py.

Environment c51_atari.py 10M steps (Bellemare et al., 2017, Figure 14)1 50M steps (Hessel et al., 2017, Figure 5)3
BreakoutNoFrameskip-v4 467.00 ± 96.11 748 ~500 at 10M steps, ~600 at 50M steps
PongNoFrameskip-v4 19.32 ± 0.92 20.9 ~20 10M steps, ~20 at 50M steps
BeamRiderNoFrameskip-v4 9986.96 ± 1953.30 14,074 ~12000 10M steps, ~14000 at 50M steps

Note that we save computational time by reducing timesteps from 50M to 10M, but our c51_atari.py scores the same or higher than (Mnih et al., 2015)1 in 10M steps.

Learning curves:

Tracked experiments and game play videos:

c51.py

The c51.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/c51.py --env-id CartPole-v1

Explanation of the logged metrics

See related docs for c51_atari.py.

Implementation details

The c51.py shares the same implementation details as c51_atari.py except the c51.py runs with different hyperparameters and neural network architecture. Specifically,

  1. c51.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),
)

  2. c51.py runs with different hyperparameters:

    python c51.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

PR vwxyzjn/cleanrl#159 tracks our effort to conduct experiments, and the reprodudction instructions can be found at vwxyzjn/cleanrl/benchmark/c51.

Below are the average episodic returns for c51.py.

Environment c51.py
CartPole-v1 498.51 ± 1.77
Acrobot-v1 -88.81 ± 8.86
MountainCar-v0 -167.71 ± 26.85

Note that the C51 has no official benchmark on classic control environments, so we did not include a comparison. That said, our c51.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:

  1. Bellemare, M.G., Dabney, W., & Munos, R. (2017). A Distributional Perspective on Reinforcement Learning. ICML. ↩↩↩↩↩

  2. [Proposal] Formal API handling of truncation vs termination. https://github.com/openai/gym/issues/2510 ↩

  3. 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. ↩

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