Twin Delayed Deep Deterministic Policy Gradient (TD3)

Overview

TD3 is a popular DRL algorithm for continuous control. It extends DDPG with three techniques: 1) Clipped Double Q-Learning, 2) Delayed Policy Updates, and 3) Target Policy Smoothing Regularization. With these three techniques TD3 shows significantly better performance compared to DDPG.

Original paper:

Addressing Function Approximation Error in Actor-Critic Methods

Reference resources:

Implemented Variants

Variants Implemented	Description
`td3_continuous_action.py`, docs	For continuous action space

Below are our single-file implementations of TD3:

`td3_continuous_action.py`

The td3_continuous_action.py has the following features:

For continuous action space
Works with the Box observation space of low-level features
Works with the Box (continuous) action space

Usage

poetry install
poetry install --with pybullet
python cleanrl/td3_continuous_action.py --help
python cleanrl/td3_continuous_action.py --env-id HopperBulletEnv-v0
poetry install --with mujoco_py # only works in Linux
python cleanrl/td3_continuous_action.py --env-id Hopper-v3

Explanation of the logged metrics

Running python cleanrl/td3_continuous_action.py will automatically record various metrics such as various losses in Tensorboard. Below are the documentation for these metrics:

charts/episodic_return: episodic return of the game
charts/SPS: number of steps per second
losses/qf1_loss: the MSE between the Q values at timestep \(t\) and the target Q values at timestep \(t+1\), which minimizes temporal difference.
losses/actor_loss: implemented as -qf1(data.observations, actor(data.observations)).mean(); it is the negative average Q values calculated based on the 1) observations and the 2) actions computed by the actor based on these observations. By minimizing actor_loss, the optimizer updates the actors parameter using the following gradient (Fujimoto et al., 2018, Algorithm 1)²:

\[ \nabla_{\phi} J(\phi)=\left.N^{-1} \sum \nabla_{a} Q_{\theta_{1}}(s, a)\right|_{a=\pi_{\phi}(s)} \nabla_{\phi} \pi_{\phi}(s) \]

losses/qf1_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 esitmations happen

Implementation details

Our td3_continuous_action.py is based on the TD3.py from sfujim/TD3. Our td3_continuous_action.py presents the following implementation differences.

td3_continuous_action.py uses a two separate objects qf1 and qf2 to represents the two Q functions in the Clipped Double Q-learning architecture, whereas TD3.py (Fujimoto et al., 2018)² uses a single Critic class that contains both Q networks. That said, these two implementations are virtually the same.

td3_continuous_action.py also adds support for handling continuous environments where the lower and higher bounds of the action space are not \([-1,1]\), or are asymmetric. The case where the bounds are not \([-1,1]\) is handled in TD3.py (Fujimoto et al., 2018)² as follows:

class Actor(nn.Module):

    ...

    def forward(self, state):
        a = F.relu(self.l1(state))
        a = F.relu(self.l2(a))
        return self.max_action * torch.tanh(self.l3(a)) # Scale from [-1,1] to [-action_high, action_high]

On the other hand, in CleanRL's td3_continuous_action.py, the mean and the scale of the action space are computed as action_bias and action_scale respectively. Those scalars are in turn used to scale the output of a tanh activation function in the actor to the original action space range:

class Actor(nn.Module):
    def __init__(self, env):
        ...
        # action rescaling
        self.register_buffer("action_scale", torch.FloatTensor((env.action_space.high - env.action_space.low) / 2.0))
        self.register_buffer("action_bias", torch.FloatTensor((env.action_space.high + env.action_space.low) / 2.0))

    def forward(self, x):
        x = F.relu(self.fc1(x))
        x = F.relu(self.fc2(x))
        x = torch.tanh(self.fc_mu(x))
        return x * self.action_scale + self.action_bias # Scale from [-1,1] to [-action_low, action_high]

Additionally, when drawing exploration noise that is added to the actions produced by the actor, CleanRL's td3_continuous_action.py centers the distribution the sampled from at action_bias, and the scale of the distribution is set to action_scale * exploration_noise.

Info

Note that Humanoid-v2, InvertedPendulum-v2, Pusher-v2 have action space bounds that are not the standard [-1, 1]. See below and PR #196

Ant-v2 Observation space: Box(-inf, inf, (111,), float64) Action space: Box(-1.0, 1.0, (8,), float32)
HalfCheetah-v2 Observation space: Box(-inf, inf, (17,), float64) Action space: Box(-1.0, 1.0, (6,), float32)
Hopper-v2 Observation space: Box(-inf, inf, (11,), float64) Action space: Box(-1.0, 1.0, (3,), float32)
Humanoid-v2 Observation space: Box(-inf, inf, (376,), float64) Action space: Box(-0.4, 0.4, (17,), float32)
InvertedDoublePendulum-v2 Observation space: Box(-inf, inf, (11,), float64) Action space: Box(-1.0, 1.0, (1,), float32)
InvertedPendulum-v2 Observation space: Box(-inf, inf, (4,), float64) Action space: Box(-3.0, 3.0, (1,), float32)
Pusher-v2 Observation space: Box(-inf, inf, (23,), float64) Action space: Box(-2.0, 2.0, (7,), float32)
Reacher-v2 Observation space: Box(-inf, inf, (11,), float64) Action space: Box(-1.0, 1.0, (2,), float32)
Swimmer-v2 Observation space: Box(-inf, inf, (8,), float64) Action space: Box(-1.0, 1.0, (2,), float32)
Walker2d-v2 Observation space: Box(-inf, inf, (17,), float64) Action space: Box(-1.0, 1.0, (6,), float32)

Experiment results

To run benchmark experiments, see benchmark/td3.sh. Specifically, execute the following command:

Below are the average episodic returns for td3_continuous_action.py (3 random seeds). To ensure the quality of the implementation, we compared the results against (Fujimoto et al., 2018)².

Environment	`td3_continuous_action.py`	`TD3.py` (Fujimoto et al., 2018, Table 1)²
HalfCheetah	9449.94 ± 1586.49	9636.95 ± 859.065
Walker2d	3851.55 ± 335.29	4682.82 ± 539.64
Hopper	3162.21 ± 261.08	3564.07 ± 114.74
Humanoid	5011.05 ± 254.89	not available
Pusher	-37.49 ± 10.22	not available
InvertedPendulum	996.81 ± 4.50	1000.00 ± 0.00

Info

Note that td3_continuous_action.py uses gym MuJoCo v2 environments while TD3.py (Fujimoto et al., 2018)² uses the gym MuJoCo v1 environments. According to the openai/gym#834, gym MuJoCo v2 environments should be equivalent to the gym MuJoCo v1 environments.

Also note the performance of our td3_continuous_action.py seems to be worse than the reference implementation on Walker2d. This is likely due to openai/gym#938. We would have a hard time reproducing gym MuJoCo v1 environments because they have been long deprecated.

One other thing could cause the performance difference: the original code reported the average episodic return using determinisitc evaluation (i.e., without exploration noise), see sfujim/TD3/main.py#L15-L32, whereas we reported the episodic return during training and the policy gets updated between environments steps.

Learning curves:

Tracked experiments and game play videos:

`td3_continuous_action_jax.py`

The td3_continuous_action_jax.py has the following features:

Uses Jax, Flax, and Optax instead of torch. td3_continuous_action_jax.py is roughly 2.5-4x faster than td3_continuous_action.py
For continuous action space
Works with the Box observation space of low-level features
Works with the Box (continuous) action space

Usage

poetry install --with mujoco_py,jax
poetry run pip install --upgrade "jax[cuda]==0.3.17" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
poetry run python -c "import mujoco_py"
python cleanrl/td3_continuous_action_jax.py --help
poetry install --with mujoco_py # only works in Linux
python cleanrl/td3_continuous_action_jax.py --env-id Hopper-v3

Explanation of the logged metrics

See related docs for td3_continuous_action.py.

Implementation details

See related docs for td3_continuous_action.py.

Experiment results

To run benchmark experiments, see benchmark/td3.sh. Specifically, execute the following command:

Below are the average episodic returns for td3_continuous_action.py (3 random seeds). To ensure the quality of the implementation, we compared the results against (Fujimoto et al., 2018)².

Environment	`td3_continuous_action_jax.py` (RTX 3060 TI)	`td3_continuous_action_jax.py` (VM w/ TPU)	`td3_continuous_action.py` (RTX 3060 TI)	`TD3.py` (Fujimoto et al., 2018, Table 1)²
HalfCheetah	9408.62 ± 473.23	8948.33 ± 1196.87	9449.94 ± 1586.49	9636.95 ± 859.065
Walker2d	3512.14 ± 1576.59	4107.63 ± 173.93	3851.55 ± 335.29	4682.82 ± 539.64
Hopper	2898.62 ± 485.18	3151.80 ± 458.68	3162.21 ± 261.08	3564.07 ± 114.74

Info

Note that the experiments were conducted on different hardwares, so your mileage might vary. This inconsistency is because 1) re-running expeirments on the same hardware is computationally expensive and 2) requiring the same hardware is not inclusive nor feasible to other contributors who might have different hardwares.

That said, we roughly expect to see a 2-4x speed improvement from using td3_continuous_action_jax.py under the same hardware. And if you disable the --capture-video overhead, the speed improvement will be even higher.

Learning curves:

Tracked experiments and game play videos:

Lillicrap, T.P., Hunt, J.J., Pritzel, A., Heess, N.M., Erez, T., Tassa, Y., Silver, D., & Wierstra, D. (2016). Continuous control with deep reinforcement learning. CoRR, abs/1509.02971. https://arxiv.org/abs/1509.02971 ↩
Fujimoto, S., Hoof, H.V., & Meger, D. (2018). Addressing Function Approximation Error in Actor-Critic Methods. ArXiv, abs/1802.09477. https://arxiv.org/abs/1802.09477 ↩↩↩↩↩↩↩↩