cleanrl/docs/rl-algorithms/rpo.md

# Robust Policy Optimization (RPO)

## Overview

RPO leverages a method of perturbing the distribution representing actions. The goal is to encourage high-entropy actions and provide a better representation of the action space. The method consists of a simple modification on top of the objective of the PPO algorithm. In the RPO algorithm, the mean of the action distribution is perturbed using a random number drawn from a Uniform distribution.

Original paper: 

* [Robust Policy Optimization in Deep Reinforcement Learning](https://arxiv.org/abs/2212.07536)

## Implemented Variants


| Variants Implemented      | Description |
| ----------- | ----------- |
| :material-github: [`rpo_continuous_action.py`](https://github.com/vwxyzjn/cleanrl/blob/master/cleanrl/rpo_continuous_action.py), :material-file-document: [docs](/rl-algorithms/rpo/#rpo_continuous_actionpy) | For classic control tasks like Gym `Pendulum-v1`, and dm_control. |

Below are our single-file implementations of RPO:

## `rpo_continuous_action.py`

`rpo_continuous_action.py` works with Gym (Gymnasium), dm_control, Mujoco environments with continuous action and vector observations.

The [rpo_continuous_action.py](https://github.com/vwxyzjn/cleanrl/blob/master/cleanrl/rpo_continuous_action.py) has the following features (similar to [ppo_continuous_action.py](https://github.com/vwxyzjn/cleanrl/blob/master/cleanrl/ppo_continuous_action.py)):

* For continuous action space. Also implemented Mujoco-specific code-level optimizations
* Works with the `Box` observation space of low-level features
* Works with the `Box` (continuous) action space
* adding experimental support for [Gymnasium](https://gymnasium.farama.org/)
* 🧪 support `dm_control` environments via [Shimmy](https://github.com/Farama-Foundation/Shimmy)

### Usage

```bash
# mujoco v4 environments
uv pip install ".[mujoco]"
python cleanrl/rpo_continuous_action.py --help
python cleanrl/rpo_continuous_action.py --env-id Walker2d-v4
# NOTE: we recommend using --rpo-alpha 0.01 for Ant Hopper InvertedDoublePendulum Reacher Pusher
python cleanrl/rpo_continuous_action.py --env-id Ant-v4 --rpo-alpha 0.01
# dm_control v4 environments
uv pip install ".[mujoco, dm_control]"
python cleanrl/rpo_continuous_action.py --env-id dm_control/cartpole-balance-v0
# BipedalWalker-v3 experiment (hack)
uv pip install .
uv pip install box2d-py==2.3.5
python cleanrl/rpo_continuous_action.py --env-id BipedalWalker-v3
```


=== "poetry"

    ```bash
    # mujoco v4 environments
    uv pip install ".[mujoco]"
    python cleanrl/rpo_continuous_action.py --help
    python cleanrl/rpo_continuous_action.py --env-id Hopper-v4
    # NOTE: we recommend using --rpo-alpha 0.01 for Ant Hopper InvertedDoublePendulum Reacher Pusher
    python cleanrl/rpo_continuous_action.py --env-id Ant-v4 --rpo-alpha 0.01
    # dm_control environments
    uv pip install ".[mujoco, dm_control]"
    python cleanrl/rpo_continuous_action.py --env-id dm_control/cartpole-balance-v0
    # BipedalWalker-v3 experiment (hack)
    uv pip install box2d-py==2.3.5
    uv run python cleanrl/rpo_continuous_action.py --env-id BipedalWalker-v3
    ```

=== "pip"

    ```bash
    pip install -r requirements/requirements-mujoco.txt
    python cleanrl/rpo_continuous_action.py --help
    python cleanrl/rpo_continuous_action.py --env-id Hopper-v4
    # NOTE: we recommend using --rpo-alpha 0.01 for Ant Hopper InvertedDoublePendulum Reacher Pusher
    python cleanrl/rpo_continuous_action.py --env-id Ant-v4 --rpo-alpha 0.01
    pip install -r requirements/requirements-dm_control.txt
    python cleanrl/rpo_continuous_action.py --env-id dm_control/cartpole-balance-v0
    pip install box2d-py==2.3.5
    python cleanrl/rpo_continuous_action.py --env-id BipedalWalker-v3
    ```


### Explanation of the logged metrics

See [related docs](/rl-algorithms/ppo/#explanation-of-the-logged-metrics) for `ppo.py`.

### Implementation details
[rpo_continuous_action.py](https://github.com/vwxyzjn/cleanrl/blob/master/cleanrl/rpo_continuous_action.py) has the same implementation details as `ppo_continuous_action.py` (see related [docs](/rl-algorithms/ppo/#ppo_continuous_actionpy)) but with a few lines of code differences.

```python hl_lines="30-34"
class Agent(nn.Module):
    def __init__(self, envs):
        super().__init__()
        self.critic = nn.Sequential(
            layer_init(nn.Linear(np.array(envs.single_observation_space.shape).prod(), 64)),
            nn.Tanh(),
            layer_init(nn.Linear(64, 64)),
            nn.Tanh(),
            layer_init(nn.Linear(64, 1), std=1.0),
        )
        self.actor_mean = nn.Sequential(
            layer_init(nn.Linear(np.array(envs.single_observation_space.shape).prod(), 64)),
            nn.Tanh(),
            layer_init(nn.Linear(64, 64)),
            nn.Tanh(),
            layer_init(nn.Linear(64, np.prod(envs.single_action_space.shape)), std=0.01),
        )
        self.actor_logstd = nn.Parameter(torch.zeros(1, np.prod(envs.single_action_space.shape)))

    def get_value(self, x):
        return self.critic(x)

    def get_action_and_value(self, x, action=None):
        action_mean = self.actor_mean(x)
        action_logstd = self.actor_logstd.expand_as(action_mean)
        action_std = torch.exp(action_logstd)
        probs = Normal(action_mean, action_std)
        if action is None:
            action = probs.sample()
        else: # new to RPO
            # sample again to add stochasticity, for the policy update
            z = torch.FloatTensor(action_mean.shape).uniform_(-self.rpo_alpha, self.rpo_alpha)
            action_mean = action_mean + z
            probs = Normal(action_mean, action_std)
        
```

???+ note 

    RPO usages the same PPO-specific hyperparameters. In benchmarking results, we run both algorithms for 8M timesteps.
    RPO has one additional hyperparameter, `rpo_alpha`, which determines the amount of random perturbation on the action mean. 
    We set a default value of `rpo_alpha=0.5` at which RPO is strictly equal to or better than the default PPO in 93% of environments tested (all 48/48 dm_control, 2/2 Gym, 7/11 mujoco_v4. Total 57 out of 61 environments tested.).
    With finetuning `rpo_alpha=0.01` on four mujoco environments, namely, Ant, InvertedDoublePendulum, Reacher, and Pusher, RPO is strictly equal to or better than the default PPO in all tested environments.

### Experiment results

To run benchmark experiments, see  [benchmark/rpo.sh](https://github.com/vwxyzjn/cleanrl/blob/master/benchmark/rpo.sh). Specifically, execute the following command:
<script src="https://emgithub.com/embed.js?target=https%3A%2F%2Fgithub.com%2Fvwxyzjn%2Fcleanrl%2Fblob%2Fmaster%2Fbenchmark%2Frpo.sh%23L1-L6&style=github&showBorder=on&showLineNumbers=on&showFileMeta=on&showCopy=on"></script>

???+ note "Result tables, learning curves"

    === "dm_control"

        Results on all dm_control environments. The PPO and RPO run for 8M timesteps, and results are computed over 10 random seeds.

        |                                       | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:--------------------------------------|:-------------------------------------------------------------|:----------------------------------------------|
        | dm_control/acrobot-swingup-v0         | 26.87 ± 7.93                                                 | 42.97 ± 2.71                                  |
        | dm_control/acrobot-swingup_sparse-v0  | 1.70 ± 0.88                                                  | 3.31 ± 0.84                                   |
        | dm_control/ball_in_cup-catch-v0       | 935.26 ± 12.57                                               | 939.75 ± 10.18                                |
        | dm_control/cartpole-balance-v0        | 790.36 ± 17.64                                               | 795.12 ± 10.49                                |
        | dm_control/cartpole-balance_sparse-v0 | 986.04 ± 9.93                                                | 988.56 ± 4.28                                 |
        | dm_control/cartpole-swingup-v0        | 590.21 ± 16.72                                               | 613.46 ± 10.91                                |
        | dm_control/cartpole-swingup_sparse-v0 | 240.14 ± 299.93                                              | 525.49 ± 185.96                               |
        | dm_control/cartpole-two_poles-v0      | 216.31 ± 4.03                                                | 218.31 ± 7.30                                 |
        | dm_control/cartpole-three_poles-v0    | 160.03 ± 2.52                                                | 159.97 ± 2.28                                 |
        | dm_control/cheetah-run-v0             | 472.14 ± 99.62                                               | 565.51 ± 58.03                                |
        | dm_control/dog-stand-v0               | 332.06 ± 23.66                                               | 501.22 ± 131.98                               |
        | dm_control/dog-walk-v0                | 124.92 ± 23.13                                               | 166.39 ± 44.65                                |
        | dm_control/dog-trot-v0                | 79.89 ± 12.30                                                | 115.39 ± 29.68                                |
        | dm_control/dog-run-v0                 | 69.07 ± 8.17                                                 | 104.27 ± 24.44                                |
        | dm_control/dog-fetch-v0               | 28.34 ± 4.87                                                 | 43.58 ± 6.88                                  |
        | dm_control/finger-spin-v0             | 630.06 ± 252.99                                              | 848.67 ± 25.21                                |
        | dm_control/finger-turn_easy-v0        | 237.76 ± 78.10                                               | 450.88 ± 133.54                               |
        | dm_control/finger-turn_hard-v0        | 83.76 ± 28.96                                                | 259.99 ± 144.83                               |
        | dm_control/fish-upright-v0            | 559.72 ± 65.79                                               | 803.21 ± 28.36                                |
        | dm_control/fish-swim-v0               | 80.42 ± 9.18                                                 | 140.33 ± 49.10                                |
        | dm_control/hopper-stand-v0            | 3.26 ± 1.65                                                  | 404.39 ± 198.17                               |
        | dm_control/hopper-hop-v0              | 6.48 ± 18.92                                                 | 62.60 ± 87.29                                 |
        | dm_control/humanoid-stand-v0          | 20.76 ± 29.35                                                | 140.43 ± 57.27                                |
        | dm_control/humanoid-walk-v0           | 8.92 ± 18.01                                                 | 77.00 ± 53.00                                 |
        | dm_control/humanoid-run-v0            | 5.44 ± 9.16                                                  | 24.00 ± 19.54                                 |
        | dm_control/humanoid-run_pure_state-v0 | 1.13 ± 0.11                                                  | 3.24 ± 2.41                                   |
        | dm_control/humanoid_CMU-stand-v0      | 4.64 ± 0.37                                                  | 4.32 ± 0.33                                   |
        | dm_control/humanoid_CMU-run-v0        | 0.88 ± 0.09                                                  | 0.80 ± 0.09                                   |
        | dm_control/manipulator-bring_ball-v0  | 0.42 ± 0.14                                                  | 0.44 ± 0.23                                   |
        | dm_control/manipulator-bring_peg-v0   | 0.95 ± 0.43                                                  | 1.07 ± 1.01                                   |
        | dm_control/manipulator-insert_ball-v0 | 41.24 ± 27.27                                                | 43.63 ± 12.77                                 |
        | dm_control/manipulator-insert_peg-v0  | 40.72 ± 15.95                                                | 44.87 ± 26.55                                 |
        | dm_control/pendulum-swingup-v0        | 472.19 ± 385.47                                              | 774.30 ± 21.03                                |
        | dm_control/point_mass-easy-v0         | 534.23 ± 264.35                                              | 653.73 ± 23.14                                |
        | dm_control/point_mass-hard-v0         | 129.75 ± 61.18                                               | 185.81 ± 36.25                                |
        | dm_control/quadruped-walk-v0          | 247.29 ± 90.48                                               | 602.64 ± 223.23                               |
        | dm_control/quadruped-run-v0           | 171.50 ± 37.90                                               | 367.98 ± 117.18                               |
        | dm_control/quadruped-escape-v0        | 23.11 ± 10.48                                                | 68.50 ± 27.81                                 |
        | dm_control/quadruped-fetch-v0         | 183.71 ± 25.14                                               | 216.32 ± 17.44                                |
        | dm_control/reacher-easy-v0            | 773.01 ± 56.70                                               | 716.89 ± 50.07                                |
        | dm_control/reacher-hard-v0            | 637.84 ± 81.15                                               | 576.81 ± 48.25                                |
        | dm_control/stacker-stack_2-v0         | 58.02 ± 11.04                                                | 70.95 ± 16.84                                 |
        | dm_control/stacker-stack_4-v0         | 73.84 ± 14.48                                                | 65.54 ± 18.06                                 |
        | dm_control/swimmer-swimmer6-v0        | 164.22 ± 18.44                                               | 159.60 ± 39.52                                |
        | dm_control/swimmer-swimmer15-v0       | 161.02 ± 24.56                                               | 153.91 ± 28.08                                |
        | dm_control/walker-stand-v0            | 439.24 ± 210.22                                              | 734.74 ± 142.52                               |
        | dm_control/walker-walk-v0             | 305.74 ± 92.15                                               | 787.11 ± 125.97                               |
        | dm_control/walker-run-v0              | 128.18 ± 91.52                                               | 391.56 ± 119.75                               |
                
        Learning curves:
        ![](../rpo/dm_control_all_ppo_rpo_8M.png)

        Tracked experiments: 
        
        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-dm_control-Part-1--VmlldzozMjU4NTE4" style="width:100%; height:500px" title="dm_control-CleanRL-s-RPO-part-1"></iframe>
        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-dm_control-Part-2--VmlldzozMjU4NjYy" style="width:100%; height:500px" title="dm_control-CleanRL-s-RPO-part-2"></iframe>


    
    
    === "MuJoCo v4"

        |                     | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:--------------------|:-------------------------------------------------------------|:----------------------------------------------|
        | HumanoidStandup-v4  | 109325.87 ± 16161.71                                         | 150972.11 ± 6926.19                           |
        | Humanoid-v4         | 583.17 ± 27.88                                               | 799.44 ± 170.85                               |
        | InvertedPendulum-v4 | 888.83 ± 34.66                                               | 879.81 ± 35.52                                |
        | Walker2d-v4         | 2872.92 ± 690.53                                             | 3665.48 ± 278.61                              |

        Learning curves:
        ![](../rpo/mujoco_v4_part1.png)


        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-Mujoco_v4-Part-1--VmlldzozMjU3ODIz" style="width:100%; height:500px" title="RPO-mujoco-v4-part1"></iframe>

        
        The following environments require tuning of `alpha` (Algorithm 1, line 13, paper: https://arxiv.org/pdf/2212.07536.pdf). As described in the paper, this variable should be tuned for environments tested. A larger value means more randomness, whereas a smaller value indicates less randomness. Some mujoco environments require a smaller `alpha=0.01` value to achieve a reasonable performance compared to `alpha=0.5` for the rest of the environments. This version (`alpha=0.01`) of runs is indicated as `rpo_continuous_action_alpha_0_01` in the table and learning curves.

        |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action_alpha_0_01 ({'tag': ['pr-331']})   |
        |:--------------------------|:-------------------------------------------------------------|:---------------------------------------------------------|
        | Ant-v4                    | 1824.17 ± 905.78                                             | 2702.91 ± 683.53                                         |
        | HalfCheetah-v4            | 2637.19 ± 1068.49                                            | 2716.51 ± 1314.93                                        |
        | Hopper-v4                 | 2741.42 ± 269.11                                             | 2334.22 ± 441.89                                         |
        | InvertedDoublePendulum-v4 | 5626.22 ± 289.23                                             | 5409.03 ± 318.68                                         |
        | Reacher-v4                | -4.65 ± 0.96                                                 | -3.93 ± 0.19                                             |
        | Swimmer-v4                | 124.88 ± 22.24                                               | 129.97 ± 12.02                                           |
        | Pusher-v4                 | -30.35 ± 6.43                                                | -31.48 ± 9.83                                            |

        Learning curves:
        ![](../rpo/mujoco_v4_part2.png)

        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-Mujoco_v4-Part-2--VmlldzozMjU3OTM4" style="width:100%; height:500px" title="RPO-mujoco-v4-part2"></iframe>
        

        Results with `rpo_alpha=0.5` (not tuned) on the tuned environments:

        |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:--------------------------|:-------------------------------------------------------------|:----------------------------------------------|
        | Ant-v4                    | 1774.42 ± 819.08                                             | -7.99 ± 2.47                                  |
        | HalfCheetah-v4            | 2667.34 ± 1109.99                                            | 2163.57 ± 790.16                              |
        | Hopper-v4                 | 2761.77 ± 286.88                                             | 1557.18 ± 206.74                              |
        | InvertedDoublePendulum-v4 | 5644.00 ± 353.46                                             | 296.97 ± 15.95                                |
        | Reacher-v4                | -4.67 ± 0.88                                                 | -66.35 ± 0.66                                 |
        | Swimmer-v4                | 124.52 ± 22.10                                               | 117.82 ± 10.07                                |
        | Pusher-v4                 | -30.62 ± 6.80                                                | -276.32 ± 26.99                               |

        Learning curves:
        ![](../rpo/mujoco_v4_part2_0_5.png)


        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-alpha-0-5-on-Mujoco_v4-Part-2--VmlldzozMjU4MTM1" style="width:100%; height:500px" title="RPO-mujoco-v4-0-5-part-2"></iframe>

 
    
    === "MuJoCo v2"

        |                     | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:--------------------|:-------------------------------------------------------------|:----------------------------------------------|
        | HumanoidStandup-v2  | 109118.07 ± 19422.20                                         | 156848.90 ± 11414.50                          |
        | Humanoid-v2         | 588.22 ± 43.80                                               | 717.37 ± 97.18                                |
        | InvertedPendulum-v2 | 867.64 ± 19.97                                               | 866.60 ± 27.06                                |
        | Walker2d-v2         | 3220.99 ± 923.84                                             | 4150.51 ± 348.03                              |

        Learning curves:
        ![](../rpo/mujoco_v2_part1.png)

        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-Mujoco_v2-Part-1--VmlldzozMjU4Mjc5" style="width:100%; height:500px" title="RPO-mujoco-v2-part1"></iframe>

        The following environments require tuning of `alpha` (Algorithm 1, line 13, paper: https://arxiv.org/pdf/2212.07536.pdf). As described in the paper, this variable should be tuned for environments tested. A larger value means more randomness, whereas a smaller value indicates less randomness. Some mujoco environments require a smaller `alpha=0.01` value to achieve a reasonable performance compared to `alpha=0.5` for the rest of the environments. This version (`alpha=0.01`) of runs is indicated as `rpo_continuous_action_alpha_0_01` in the table and learning curves.

        |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action_alpha_0_01 ({'tag': ['pr-331']})   |
        |:--------------------------|:-------------------------------------------------------------|:---------------------------------------------------------|
        | Ant-v2                    | 2412.35 ± 949.44                                             | 3084.95 ± 759.51                                         |
        | HalfCheetah-v2            | 2717.27 ± 1269.85                                            | 2707.91 ± 1215.21                                        |
        | Hopper-v2                 | 2387.39 ± 645.41                                             | 2272.78 ± 588.66                                         |
        | InvertedDoublePendulum-v2 | 5630.91 ± 377.93                                             | 5661.29 ± 316.04                                         |
        | Reacher-v2                | -4.61 ± 0.53                                                 | -4.24 ± 0.25                                             |
        | Swimmer-v2                | 132.07 ± 9.92                                                | 141.37 ± 8.70                                            |
        | Pusher-v2                 | -33.93 ± 8.55                                                | -26.22 ± 2.52                                            |
                
        
        Learning curves:
        ![](../rpo/mujoco_v2_part2.png)

        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-Mujoco_v2-Part-2--VmlldzozMjU4MzI1" style="width:100%; height:500px" title="RPO-mujoco-v2-part1"></iframe>

        Results with `rpo_alpha=0.5` (not tuned) on the tuned environments:

        |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:--------------------------|:-------------------------------------------------------------|:----------------------------------------------|
        | Ant-v2                    | 2495.65 ± 991.65                                             | -7.81 ± 3.57                                  |
        | HalfCheetah-v2            | 2722.03 ± 1231.28                                            | 2605.06 ± 1183.30                             |
        | Hopper-v2                 | 2356.83 ± 650.91                                             | 1609.79 ± 164.16                              |
        | InvertedDoublePendulum-v2 | 5675.31 ± 244.34                                             | 274.78 ± 16.40                                |
        | Reacher-v2                | -4.67 ± 0.48                                                 | -66.55 ± 0.20                                 |
        | Swimmer-v2                | 131.53 ± 9.94                                                | 114.34 ± 3.95                                 |
        | Pusher-v2                 | -33.46 ± 8.41                                                | -275.09 ± 15.65                               |

        Learning curves:
        ![](../rpo/mujoco_v2_part2_0_5.png)


        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-alpha-0-5-on-Mujoco_v2-Part-2--VmlldzozMjU4MzQ0" style="width:100%; height:500px" title="RPO-mujoco-v2-0-5-part-2s"></iframe>

        

    
    === "Gym(Gymnasium)"

        Results on two continuous gym environments. The PPO and RPO run for 8M timesteps, and results are computed over 10 random seeds.


        |                  | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
        |:-----------------|:-------------------------------------------------------------|:----------------------------------------------|
        | Pendulum-v1      | -1141.98 ± 135.55                                            | -151.08 ± 3.73                                |
        | BipedalWalker-v3 | 172.12 ± 96.05                                               | 227.11 ± 18.23                                |

        Learning curves:
        ![](../rpo/gym.png)

        Tracked experiments:     

        <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-on-Gym-Gymnasium---VmlldzozMjU3NzUy" style="width:100%; height:500px" title="RPO-gymnasium"></iframe>



???+ failure 

    Failure case of `rpo_alpha=0.5`:

    Overall, we observed that `rpo_alpha=0.5` is strictly equal to or better than the default PPO in 93% of environments tested (all 48/48 dm_control, 2/2 Gym, 7/11 mujoco_v4. Total 57 out of 61 environments tested). 

    Here are the failure cases:
    `Mujoco v4 and v2: Ant InvertedDoublePendulum  Reacher Pusher`

    |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
    |:--------------------------|:-------------------------------------------------------------|:----------------------------------------------|
    | Ant-v4                    | 1831.63 ± 867.71                                             | -10.43 ± 8.16                                 |
    | InvertedDoublePendulum-v4 | 5490.71 ± 261.50                                             | 303.36 ± 13.39                                |
    | Reacher-v4                | -4.58 ± 0.73                                                 | -66.62 ± 0.56                                 |
    | Pusher-v4                 | -30.63 ± 6.42                                                | -276.11 ± 26.52                               |

    Learning curves:
    ![](../rpo/mujoco_v4_failure_0_5.png)

    Tracked experiments:     

    <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-alpha-0-5-s-failure-cases-on-Mujoco_v4--VmlldzozMjU4MTYy" style="width:100%; height:500px" title="RPO-mujoco-v4-failure-cases"></iframe>



    |                           | ppo_continuous_action_8M ({'tag': ['v1.0.0-13-gcbd83f6']})   | rpo_continuous_action ({'tag': ['pr-331']})   |
    |:--------------------------|:-------------------------------------------------------------|:----------------------------------------------|
    | Ant-v2                    | 2493.50 ± 993.24                                             | -7.26 ± 2.28                                  |
    | InvertedDoublePendulum-v2 | 5568.37 ± 401.65                                             | 278.94 ± 15.34                                |
    | Reacher-v2                | -4.62 ± 0.47                                                 | -66.61 ± 0.23                                 |
    | Pusher-v2                 | -33.51 ± 8.47                                                | -276.01 ± 15.93                               |


    Learning curves:
    ![](../rpo/mujoco_v2_failure_0_5.png)


    Tracked experiments:     

    <iframe loading="lazy" src="https://wandb.ai/openrlbenchmark/cleanrl/reports/RPO-alpha-0-5-s-failure-cases-on-Mujoco_v2--VmlldzozMjU4MjQ1" style="width:100%; height:500px" title="RPO-mujoco-v4-failure-cases"></iframe>


    However, tuning of `rpo_alpha` (`rpo_alpha=0.01` on failed cases) helps RPO to overcome the failure, and it performs strictly equal to or better than the default PPO in all (100%) of tested environments.