On-Policy Algorithms

The OmniSafe Safety-Gymnasium Benchmark for on-policy algorithms evaluates the effectiveness of OmniSafe’s on-policy algorithms across multiple environments from the Safety-Gymnasium task suite. For each supported algorithm and environment, we offer the following:

  • Default hyperparameters used for the benchmark and scripts that enable result replication.

  • Performance comparison with other open-source implementations.

  • Graphs and raw data that can be utilized for research purposes.

  • Detailed logs obtained during training.

Supported algorithms are listed below:

First-Order

Second-Order

Saute RL

Simmer

PID-Lagrangian

Early Terminated MDP

Safety-Gymnasium

We highly recommend using Safety-Gymnasium to run the following experiments. To install, in a linux machine, type:

pip install safety_gymnasium

Run the Benchmark

You can set the main function of examples/benchmarks/experiment_grid.py as:

if __name__ == '__main__':
    eg = ExperimentGrid(exp_name='On-Policy-Benchmarks')

    # set up the algorithms.
    base_policy = ['PolicyGradient', 'NaturalPG', 'TRPO', 'PPO']
    naive_lagrange_policy = ['PPOLag', 'TRPOLag', 'RCPO']
    first_order_policy = ['CUP', 'FOCOPS', 'P3O']
    second_order_policy = ['CPO', 'PCPO']
    saute_policy = ['PPOSaute', 'TRPOSaute']
    simmer_policy = ['PPOSimmerPID', 'TRPOSimmerPID']
    pid_policy = ['CPPOPID', 'TRPOPID']
    early_mdp_policy = ['PPOEarlyTerminated', 'TRPOEarlyTerminated']

    eg.add(
        'algo',
        base_policy +
        naive_lagrange_policy +
        first_order_policy +
        second_order_policy +
        saute_policy +
        simmer_policy +
        pid_policy +
        early_mdp_policy
    )

    # you can use wandb to monitor the experiment.
    eg.add('logger_cfgs:use_wandb', [False])
    # you can use tensorboard to monitor the experiment.
    eg.add('logger_cfgs:use_tensorboard', [True])

    # the default configs here are as follows:
    # eg.add('algo_cfgs:steps_per_epoch', [20000])
    # eg.add('train_cfgs:total_steps', [20000 * 500])
    # which can reproduce results of 1e7 steps.

    # if you want to reproduce results of 1e6 steps, using
    # eg.add('algo_cfgs:steps_per_epoch', [2048])
    # eg.add('train_cfgs:total_steps', [2048 * 500])

    # set the device.
    avaliable_gpus = list(range(torch.cuda.device_count()))
    # if you want to use GPU, please set gpu_id like follows:
    # gpu_id = [0, 1, 2, 3]
    # if you want to use CPU, please set gpu_id = None
    # we recommends using CPU to obtain results as consistent
    # as possible with our publicly available results,
    # since the performance of all on-policy algorithms
    # in OmniSafe is tested on CPU.
    gpu_id = None

    if gpu_id and not set(gpu_id).issubset(avaliable_gpus):
        warnings.warn('The GPU ID is not available, use CPU instead.', stacklevel=1)
        gpu_id = None

    # set up the environment.
    eg.add('env_id', [
        'SafetyHopper',
        'SafetyWalker2d',
        'SafetySwimmer',
        'SafetyAnt',
        'SafetyHalfCheetah',
        'SafetyHumanoid'
        ])
    eg.add('seed', [0, 5, 10, 15, 20])

    # total experiment num must can be divided by num_pool.
    # meanwhile, users should decide this value according to their machine.
    eg.run(train, num_pool=5, gpu_id=gpu_id)

After that, you can run the following command to run the benchmark:

cd examples/benchmarks
python run_experiment_grid.py

You can also plot the results by running the following command:

cd examples
python analyze_experiment_results.py

For a detailed usage of OmniSafe statistics tool, please refer to this tutorial.

Logs is saved in examples/benchmarks/exp-x and can be monitored with tensorboard or wandb.

tensorboard --logdir examples/benchmarks/exp-x

After the experiment is finished, you can use the following command to generate the video of the trained agent:

cd examples
python evaluate_saved_policy.py

Please note that before you evaluate, set the LOG_DIR in evaluate_saved_policy.py.

For example, if I train PPOLag in SafetyHumanoid

LOG_DIR = '~/omnisafe/examples/runs/PPOLag-<SafetyHumanoid>/seed-000'
play = True
save_replay = True
if __name__ == '__main__':
    evaluator = omnisafe.Evaluator(play=play, save_replay=save_replay)
    for item in os.scandir(os.path.join(LOG_DIR, 'torch_save')):
        if item.is_file() and item.name.split('.')[-1] == 'pt':
            evaluator.load_saved(
                save_dir=LOG_DIR, model_name=item.name, camera_name='track', width=256, height=256
            )
            evaluator.render(num_episodes=1)
            evaluator.evaluate(num_episodes=1)

OmniSafe Benchmark

Classic Reinforcement Learning Algorithms

To ascertain the credibility of OmniSafe ’s algorithmic implementation, a comparative assessment was conducted, juxtaposing the performance of classical reinforcement learning algorithms. Such as Policy Gradient, Natural Policy Gradient, TRPO and PPO. The performance table is provided in Table 1. with well-established open-source implementations, specifically Tianshou and Stable-Baselines3.

Policy Gradient PPO
Environment OmniSafe (Ours) Tianshou Stable-Baselines3 OmniSafe (Ours) Tianshou Stable-Baselines3
SafetyAntVelocity-v1 2769.45 ± 550.71 145.33 ± 127.55 - ±- 4295.96 ± 658.2 2607.48 ± 1415.78 1780.61 ± 780.65
SafetyHalfCheetahVelocity-v1 2625.44 ± 1079.04 707.56 ± 158.59 - ±- 3507.47 ± 1563.69 6299.27 ± 1692.38 5074.85 ± 2225.47
SafetyHopperVelocity-v1 1884.38 ± 825.13 343.88 ± 51.85 - ±- 2679.98 ± 921.96 1834.7 ± 862.06 838.96 ± 351.10
SafetyHumanoidVelocity-v1 647.52 ± 154.82 438.97 ± 123.68 - ±- 1106.09 ± 607.6 677.43 ± 189.96 762.73 ± 170.22
SafetySwimmerVelocity-v1 47.31 ± 16.19 27.12 ±7.47 - ±- 113.28 ± 20.22 37.93 ±8.68 273.86 ± 87.76
SafetyWalker2dVelocity-v1 1665 .00 ± 930.18 373.63 ± 129.2 - ±- 3806.39 ± 1547.48 3748.26 ± 1832.83 3304.35 ± 706.13
NaturalPG TRPO
Environment OmniSafe (Ours) Tianshou Stable-Baselines3 OmniSafe (Ours) Tianshou Stable-Baselines3
SafetyAntVelocity-v1 3793.70 ± 583.66 2062.45 ± 876.43 - ±- 4362.43 ± 640.54 2521.36 ± 1442.10 3233.58 ± 1437.16
SafetyHalfCheetahVelocity-v1 4096.77 ± 1223.70 3430.9 ± 239.38 - ±- 3313.31 ± 1048.78 4255.73 ± 1053.82 7185.06 ± 3650.82
SafetyHopperVelocity-v1 2590.54 ± 631.05 993.63 ± 489.42 - ±- 2698.19 ± 568.80 1346.94 ± 984.09 2467.10 ± 1160.25
SafetyHumanoidVelocity-v1 3838.67 ± 1654.79 810.76 ± 270.69 - ±- 1461.51 ± 602.23 749.42 ± 149.81 2828.18 ± 2256.38
SafetySwimmerVelocity-v1 116.33 ± 5.97 29.75 ±12.00 - ±- 105.08 ± 31.00 37.21 ±4.04 258.62 ± 124.91
SafetyWalker2dVelocity-v1 4054.62 ± 1266.76 3372.59 ± 1049.14 - ±- 4099.97 ± 409.05 3372.59 ± 961.74 4227.91 ± 760.93

Table 1:The performance of OmniSafe, which was evaluated in relation to published baselines within the Safety-Gymnasium MuJoCo Velocity environments. Experimental outcomes, comprising mean and standard deviation, were derived from 10 assessment iterations encompassing multiple random seeds.

Safe Reinforcement Learning Algorithms

To demonstrate the high reliability of the algorithms implemented, OmniSafe offers performance insights within the Safety-Gymnasium environment. It should be noted that all data is procured under the constraint of cost_limit=25.00. The results are presented in Table 2 and the training curves are in the following sections (Please click the triangle button to see the training curves).

Performance Table

Policy Gradient Natural PG TRPO PPO
Environment Reward Cost Reward Cost Reward Cost Reward Cost
SafetyAntVelocity-v1 5292.29 ± 913.44 919.42 ± 158.61 5547.20 ± 807.89 895.56 ± 77.13 6026.79 ± 314.98 933.46 ± 41.28 5977.73 ± 885.65 958.13 ± 134.5
SafetyHalfCheetahVelocity-v1 5188.46 ± 1202.76 896.55 ± 184.7 5878.28 ± 2012.24 847.74 ± 249.02 6490.76 ± 2507.18 734.26 ± 321.88 6921.83 ± 1721.79 919.2 ±173.08
SafetyHopperVelocity-v1 3218.17 ± 672.88 881.76 ± 198.46 2613.95 ± 866.13 587.78 ± 220.97 2047.35 ± 447.33 448.12 ± 103.87 2337.11 ± 942.06 550.02 ± 237.70
SafetyHumanoidVelocity-v1 7001.78 ± 419.67 834.11 ± 212.43 8055.20 ± 641.67 946.40 ± 9.11 8681.24 ± 3934.08 718.42 ± 323.30 9115.93 ± 596.88 960.44 ± 7.06
SafetySwimmerVelocity-v1 77.05 ±33.44 107.1 ±60.58 120.19 ± 7.74 161.78 ± 17.51 124.91 ± 6.13 176.56 ± 15.95 119.77 ± 13.8 165.27 ± 20.15
SafetyWalker2dVelocity-v1 4832.34 ± 685.76 866.59 ± 93.47 5347.35 ± 436.86 914.74 ± 32.61 6096.67 ± 723.06 914.46 ± 27.85 6239.52 ± 879.99 902.68 ± 100.93
SafetyCarGoal1-v0 35.86 ±1.97 57.46 ±48.34 36.07 ±1.25 58.06 ±10.03 36.60 ±0.22 55.58 ±12.68 33.41 ±2.89 58.06 ±42.06
SafetyCarButton1-v0 19.76 ±10.15 353.26 ± 177.08 22.16 ±4.48 333.98 ± 67.49 21.98 ±2.06 343.22 ± 24.60 17.51 ±9.46 373.98 ± 156.64
SafetyCarGoal2-v0 29.43 ±4.62 179.2 ±84.86 30.26 ±0.38 209.62 ± 29.97 32.17 ±1.24 190.74 ± 21.05 29.88 ±4.55 194.16 ± 106.2
SafetyCarButton2-v0 18.06 ±10.53 349.82 ± 187.07 20.85 ±3.14 313.88 ± 58.20 20.51 ±3.34 316.42 ± 35.28 21.35 ±8.22 312.64 ± 138.4
SafetyPointGoal1-v0 26.19 ±3.44 201.22 ± 80.4 26.92 ±0.58 57.92 ±9.97 27.20 ±0.44 45.88 ±11.27 25.44 ±5.43 55.72 ±35.55
SafetyPointButton1-v0 29.98 ±5.24 141.74 ± 75.13 31.95 ±1.53 123.98 ± 32.05 30.61 ±0.40 134.38 ± 22.06 27.03 ±6.14 152.48 ± 80.39
SafetyPointGoal2-v0 25.18 ±3.62 204.96 ± 104.97 26.19 ±0.84 193.60 ± 18.54 25.61 ±0.89 202.26 ± 15.15 25.49 ±2.46 159.28 ± 87.13
SafetyPointButton2-v0 26.88 ±4.38 153.88 ± 65.54 28.45 ±1.49 160.40 ± 20.08 28.78 ±2.05 170.30 ± 30.59 25.91 ±6.15 166.6 ±111.21
RCPO TRPOLag PPOLag P3O
Environment Reward Cost Reward Cost Reward Cost Reward Cost
SafetyAntVelocity-v1 3139.52 ± 110.34 12.34 ±3.11 3041.89 ± 180.77 19.52 ±20.21 3261.87 ± 80.00 12.05 ±6.57 2636.62 ± 181.09 20.69 ±10.23
SafetyHalfCheetahVelocity-v1 2440.97 ± 451.88 9.02 ±9.34 2884.68 ± 77.47 9.04 ±11.83 2946.15 ± 306.35 3.44 ±4.77 2117.84 ± 313.55 27.6 ±8.36
SafetyHopperVelocity-v1 1428.58 ± 199.87 11.12 ±12.66 1391.79 ± 269.07 11.22 ±9.97 961.92 ± 752.87 13.96 ±19.33 1231.52 ± 465.35 16.33 ±11.38
SafetyHumanoidVelocity-v1 6286.51 ± 151.03 19.47 ±7.74 6551.30 ± 58.42 59.56 ±117.37 6624.46 ± 25.9 5.87 ±9.46 6342.47 ± 82.45 126.4 ±193.76
SafetySwimmerVelocity-v1 61.29 ±18.12 22.60 ±1.16 81.18 ±16.33 22.24 ±3.91 64.74 ±17.67 28.02 ±4.09 38.02 ±34.18 18.4 ±12.13
SafetyWalker2dVelocity-v1 3064.43 ± 218.83 3.02 ±1.48 3207.10 ± 7.88 14.98 ±9.27 2982.27 ± 681.55 13.49 ±14.55 2713.57 ± 313.2 20.51 ±14.09
SafetyCarGoal1-v0 18.71 ±2.72 23.10 ±12.57 27.04 ±1.82 26.80 ±5.64 13.27 ±9.26 21.72 ±32.06 -1.10 ±6.851 50.58 ±99.24
SafetyCarButton1-v0 -2.04 ±2.98 43.48 ±31.52 -0.38 ±0.85 37.54 ±31.72 0.33 ±1.96 55.5 ±89.64 -2.06 ±7.2 43.78 ±98.01
SafetyCarGoal2-v0 2.30 ±1.76 22.90 ±16.22 3.65 ±1.09 39.98 ±20.29 1.58 ±2.49 13.82 ±24.62 -0.07 ±1.62 43.86 ±99.58
SafetyCarButton2-v0 -1.35 ±2.41 42.02 ±31.77 -1.68 ±2.55 20.36 ±13.67 0.76 ±2.52 47.86 ±103.27 0.11 ±0.72 85.94 ±122.01
SafetyPointGoal1-v0 15.27 ±4.05 30.56 ±19.15 18.51 ±3.83 22.98 ±8.45 12.96 ±6.95 25.80 ±34.99 1.6 ±3.01 31.1 ±80.03
SafetyPointButton1-v0 3.65 ±4.47 26.30 ±9.22 6.93 ±1.84 31.16 ±20.58 4.60 ±4.73 20.8 ±35.78 -0.34 ±1.53 52.86 ±85.62
SafetyPointGoal2-v0 2.17 ±1.46 33.82 ±21.93 4.64 ±1.43 26.00 ±4.70 1.98 ±3.86 41.20 ±61.03 0.34 ±2.2 65.84 ±195.76
SafetyPointButton2-v0 7.18 ±1.93 45.02 ±25.28 5.43 ±3.44 25.10 ±8.98 0.93 ±3.69 33.72 ±58.75 0.33 ±2.44 28.5 ±49.79
CUP PCPO FOCOPS CPO
Environment Reward Cost Reward Cost Reward Cost Reward Cost
SafetyAntVelocity-v1 3215.79 ± 346.68 18.25 ±17.12 2257.07 ± 47.97 10.44 ±5.22 3184.48 ± 305.59 14.75 ±6.36 3098.54 ± 78.90 14.12 ±3.41
SafetyHalfCheetahVelocity-v1 2850.6 ± 244.65 4.27 ±4.46 1677.93 ± 217.31 19.06 ±15.26 2965.2 ± 290.43 2.37 ±3.5 2786.48 ± 173.45 4.70 ±6.72
SafetyHopperVelocity-v1 1716.08 ± 5.93 7.48 ±5.535 1551.22 ± 85.16 15.46 ±9.83 1437.75 ± 446.87 10.13 ±8.87 1713.71 ± 18.26 13.40 ±5.82
SafetyHumanoidVelocity-v1 6109.94 ± 497.56 24.69 ±20.54 5852.25 ± 78.01 0.24 ±0.48 6489.39 ± 35.1 13.86 ±39.33 6465.34 ± 79.87 0.18 ±0.36
SafetySwimmerVelocity-v1 63.83 ±46.45 21.95 ±11.04 54.42 ±38.65 17.34 ±1.57 53.87 ±17.9 29.75 ±7.33 65.30 ±43.25 18.22 ±8.01
SafetyWalker2dVelocity-v1 2466.95 ± 1114.13 6.63 ±8.25 1802.86 ± 714.04 18.82 ±5.57 3117.05 ± 53.60 8.78 ±12.38 2074.76 ± 962.45 21.90 ±9.41
SafetyCarGoal1-v0 6.14 ±6.97 36.12 ±89.56 21.56 ±2.87 38.42 ±8.36 15.23 ±10.76 31.66 ±93.51 25.52 ±2.65 43.32 ±14.35
SafetyCarButton1-v0 1.49 ±2.84 103.24 ± 123.12 0.36 ±0.85 40.52 ±21.25 0.21 ±2.27 31.78 ±47.03 0.82 ±1.60 37.86 ±27.41
SafetyCarGoal2-v0 1.78 ±4.03 95.4 ±129.64 1.62 ±0.56 48.12 ±31.19 2.09 ±4.33 31.56 ±58.93 3.56 ±0.92 32.66 ±3.31
SafetyCarButton2-v0 1.49 ±2.64 173.68 ± 163.77 0.66 ±0.42 49.72 ±36.50 1.14 ±3.18 46.78 ±57.47 0.17 ±1.19 48.56 ±29.34
SafetyPointGoal1-v0 14.42 ±6.74 19.02 ±20.08 18.57 ±1.71 22.98 ±6.56 14.97 ±9.01 33.72 ±42.24 20.46 ±1.38 28.84 ±7.76
SafetyPointButton1-v0 3.5 ±7.07 39.56 ±54.26 2.66 ±1.83 49.40 ±36.76 5.89 ±7.66 38.24 ±42.96 4.04 ±4.54 40.00 ±4.52
SafetyPointGoal2-v0 1.06 ±2.67 107.3 ±204.26 1.06 ±0.69 51.92 ±47.40 2.21 ±4.15 37.92 ±111.81 2.50 ±1.25 40.84 ±23.31
SafetyPointButton2-v0 2.88 ±3.65 54.24 ±71.07 1.05 ±1.27 41.14 ±12.35 2.43 ±3.33 17.92 ±26.1 5.09 ±1.83 48.92 ±17.79
PPOSaute TRPOSaute PPOSimmerPID TRPOSimmerPID
Environment Reward Cost Reward Cost Reward Cost Reward Cost
SafetyAntVelocity-v1 2978.74 ± 93.65 16.77 ±0.92 2507.65 ± 63.97 8.036 ±0.39 2944.84 ± 60.53 16.20 ±0.66 3018.95 ± 66.44 16.52 ±0.23
SafetyHalfCheetahVelocity-v1 2901.40 ± 25.49 16.20 ± 0.60 2521.80 ± 477.29 7.61 ±0.39 2922.17 ± 24.84 16.14 ±0.14 2737.79 ± 37.53 16.44 ±0.21
SafetyHopperVelocity-v1 1650.91 ± 152.65 17.87 ±1.33 1368.28 ± 576.08 10.38 ±4.38 1699.94 ± 24.25 17.04 ±0.41 1608.41 ± 88.23 16.30 ±0.30
SafetyHumanoidVelocity-v1 6401.00 ± 32.23 17.10 ±2.41 5759.44 ± 75.73 15.84 ±1.42 6401.85 ± 57.62 11.06 ±5.35 6411.32 ± 44.26 13.04 ±2.68
SafetySwimmerVelocity-v1 35.61 ±4.37 3.44 ±1.35 34.72 ±1.37 10.19 ±2.32 77.52 ±40.20 0.98 ±1.91 51.39 ±40.09 0.00 ±0.00
SafetyWalker2dVelocity-v1 2410.89 ± 241.22 18.88 ±2.38 2548.82 ± 891.65 13.21 ±6.09 3187.56 ± 32.66 17.10 ±0.49 3156.99 ± 30.93 17.14 ±0.54
SafetyCarGoal1-v0 7.12 ±5.41 21.68 ±29.11 16.67 ±10.57 23.58 ±26.39 8.45 ±7.16 18.98 ±25.63 15.08 ±13.41 23.22 ±19.80
SafetyCarButton1-v0 -1.72 ±0.89 51.88 ±28.18 -2.03 ±0.40 6.24 ±6.14 -0.57 ±0.63 49.14 ±37.77 -1.24 ±0.47 17.26 ±16.13
SafetyCarGoal2-v0 0.90 ±1.20 19.98 ±10.12 1.76 ±5.20 31.50 ±45.50 1.02 ±1.41 27.32 ±60.12 0.93 ±2.21 26.66 ±60.07
SafetyCarButton2-v0 -1.89 ±1.86 47.33 ±28.90 -2.60 ±0.40 74.57 ±84.95 -1.31 ±0.93 52.33 ±19.96 -0.99 ±0.63 20.40 ±12.77
SafetyPointGoal1-v0 7.06 ±5.85 20.04 ±21.91 16.18 ±9.55 29.94 ±26.68 8.30 ±6.03 25.32 ±31.91 11.64 ±8.46 30.00 ±27.67
SafetyPointButton1-v0 -1.47 ±0.98 22.60 ±13.91 -3.13 ±3.51 9.04 ±3.94 -1.97 ±1.41 12.80 ±7.84 -1.36 ±0.37 2.14 ±1.73
SafetyPointGoal2-v0 0.84 ±2.93 14.06 ±30.21 1.64 ±4.02 19.00 ±34.69 0.56 ±2.52 12.36 ±43.39 1.55 ±4.68 14.90 ±27.82
SafetyPointButton2-v0 -1.38 ±0.11 12.00 ±8.60 -2.56 ±0.67 17.27 ±10.01 -1.70 ±0.29 7.90 ±3.30 -1.66 ±0.99 6.70 ±4.74
CPPOPID TRPOPID PPOEarlyTerminated TRPOEarlyTerminated
Environment Reward Cost Reward Cost Reward Cost Reward Cost
SafetyAntVelocity-v1 3213.36 ± 146.78 14.30 ±7.39 3052.94 ± 139.67 15.22 ±3.68 2801.53 ± 19.66 0.23 ±0.09 3052.63 ± 58.41 0.40 ±0.23
SafetyHalfCheetahVelocity-v1 2837.89 ± 398.52 8.06 ±9.62 2796.75 ± 190.84 11.16 ±9.80 2447.25 ± 346.84 3.47 ±4.90 2555.70 ± 368.17 0.06 ±0.08
SafetyHopperVelocity-v1 1713.29 ± 10.21 8.96 ±4.28 1178.59 ± 646.71 18.76 ±8.93 1643.39 ± 2.58 0.77 ±0.26 1646.47 ± 49.95 0.42 ±0.84
SafetyHumanoidVelocity-v1 6579.26 ± 55.70 3.76 ±3.61 6407.95 ± 254.06 7.38 ±11.34 6321.45 ± 35.73 0.00 ±0.00 6332.14 ± 89.86 0.00 ±0.00
SafetySwimmerVelocity-v1 91.05 ±62.68 19.12 ±8.33 69.75 ±46.52 20.48 ±9.13 33.02 ±7.26 24.23 ±0.54 39.24 ±5.01 23.20 ±0.48
SafetyWalker2dVelocity-v1 2183.43 ± 1300.69 14.12 ±10.28 2707.75 ± 980.56 9.60 ±8.94 2195.57 ± 1046.29 7.63 ±10.44 2079.64 ± 1028.73 13.74 ±15.94
SafetyCarGoal1-v0 10.60 ±2.51 30.66 ±7.53 25.49 ±1.31 28.92 ±7.66 17.92 ±1.54 21.60 ±0.83 22.09 ±3.07 17.97 ±1.35
SafetyCarButton1-v0 -1.36 ±0.68 14.62 ±9.40 -0.31 ±0.49 15.24 ±17.01 4.47 ±1.12 25.00 ±0.00 4.34 ±0.72 25.00 ±0.00
SafetyCarGoal2-v0 0.13 ±1.11 23.50 ±1.22 1.77 ±1.20 17.43 ±12.13 6.59 ±0.58 25.00 ±0.00 7.12 ±4.06 23.37 ±1.35
SafetyCarButton2-v0 -1.59 ±0.70 39.97 ±26.91 -2.95 ±4.03 27.90 ±6.37 4.86 ±1.57 25.00 ±0.00 5.07 ±1.24 25.00 ±0.00
SafetyPointGoal1-v0 8.43 ±3.43 25.74 ±7.83 19.24 ±3.94 21.38 ±6.96 16.03 ±8.60 19.17 ±9.42 16.31 ±6.99 22.10 ±6.13
SafetyPointButton1-v0 1.18 ±1.02 29.42 ±12.10 6.40 ±1.43 27.90 ±13.27 7.48 ±8.47 24.27 ±3.95 9.52 ±7.86 25.00 ±0.00
SafetyPointGoal2-v0 -0.56 ±0.06 48.43 ±40.55 1.67 ±1.43 23.50 ±11.17 6.09 ±5.03 25.00 ±0.00 8.62 ±7.13 25.00 ±0.00
SafetyPointButton2-v0 0.42 ±0.63 28.87 ±11.27 1.00 ±1.00 30.00 ±9.50 6.94 ±4.47 25.00 ±0.00 8.35 ±10.44 25.00 ±0.00

Table 2: The performance of OmniSafe on-policy algorithms, encompassing both reward and cost, was assessed within the Safety-Gymnasium environments. It is crucial to highlight that all on-policy algorithms underwent evaluation following 1e7 training steps.

First Order Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 1.1: Training curves in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 1.2: Training curves in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 1.3: Training curves in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps

Second Order Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 2.1: Training curves of second order algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 2.2: Training curves of second order algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 2.3: Training curves of second order algorithms in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps

Saute Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 3.1: Training curves of Saute MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 3.2: Training curves of Saute MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarCircle1-v0

SafetyCarCircle2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointCircle1-v0

SafetyPointCircle2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 3.3: Training curves of Saute MDP algorithms in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps

Simmer Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 4.1: Training curves of Simmer MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 4.2: Training curves of Simmer MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 4.3: Training curves of Simmer MDP algorithms in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps

PID-Lagrangian Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 5.1: Training curves of PID-Lagrangian algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 5.2: Training curves of PID-Lagrangian algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 5.3: Training curves of PID-Lagrangian algorithms in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps.

Early Terminated MDP Algorithms

1e6 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 6.1: Training curves of early terminated MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e6 steps.

1e7 Steps Velocity Results

SafetyAntVelocity-v1

SafetyHalfCheetahVelocity-v1

SafetyHopperVelocity-v1

SafetyHumanoidVelocity-v1

SafetyWalker2dVelocity-v1

SafetySwimmerVelocity-v1

Figure 6.2: Training curves of early terminated MDP algorithms in Safety-Gymnasium MuJoCo Velocity environments within 1e7 steps.

1e7 Steps Navigation Results

SafetyCarButton1-v0

SafetyCarButton2-v0

SafetyCarGoal1-v0

SafetyCarGoal2-v0

SafetyPointButton1-v0

SafetyPointButton2-v0

SafetyPointGoal1-v0

SafetyPointGoal2-v0

Figure 6.3: Training curves of early terminated MDP algorithms in Safety-Gymnasium MuJoCo Navigation environments within 1e7 steps.