Other graphs can be found under `/examples/mujuco/benchmark/`
#### Hints
In offpolicy algorithms(DDPG, TD3, SAC), the shared hyperparameters are almost the same<sup>[[8]](#footnote8)</sup>, and most hyperparameters are consistent with those used for benchmark in SpinningUp's implementations<sup>[[9]](#footnote9)</sup>.
By comparison to both classic literature and open source implementations (e.g., SpinningUp)<sup>[[1]](#footnote1)</sup><sup>[[2]](#footnote2)</sup>, Tianshou's implementations of DDPG, TD3, and SAC are roughly at-parity with or better than the best reported results for these algorithms.
### DDPG
| Environment | Tianshou | [SpinningUp (PyTorch)](https://spinningup.openai.com/en/latest/spinningup/bench.html) | [TD3 paper (DDPG)](https://arxiv.org/abs/1802.09477) | [TD3 paper (OurDDPG)](https://arxiv.org/abs/1802.09477) |
<aname="footnote1">[1]</a> Supported environments include HalfCheetah-v3, Hopper-v3, Swimmer-v3, Walker2d-v3, Ant-v3, Humanoid-v3, Reacher-v2, InvertedPendulum-v2 and InvertedDoublePendulum-v2. Pusher, Thrower, Striker and HumanoidStandup are not supported because they are not commonly seen in literatures.
<aname="footnote2">[2]</a> Pretrained agents, detailed graphs (single agent, single game) and log details can all be found [here](https://cloud.tsinghua.edu.cn/d/356e0f5d1e66426b9828/).
<aname="footnote3">[3]</a> We used the latest version of all mujoco environments in gym (0.17.3 with mujoco==2.0.2.13), but it's not often the case with other benchmarks. Please check for details yourself in the original paper. (Different version's outcomes are usually similar, though)
<aname="footnote4">[4]</a> We didn't compare offpolicy algorithms to OpenAI baselines [benchmark](https://github.com/openai/baselines/blob/master/benchmarks_mujoco1M.htm), because for now it seems that they haven't provided benchmark for offpolicy algorithms, but in [SpinningUp docs](https://spinningup.openai.com/en/latest/spinningup/bench.html) they stated that "SpinningUp implementations of DDPG, TD3, and SAC are roughly at-parity with the best-reported results for these algorithms", so we think lack of comparisons with OpenAI baselines is okay.
<aname="footnote5">[5]</a> ~ means the number is approximated from the graph because accurate numbers is not provided in the paper. N means graphs not provided.
<aname="footnote6">[6]</a> Reward metric: The meaning of the table value is the max average return over 10 trails (different seeds) ± a single standard deviation over trails. Each trial is averaged on another 10 test seeds. Only the first 1M steps data will be considered. The shaded region on the graph also represents a single standard deviation. It is the same as [TD3 evaluation method](https://github.com/sfujim/TD3/issues/34).
<aname="footnote7">[7]</a> In TD3 paper, shaded region represents only half of standard deviation.
<aname="footnote8">[8]</a> SAC's start-timesteps is set to 10000 by default while it is 25000 is DDPG/TD3. TD3's learning rate is set to 3e-4 while it is 1e-3 for DDPG/SAC. However, there is NO enough evidence to support our choice of such hyperparameters (we simply choose them because of SpinningUp) and you can try playing with those hyperparameters to see if you can improve performance. Do tell us if you can!
<aname="footnote9">[9]</a> We use batchsize of 256 in DDPG/TD3/SAC while SpinningUp use 100. Minor difference also lies with `start-timesteps`, data loop method `step_per_collect`, method to deal with/bootstrap truncated steps because of timelimit and unfinished/collecting episodes (contribute to performance improvement), etc.
