In essence, Average Reward and Test Score are two different things. The former represents a fixed test result indicator. The latter is a score for the test result. The scoring logic for different tasks and users may be different. For example, some consider the standard deviation and some do not.
Currently, tianshou uses best_reawrd for both average reward and test score. It is difficult for users to implement custom scoring logic. So I suggest that best_reward be used only for average reward, and best_score be added for test score. In this way, best_reward and best_score are two different things. If it is called best_custom_score, people will think that there is a system default score field, so I think it is better not to add 'custom'.

Update:

• Added explanation for InfoStats.best_score.
• Use lambda function when compute_score_fn is None to avoid multiple if-else

@anyongjin the "terminating" part was not actually implemented. If it is the score we seek to maximize, then the early stopping criterion (stop_fn) should also use scores instead of mean returns, don't you agree?
I noticed this, because I am refactoring and improving the library for v2. I will change this in the v2 branch.

Yes, if best_score is used to determine whether it is the optimal model, then best_score should also be passed when calling stop_fn instead of the previously default average return. I forgot to modify this part earlier, and it should be corrected in v2.