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What are the state-of-the-art results in OpenAI's gym environments? Is there a link to a paper/article that describes them and how these SOTA results were calculated?

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There is the leaderboard page at the gym GitHub repository that contains links to specific implementations that "solve" the different gym environments, where "to solve" means "to reach a certain level of performance", which, given a fixed reward function, is typically measured as the average (episodic) return/reward. For example, in the case of the CartPole environment, you solve it when you get an average reward of $195.0$ over $100$ consecutive trials.

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