Kaggle is limited to only supervised learning problems. There used to be www.rl-competition.org but they've stopped.
Is there anything else I can do other than locally trying out different algorithms for various RL problems?
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Kaggle recently started adding 'Simulation' competitions, which are well-suited for reinforcement learning.
The first competition that's live (no prizes) is ConnectX, like a generalised Connect Four.
The first competition with prize money is likely to be the next iteration of TwoSigma's Halite. There's a page for it here, but it hasn't been launched yet: https://www.kaggle.com/c/halite/overview
I created a site that lists ongoing machine learning competitions including Reinforcement Learning competitions - you can also sign up to the email list in case you want to get emails (roughly monthly) when new competitions launch. As of right now (May 2020) there are a few live RL competitions on there - the KDD cup, and AWS DeepRacer.
AICrowd has numerous challenges in the domain, with some very interesting challenges running currently. Here is a short list:
Hope this helps!
OpenAI has leaderboards for their gym-environments, if you want to compete with other people on runtime and efficiency.