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Printing action_space for Pong-v0 gives Discrete(6) as output, i.e. $0, 1, 2, 3, 4, 5$ are actions defined in the environment as per the documentation. However, the game needs only 2 controls. Why do we have this discrepancy? Further, is that necessary to identify which number from 0 to 5 corresponds to which action in a gym environment?

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You can try the actions yourselves, but if you want another reference, check out the documentation for ALE at GitHub.

In particular, 0 means no action, 1 means fire, which is why they don't have an effect on the racket.

Here's a better way:

env.unwrapped.get_action_meanings()
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You can try to figure out what exactly does an action do using such script:

action = 0  # modify this!
o = env.reset()
for i in xrange(5): # repeat one action for five times
    o = env.step(action)[0]
IPython.display.display(
    Image.fromarray(
        o[:,140:142]  # extract your bat
    ).resize((300, 300))  # bigger image, easy for visualization
)

action 0 and 1 seems useless, as nothing happens to the racket.

action 2 & 4 makes the racket go up, and action 3 & 5 makes the racket go down.

The interesting part is, when I run the script above for the same action(from 2 to 5) two times, I have different results. Sometimes the racket reaches the top(bottom) border, and sometimes it doesn't. I think there might be some randomness on the speed of the racket, so it might be hard to measure which type of UP(2 or 4) is faster.

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There seems to be no difference between 2 & 4 and 3 & 5. The inconsistency mentioned by Icyblade is due to the mechanics of the Pong environment.

"Each action is repeatedly performed for a duration of k frames, where k is uniformly sampled from {2,3,4}"

So the action is just repeated a different number of times due to randomness

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