# What is meant by a multi-dimensional continuous action space?

In the context of Reinforcement Learning, what does it mean to have a multi-dimensional continuous action space?

I came across the following in the COBRA Paper

A method for learning a distribution over a multi-dimensional continuous action space. This learned distribution can be sampled efficiently.

and

During the initial exploration phase it explores its environment, in which it can move objects freely with a continuous action space but is not rewarded for its actions.

So, what do the multi-dimensionality and the continuity of the action space refer to? It'd be great if someone could provide an explanation with examples!

• It means $a \in R^n$, where $a$ is action May 1 '20 at 13:59
• Ohh, okay! I don't see why researchers resort to complicated terms in papers. May 1 '20 at 14:00
• I wouldn't know how to write it simpler. It is just the translation of $a \in \mathbb{R}^n$ into text. Continuous values means (most likely) $\mathbb{R}$ and multidimensional $^n$. If you understand the mathematical expression you are most likely familiar with math and if that is the case then you most likely also know about these two terms. Maybe action space is a term that is quite unfamiliar for people who are learning about reinforcement learning? That just means the set of all possible actions.
– alfa
May 1 '20 at 14:33

Let me rephrase it a little - it's a multidimensional continuous space of actions. So, you assign each action some vector from $$R^{n}$$. For intuition -- imagine you have a robot arm with four joints. For every joint you could applied a rotation force from [-1, 1] and thus you get a 4-D vector with float numbers for each possible action.