# Which RL algorithm would be suitable for this multi-dimensional and continuous action space?

Is there an RL approach/algorithm that would be suited for the following kind of problem?

• There is a continuous action space with an action value $$A_{a,t}$$ for each action dimension $$a$$.
• The objective function is a non-linear function of the satisfaction factors $$S_{s}$$ for each satisfaction dimension $$s$$ and some other random & independent factors. This objective function can be known to the agent.
• Each satisfaction factor depends on an independent variable $$\Delta^S_{s,t}$$ and the effect $$\delta^S_{a,s,t}$$ of each action: $$S_{s,t}=\Delta^S_{s,t} +\sum_a A_{a,t} * \delta^S_{a,s,t}$$.
• Each action can further have an effect $$\delta^R_{a,r,t}$$ on the inventory factors $$I_{r,t}$$ for each resource dimension $$r$$, with inventories being kept between time-steps and a factor $$\Delta^R_{r,t}$$ that is added or removed from the inventory at each step independent of the actions: $$I_{r,t+1}=I_{r,t}+\Delta^R_{r,t} + \sum_a A_{a,t} * \delta^R_{a,r,t}$$
• The agent is constrained by each of these resources (i.e. the inventory has to remain positive).
• The agent should be able to deal both with $$\delta$$ and $$\Delta$$ factors that are visible (states) and invisible (have to be learned).
• A trained agent should be able to know how to adapt to changes of the $$\delta$$ and $$\Delta$$ factors, as well as the introduction or removal of activity dimensions.

EDIT: I have adapted the problem description after some feedback.