All the reinforcement learning algorithms I've read about are usually applied to a single agent that has a fixed number of actions. Are there any reinforcement learning algorithms for making a decision while taking into account a variable number of actions? For example, how would you apply a RL algorithm in a computer game where a player controls N soldiers, and each soldier has a random number of actions based its condition? You can't formulate fixed number of actions for a global decision maker (i.e. "the general") because the available actions are continually changing as soldiers are created and killed. And you can't formulate a fixed number of actions at the soldier level, since the soldier's actions are conditional based on its immediate environment. If a soldier sees no opponents, then it might only be able to walk, whereas if it sees 10 opponents, then it has 10 new possible actions, attacking 1 of the 10 opponents.
What you describe is nothing unusual. Reinforcement learning is a way of finding the value function of a Markov Decision Process. In an MDP, every state has its own set of actions. To proceed with reinforcement learning application, you have to clearly define what the states, actions, and rewards are in your problem.
If you have a number of actions for each soldier that are available or not depending on some conditions, then you can still model this as selection from a fixed set of actions. For example:
- Create a "utility value" for each of the full set of actions for each soldier
- Choose the highest valued action, ignoring those actions that are not available at a given time
If you have multiple possible targets, then the same principle applies, except this time you model your utility function to take the target designation as an additional parameter, and run the evaluation function multiple times (one for each target). You pick the target that has the highest "attack utility".