Understanding Reinforcement Learning Formalization

Reinforcement learning is a type of machine learning where an agent learns to make decisions by interacting with an environment. The agent performs actions and receives feedback, typically in the form of rewards or penalties. The goal of the agent is to learn a policy, which is a mapping from states to actions, that maximizes the cumulative reward over time.

To study and analyze reinforcement learning problems mathematically, they are often formalized using a framework. The most common mathematical framework used for this purpose is the Markov Decision Process (MDP).

Markov Decision Processes (MDPs) in Reinforcement Learning

A Markov Decision Process provides a mathematical model for sequential decision making. An MDP is formally defined by the following components:

• States (S): A set of possible states the environment can be in.
• Actions (A): A set of possible actions the agent can take.
• Transition Probabilities (P): A function P(s' | s, a) that gives the probability of transitioning to state s' from state s when taking action a. The "Markov" property implies that the next state depends only on the current state and action, not on the entire history.
• Reward Function (R): A function R(s, a, s') that gives the reward received after taking action a in state s and transitioning to state s'.
• Discount Factor ($\gamma$): A value between 0 and 1 that discounts future rewards.

In the context of reinforcement learning, the agent initially knows the set of possible states it can be in and the set of possible actions it can take. The agent typically does not initially know the transition probabilities between states or the exact rewards it will receive for specific actions and transitions. Learning these aspects of the environment is part of the reinforcement learning process.

Therefore, reinforcement learning is formalized in terms of Markov decision processes in which the agent initially only knows the set of possible states and the set of possible actions.

Analyzing the Options

Let's look at the given options:

1. Markov decision processes, objects: This option suggests formalization in MDPs but uses "objects" instead of "states". While environments might contain objects, the fundamental element describing the environment's configuration in an MDP is a "state". So, this is incorrect.
2. Hidden states, objects: "Hidden states" are relevant in Partially Observable Markov Decision Processes (POMDPs), which are an extension of MDPs, not the standard formalization mentioned. Also, "objects" is incorrect as explained above. Thus, this option is incorrect.
3. Markov decision processes, states: This option correctly identifies Markov decision processes as the formalization framework and states as one of the fundamental sets initially known by the agent, along with actions. This aligns with the definition of MDPs and the setup of typical reinforcement learning problems where the agent explores to learn dynamics and rewards.
4. Objects, states: This option incorrectly suggests "Objects" as the formalization framework instead of Markov decision processes. While "states" is correct as something the agent initially knows, the framework is incorrect. So, this is incorrect.

Based on the analysis, the correct option is the one that identifies Markov decision processes as the formalization framework and states as one of the sets initially known by the agent, along with actions.

Revision Table: Core RL and MDP Concepts

Additional Information: RL Formalization Beyond MDPs

While Markov Decision Processes are the standard formalization for many reinforcement learning problems, especially those with a fully observable environment (where the agent knows the exact state), other formalisms exist for more complex scenarios:

• Partially Observable Markov Decision Processes (POMDPs): Used when the agent does not have complete knowledge of the environment's state. Instead of knowing the state, the agent receives an observation which is probabilistically related to the true state. The agent maintains a belief distribution over the possible states.
• Dec-MDPs and MMDPs: Frameworks for modeling problems with multiple agents, considering coordination and communication aspects.

However, for the fundamental understanding and formalization of reinforcement learning, the Markov Decision Process is the most widely used and foundational model, and in this standard model, the agent is assumed to initially know the sets of possible states and actions.