Question

Consider an MDP with 3 states, A, B and C; and 2 actions Clockwise and Counterclockwise. We do not know the transition function or the reward function for the MDP, but instead, we are given with samples of what an agent actually experiences when it interacts with the environment (although, we do know that we do not remain in the same state after taking an action). In this problem, instead of first estimating the transition and reward functions, we will directly estimate the Q function using Q-learning.

Answer 1

In this problem, we will directly estimate the Q function using Q-learning for an MDP with 3 states (A, B, and C) and 2 actions (Clockwise and Counterclockwise).

Step-by-step explanation:

Q-learning is a model-free reinforcement learning algorithm that directly estimates the quality of actions, represented by the Q function. In this scenario, we have 3 states (A, B, and C) and 2 actions (Clockwise and Counterclockwise). Rather than first estimating the transition and reward functions, we directly approximate the Q function based on samples of agent experiences. The Q function represents the expected cumulative reward of taking an action in a particular state and following the optimal policy thereafter.

The Q-learning algorithm updates Q values iteratively using the formula
`\(Q(s, a) \leftarrow Q(s, a) + \alpha \cdot [r + \gamma \cdot \max_a Q(s', a) - Q(s, a)]\)` , where s is the current state, a is the taken action, \(r\) is the immediate reward, s is the next state,
`\(\alpha\)` is the learning rate, and \(\gamma\) is the discount factor. Through repeated interactions with the environment, the Q function converges to optimal values.

By directly estimating the Q function, we can learn the optimal action-value mapping without explicitly modeling the transition and reward functions. This approach is particularly useful when the transition and reward functions are complex or unknown, allowing us to focus on learning the optimal policy through exploration and exploitation of agent experiences.

Answer 2

We are dealing with Q-learning to estimate the Q-function of an MDP without knowing the transition and reward functions.

Step-by-step explanation:

In this problem, the subject we are dealing with is Reinforcement Learning in the field of Artificial Intelligence. Specifically, we are using a technique called Q-learning to estimate the Q-function of an MDP (Markov Decision Process) without knowing the transition and reward functions.

Q-learning is a model-free algorithm, meaning that it learns directly from the samples or experiences gathered by the agent. The Q-function represents the expected future rewards for each action in a given state. The algorithm uses a temporal difference update rule to iteratively update the Q-values based on the observed rewards and next states.

In this case, we have an MDP with three states and two actions. The agent takes actions, observes rewards, and transitions to new states. By applying Q-learning, we can estimate the Q-values for each state-action pair and use them to make informed decisions in future interactions with the environment.