Question

Consider a tiny MDP with states S={0,1,2,3} and actions A={b,c}. Given the reward and transition functions below with an infinite horizon and a discount factor of 0.9, compute the value function for the first three iterations using value iteration.

Answer 1

Value iteration is an algorithm used to solve Markov Decision Processes (MDPs) by iteratively calculating the value function.

Step-by-step explanation:

Value iteration is an algorithm used to solve Markov Decision Processes (MDPs) by iteratively calculating the value function. In this case, the MDP has states S={0,1,2,3} and actions A={b,c}. The reward and transition functions are not given in the question, so I cannot provide the specific values. However, I can explain how value iteration works.

Value iteration starts by initializing the value function V(s) for each state s to 0. Then, it iteratively updates the values based on the Bellman equation: V(s) = maxa∈A {R(s,a) + γΣs' T(s,a,s')V(s')}.

Using this equation, you can compute the value function for the first three iterations, where each iteration involves updating the values for all states based on the previous iteration's values.