Enter the immediate reward, discount factor, and the value of the next state into the calculator to determine the value function using the Bellman equation. This calculator helps in solving reinforcement learning problems.

Bellman Equation Formula

The Bellman equation is used to find the value function under a certain policy in reinforcement learning. The formula is given by:

V*(s) = R(s) + γ * V(s')

Variables:

  • V*(s) is the value function of the current state (s)
  • R(s) is the immediate reward received from the current state (s)
  • γ is the discount factor, which represents the difference in importance between future rewards and present rewards
  • V(s') is the value of the next state (s')

To calculate the value function using the Bellman equation, add the immediate reward to the product of the discount factor and the value of the next state.

What is the Bellman Equation?

The Bellman equation is a recursive equation that is central to dynamic programming and reinforcement learning. It expresses the value of a decision problem at a certain point in time in terms of the payoff from some initial choices and the value of the remaining decision problem that results from those initial choices. This equation is fundamental in finding the optimal policy in a Markov Decision Process (MDP).

How to Calculate Value Function using Bellman Equation?

The following steps outline how to calculate the value function using the Bellman Equation.

  1. First, determine the immediate reward (R) from the current state.
  2. Next, determine the discount factor (γ), which should be between 0 and 1.
  3. Then, determine the value of the next state (V).
  4. Use the Bellman equation formula: V*(s) = R(s) + γ * V(s').
  5. Finally, calculate the value function (V*) for the current state.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Immediate reward (R) = 5

Discount factor (γ) = 0.9

Value of the next state (V) = 10