Model-based value iteration and policy iteration pseudocode

Note that the symbols used in the pseudocode below have the following meanings:

• MDP: Markov Decision Process;
• V(s): Value function, the avg reture of one state;
• π(s): Policy, in the sense that for a given state s, π(s)represents the action that the agent will take in that state according to the policy,  usually can be divided into a random manner or a deterministic manner;
• R(s,a): Immediate reward when taking action a in state s;
• P(s'|s,a): Transition probability from state s to state s' under an action a;
• γ: Discount factor for future reward.

Value iteration：

function ValueIteration(MDP):
    // MDP is a Markov Decision Process
    V(s) = 0 for all states s  // Initialization

    repeat until convergence:
        delta = 0
        for each state s:
            v = V(s)
            V(s) = max over all actions a of [ R(s, a) + γ * Σ P(s' | s, a) * V(s') ]
            delta = max(delta, |v - V(s)|)

    return V  // Optimal value function

function ExtractOptimalPolicy(MDP, V):
    // MDP is a Markov Decision Process, V is the optimal value function
    for each state s:
        π(s) = argmax over all actions a of [ R(s, a) + γ * Σ P(s' | s, a) * V(s') ]

    return π  // Optimal policy

Policy iteration:

function PolicyIteration(MDP):
    // MDP is a Markov Decision Process
    Initialize a policy π arbitrarily

    repeat until policy converges:
        // Policy Evaluation
        V = EvaluatePolicy(MDP, π)

        // Policy Improvement
        π' = GreedyPolicyImprovement(MDP, V)

        if π' = π:
            break  // Policy has converged

        π = π'

    return π  // Optimal policy

function EvaluatePolicy(MDP, π):
    // MDP is a Markov Decision Process, π is a policy
    V(s) = 0 for all states s  // Initialization

    repeat until convergence:
        delta = 0
        for each state s:
            v = V(s)
            V(s) = Σ P(s' | s, π(s)) * [ R(s, π(s)) + γ * V(s') ]
            delta = max(delta, |v - V(s)|)

    return V  // Value function under the given policy

function GreedyPolicyImprovement(MDP, V):
    // MDP is a Markov Decision Process, V is a value function
    for each state s:
        π(s) = argmax over all actions a of [ R(s, a) + γ * Σ P(s' | s, a) * V(s') ]

    return π  // Improved policy

given the shiyu Zhao's course [1] ppt :

References:

[1] https://www.bilibili.com/video/BV1sd4y167NS

[2] https://chat.openai.com/