Tillståndsvärdet

Tillståndsvärdet, often translated as "state value" or "value function," is a fundamental concept in reinforcement learning and control theory. It represents the expected cumulative future reward that an agent can achieve starting from a particular state and following a specific policy. The policy dictates the agent's actions in each state, and the tillståndsvärdet quantifies the long-term desirability of being in that state, considering the future consequences of its actions.

Mathematically, the tillståndsvärdet for a state 's' under a policy 'π' is denoted as Vπ(s). It is typically defined recursively. The value of a state is the immediate reward received in that state, plus the discounted expected value of the next state, where the discount factor (gamma) balances immediate versus future rewards. The discount factor is a value between 0 and 1. A higher gamma means the agent values future rewards more.

The primary goal in many reinforcement learning problems is to find an optimal policy (π*) that maximizes the tillståndsvärdet for all states. This optimal policy leads to the highest possible expected cumulative reward. Algorithms like value iteration and policy iteration are used to compute these tillståndsvärden and derive the optimal policy. Understanding tillståndsvärdet is crucial for agents to learn effective strategies and make optimal decisions in dynamic environments.