マルコフ決定過程（MDP）
マルコフ決定過程（MDP) is a mathematical framework used to describe a decision-making problem where outcomes depend on both the actions taken by a decision maker and stochastic (random) events. MDPs are widely used in various fields, including 人工知能, robotics, economics, and 運用研究, to model situations where an agent must make a series of decisions over time.
MDPは、タプルによって定義されます （S, A, P, R, γ）, where:
- S is a finite set of states that represent all possible situations the agent can be in.
- A is a finite set of actions available to the agent that can change its state.
- P is the state transition probability function, which defines the probability of transitioning from one state to another given a specific action.
- R is the 報酬関数 that assigns a numerical reward to each state, guiding the agent toward desirable outcomes.
- γ is the discount factor, a value between 0 and 1 that determines the importance of future rewards compared to immediate rewards.
In an MDP, the decision maker (or agent) aims to find a policy, which is a strategy that defines the best action to take in each state to maximize cumulative rewards over time. The process is termed ‘Markov’ because it satisfies the 確率的に遷移することを特徴としています。このモデルは, meaning that the future state depends only on the current state and action, not on the sequence of events that preceded it.
MDPは、の分野で基礎的な概念です 強化学習, where agents learn optimal behaviors through trial and error interactions with their environment, making them crucial for developing intelligent systems.