Processus de Décision de Markov (MDP)
Un processus de décision markovien (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 intelligence artificielle, robotics, economics, and la recherche opérationnelle, to model situations where an agent must make a series of decisions over time.
Les MDP sont définis par un tuple (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 fonction de récompense 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 propriété de Markov, meaning that the future state depends only on the current state and action, not on the sequence of events that preceded it.
Les MDP sont fondamentaux dans le domaine de apprentissage par renforcement, where agents learn optimal behaviors through trial and error interactions with their environment, making them crucial for developing intelligent systems.