A 部分的 観測可能マルコフ決定過程 (POMDP) is a framework used in 人工知能 for modeling decision-making problems where the agent does not have complete information about the current state of the environment. Unlike a standard Markov Decision Process (MDP) where the state is fully observable, POMDPs incorporate uncertainty in the state representation.
POMDPでは、エージェントは信念状態に基づいて行動を決定しなければなりません。信念状態は probability distribution over all possible states, reflecting the agent’s knowledge about the environment. This belief state evolves over time as the agent takes actions and receives observations, which provide partial information about the true state.
POMDPは、次のタプルによって正式に定義されます：
- S: A set of states
- A: A set of actions
- T: A state transition function that defines the probability of moving from one state to another given an action
- R: A 報酬関数 各状態-行動ペアに数値の報酬を割り当てる
- O: An 観測関数 that defines the probability of receiving an observation given a state and action
- γ: A discount factor that determines the importance of future rewards
POMDPs are widely used in various applications, such as robotics, automated planning, and 資源管理, where decision-making must happen under uncertainty. The complexity of solving POMDPs lies in the need to maintain and update the belief state, making them computationally challenging. Various algorithms and techniques, such as value iteration and policy search methods, have been developed to approximate solutions to POMDPs.