A Partially Observable Markov Decision Process (POMDP) is a framework used in artificial intelligence 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.
In a POMDP, the agent must decide on actions based on a belief state, which is a 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.
A POMDP is formally defined by a tuple:
- 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 reward function that assigns a numerical reward for each state-action pair
- O: An observation function 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 resource management, 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.