Partially Observable Markov Decision Process (POMDP)
A Partially Observable Markov Decision Process (POMDP) is an extension of the Markov Decision Process (MDP) used in scenarios where the agent cannot fully observe the current state of the environment. In a POMDP, the decision-making process is complicated by the fact that the agent must infer the state of the system indirectly through observations that provide partial information.
Each action taken by the agent not only leads to a potential change in the environment's state but also results in a new observation that the agent uses to update its belief about the state of the world.
This belief is represented as a probability distribution over all possible states. POMDPs are characterized by a tuple containing states, actions, observations, transition model, observation model, reward function, and a discount factor. They are widely used in AI and ML for planning and decision-making problems where uncertainty and incomplete information play significant roles.
An application of POMDPs is in robotics, specifically for autonomous navigation in unknown or dynamic environments. Consider a robot exploring a new building; the exact location and layout of the building (the state) are not directly observable due to sensor limitations or obstacles blocking the line of sight.
The robot uses sensors to gather observations about its surroundings, like the presence of walls or doors, and combines these with a map it builds over time to make decisions about where to move next.
The robot's decision-making process, modeled as a POMDP, involves choosing actions (like turning or moving forward) that maximize its expected utility based on its current belief about the world, updating this belief as it gathers more observations. This allows the robot to effectively navigate and perform tasks despite the uncertainty of its environment.