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Reinforcement Learning · Intermediate · question 33 of 100

Can you provide an example of a partially observable Markov decision process (POMDP) and how it differs from an MDP?

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Let’s consider a simple example: a robot navigating a maze. In the MDP version of the problem, the robot can perfectly observe its location within the maze at every time step, and can take actions to move to adjacent cells until it reaches the goal. The MDP formulation assumes the robot has full knowledge of the state and can always accurately perceive it.

However, in a POMDP formulation, the robot’s location is not directly observable. Instead, the robot receives sensory information that is noisy and partial, such as weak signals from a GPS or proximity sensors that detect nearby walls. In this case, the robot cannot directly perceive its location, and must infer it based on its observations and previous actions.

To illustrate how the POMDP formulation differs in practice, let’s take an example of a robot that is attempting to navigate a maze using only a limited set of sensors. The robot starts at the bottom left corner of the maze and must reach the goal at the top right corner.

At each time step, the robot receives a noisy sensor reading that indicates whether it is close to a wall or not. The sensor output is probabilistic and can be misleading due to measurement noise. The robot can take four actions: move up, down, left, or right, but its motion is also stochastic - each action has some probability of failure and the robot may move in a different direction than it intended.

In this situation, the robot is faced with partial observability since it cannot directly observe its current location, but must estimate it based on the noisy sensor readings and the history of its past actions. The robot must use algorithms like the Kalman Filter, Particle Filter, or other state estimation techniques to maintain its belief about its location in the maze.

In summary, a POMDP is a more complex version of an MDP where the true state is not fully observable and must be inferred from probabilistic, partial, or noisy observations. The robot’s actions need to be based on its beliefs about the state rather than perfect knowledge about the state.

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