# What is a Partially Observable Markov Decision Process (POMDP)?

by Stephen M. Walker II, Co-Founder / CEO

## What is a POMDP?

A Partially Observable Markov Decision Process (POMDP) is a mathematical framework used to model sequential decision-making processes under uncertainty. It is a generalization of a Markov Decision Process (MDP), where the agent cannot directly observe the underlying state of the system. Instead, it must maintain a sensor model, which is the probability distribution of different observations given the current state.

A POMDP can be formally described as a 7-tuple `(P = (S, A, T, R, Ω , O, γ))`:

• S is a set of partially observable states.
• A is a set of actions.
• T is a set of conditional transition probabilities `T(s' | s,a)` for the state transition.
• R is a reward function.
• Ω is a set of observations.
• O is a set of conditional observation probabilities `O(o | s',a)` for the observation.
• `γ` is a discount factor.

The agent's understanding of the current state is represented as a belief state, which is a probability distribution over all states. The solution of the POMDP is a policy prescribing which action to take in each belief state.

POMDPs are used in a variety of real-world sequential decision processes, including robot navigation problems, machine maintenance, and planning under uncertainty in general. They are also used in various domains like AI, operations research, economics, and robotics.

## What are some common applications of POMDPs?

Partially Observable Markov Decision Processes (POMDPs) are a powerful tool for modeling and solving problems that involve decision-making under uncertainty. They have been applied in a variety of domains, including:

1. Robotics — POMDPs are used in robot navigation and path planning, especially in uncertain and dynamic environments. They help robots to make optimal decisions based on their current belief about the state of the world, which is particularly useful when the robot's sensors cannot fully observe the environment.

2. Healthcare — POMDPs have been used in managing patients with specific conditions, such as ischemic heart disease. They help in making sequential decisions based on the observations of the patient's state.

3. Conservation — POMDPs have been applied in the conservation of endangered species, such as the Sumatran tigers. They help in making decisions about conservation strategies under uncertainty.

4. Maintenance and Inspection — POMDPs are used in optimizing inspection and maintenance strategies for systems like traction power supply equipment. They help in deciding when and what kind of maintenance should be performed based on the observations of the system's state.

5. Artificial Intelligence (AI) — POMDPs are used in various AI applications that require planning under uncertainty, such as natural language processing and computer vision.

6. Manipulation Planning — POMDPs have been used in manipulation planning under object composition uncertainty. They help in making decisions about how to manipulate unknown objects in a cluttered environment.

7. Long Time Horizon Tasks — POMDPs have been used in robotic tasks with long time horizons. They help in making decisions about motion planning under uncertainty over a long period.

## What are some recent advancements in POMDP research?

Recent advancements in Partially Observable Markov Decision Processes (POMDP) research have centered around the application of Deep Reinforcement Learning (DRL) to address POMDP problems across various domains such as games, robotics, natural language processing, transportation, industries, communications, and networking.

In robotics, the POMDP framework has been instrumental in handling challenges such as noisy sensing, imperfect control, and environmental changes, which are common in real-world robot tasks. This has led to successful applications in areas like localization and navigation, search and tracking, autonomous driving, multi-robot systems, manipulation, and human-robot interaction.

In the context of DRL, strides have been made in enhancing the efficiency of learning algorithms. Techniques such as Bootstrapped DQN, which learns an ensemble of Q-networks, and Thompson Sampling for deep exploration have been employed. Additionally, the use of expert demonstrations to bootstrap the agent has improved efficiency, and this approach has been integrated with DQN and DDPG. To tackle the challenge of large discrete action spaces, innovative techniques like Action-Elimination Deep Q-Network (AE-DQN) and Deep Reinforcement Relevance Network (DRRN) have been introduced.

Moreover, progress has been made in the development of POMDP models and algorithms, aiming to bridge the gap between theoretical development and practical application. This has led to a deeper understanding of the unique challenges associated with applying POMDPs to robot systems, providing valuable insights for POMDP algorithm designers.

## More terms

### What is abductive logic programming?

Abductive Logic Programming (ALP) is a form of logic programming that allows a system to generate hypotheses based on a set of rules and data. The system then tests these hypotheses against the data to find the most plausible explanation. This approach is particularly useful in AI applications where data interpretation is challenging, such as medical diagnosis, financial fraud detection, and robotic movement planning.

### What is data fusion?

Data fusion involves integrating multiple data sources to enhance decision-making accuracy and reliability. This technique is crucial across various domains, such as autonomous vehicles, where it merges inputs from cameras, lidar, and radar to navigate safely. In healthcare, data fusion combines patient records, medical images, and test results to refine diagnoses, while in fraud detection, it aggregates financial transactions, customer data, and social media activity to identify fraudulent behavior more effectively.