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Also known as: MDP
Mathematical framework modeling sequential decisions via states, actions, transitions, rewards, and discounting.
DESCRIPTION
A Markov Decision Process defines an environment for sequential decision-making under uncertainty. It specifies a state space, action space, transition dynamics, reward function, and discount factor. The Markov property assumes future states depend only on the current state and action. MDPs enable formal derivation of optimal policies via Bellman equations and dynamic programming. They underpin reinforcement learning algorithms, from value iteration to policy gradients. Extensions include continuous spaces and function approximation. When observations are partial, POMDPs generalize MDPs.
ALTERNATIVE DEFINITIONS
Wikipedia
A Markov decision process (MDP) is a discrete-time stochastic control process.
Highlights stochastic control and discrete-time formulation.
Sutton & Barto
A finite Markov decision process is a tuple (S, A, P, R, γ).
Provides the canonical formal tuple definition used in RL theory.
UCL (David Silver)
A Markov Decision Process is a tuple (S, A, P, R, γ).
Concise lecture slide definition emphasizing components.
RELATED TERMS
Reinforcement Learning Policy Value Function Bellman Equation Q-Learning State Space Action Space Reward Function Transition Probability
COMPETING TERMS
Partially Observable Markov Decision Process
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer MLOps Engineer
EXTERNAL SOURCES
- Wikipedia - Markov decision process
- Sutton & Barto - Foundational RL textbook
- UCL (David Silver) - MDP lecture slides
- OpenAI Spinning Up - RL introduction with MDPs
- Stanford CS234 - Graduate RL course
TOP QUESTIONS
What are the core components of a Markov Decision Process?
An MDP comprises states, actions, transition probabilities, a reward function, and a discount factor. Together they specify dynamics and objectives for sequential decision-making.
Category: Requirements
Why is the Markov property important in a Markov Decision Process?
It ensures the future depends only on the present state and action, simplifying inference and control. This property enables dynamic programming and temporal-difference methods.
Category: Relevancy
How do Markov Decision Processes relate to reinforcement learning?
MDPs provide the formal problem statement for reinforcement learning. Algorithms seek optimal policies that maximize expected cumulative rewards within the MDP framework.
Category: Example
What is a practical example of a Markov Decision Process?
Robot navigation with grid states, move actions, stochastic transitions, and rewards for reaching goals. Inventory control and ad-serving also fit MDP formulations.
Category: Example
How do you solve a Markov Decision Process exactly?
Use value iteration or policy iteration to solve Bellman optimality or evaluation equations. Exact methods require known dynamics and manageable state-action spaces.
Category: HowTo
When should you use a POMDP instead of a Markov Decision Process?
Use POMDPs when the agent has partial observations rather than full state information. Belief states or recurrent models can approximate solutions under uncertainty.
Category: Alternatives
What is the biggest misunderstanding about Markov Decision Processes?
That they only handle deterministic systems; in fact, MDPs explicitly model stochastic dynamics and rewards. They also handle infinite horizons via discounting.
Category: Misunderstandings
What are common mistakes in modeling a Markov Decision Process?
Poor state representations that break the Markov property and mis-specified reward functions. Overly coarse discretization can also obscure optimal policies.
Category: Mistakes
What risks arise from an ill-defined reward in a Markov Decision Process?
Reward hacking or unintended behaviors can occur. The policy may optimize shortcuts rather than the intended objective, impacting safety and performance.
Category: Risks