Markov Decision Processes and Value Functions

2026-05-03 · Source: Daily Dose of Data Science · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Novice, medium

Summary

This content introduces the Markov Decision Process (MDP) framework, a foundational concept in reinforcement learning for modeling sequential decision-making problems with states. It builds upon the previous chapter's discussion of reinforcement learning and the multi-armed bandit problem, which isolated the exploration-exploitation tradeoff but lacked statefulness. The article emphasizes that real-world problems, such as chess or driving, are state-dependent, necessitating a formal vocabulary to describe states, transitions, and rewards. The core assumption for MDPs is the Markov property, which states that the future depends on the past only through the present state. This property simplifies prediction by making the current state a complete summary of past events. The content illustrates this with the Atari Breakout game, explaining how stacking multiple frames can transform a non-Markovian observation into an approximately Markovian state. It also briefly mentions Partially Observable Markov Decision Processes (POMDPs) for scenarios where the true state is hidden. The article sets the stage for defining the MDP as a 5-tuple, policies, and value functions like vπ and qπ.

Key takeaway

For Machine Learning Engineers designing reinforcement learning systems, understanding the Markov property is crucial. If your agent struggles with context, your current state representation might not be Markovian. You should enrich your state definition to include relevant historical information, like previous observations, to ensure the Markov property holds, simplifying model design and improving predictive accuracy.

Key insights

The Markov property enables tractable modeling of state-dependent reinforcement learning problems via Markov Decision Processes.

Principles

• Future depends on past only through present state.
• State representation is a modeling choice.
• Current state summarizes past for future prediction.

Method

To make a system Markovian, enrich the state representation to include necessary historical context, such as stacking multiple frames in video games to capture velocity.

In practice

• Redefine state to include history for Markov property.
• Consider POMDPs for hidden true states.

Topics

• Reinforcement Learning
• Markov Decision Processes
• Markov Property
• Value Functions
• Policies

Best for: AI Student, Machine Learning Engineer, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Daily Dose of Data Science.