Markov assumption

The Markov assumption is a fundamental concept in various statistical models, including reinforcement learning and Markov chains. It posits that the next state or observation in a sequence depends only on the current state and not on the entire history. This assumption simplifies the model by reducing dependency on the history of all previous states, making the mathematics of the model more manageable and allowing for practical and efficient computations.

In reinforcement learning, as discussed by Marcus Hutter, the Markov assumption means that the next state or observation depends solely on the previous state or observation, rather than on a complete history of states. This assumption is widely used because it simplifies the mathematical formulation of problems and is often practical for algorithms that deal with sequence data or time series, such as those used in robotics, gaming, and other applications 1.

The concept is similarly applied in the explanation of Markov chains and Hidden Markov Models (HMMs), where the current state relies exclusively on the preceding state. This principle is highlighted in discussions about state transitions in games or other scenarios where knowledge of the entire past isn't necessary to predict future states 2 3.