Markov decision process

Introduction

Markov decision process is a mathematical framework used for modeling decision-making problems when the outcomes are partly random and partly controllable.

Terminology

Agent: an agent is the entity which we are training to make correct decisions (we teach a robot how to move around the house without crashing).

Enviroment: is the sorrounding with which the agent interacts (a house), the agent cannot manipulate its sorroundings, it cannot only control its own actions (a robot cannot move a table in the house, it can walk around it in order to avoid crashing).

State: the state defines the current situation of the agent (the robot can be in particular room of the house, or in a particular posture, states depend on a point of view).

Action: the choice that the agent makes at the current step (move left, right, stand up, bend over etc.). We know all possible options for actions in advance.

Characteristics

Markov Property

Markov property says that current state of the agent (for example a Robot) depends solely on the previous state and doesn't depend in any way on states the agent was in prior the previous state.

Markov Process/Markov Chain

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Pss' = P[S_t+1 = s' | S_t = s]} A Markov Process is defined by (P, S), where S are the states and P is state-transition probability. It consists of a sequence of random states s1, s2 ..., where all states obey Markov Property. Pss' is the probabilty of jumping to state s' from current state s. Let's consider the example of an automatic vacuum cleaner. When it is next to a wall there is probability of 10% that it will crash it and 90% probabilty that it will change direction and proceed with cleaning. So the probability of state s' (crashed in our case) is 0.1 with respect to current state (next to a wall).