transition dynamics

Transition dynamics are the rules of the world: given where you are and what you do, where do you end up? Push a door and it usually opens, but on an icy floor your step might slide somewhere unexpected. The dynamics capture both the reliable consequences of actions and the genuine randomness the environment can throw in.

Mathematically the dynamics are a conditional probability of landing in each next state after taking an action in a state. Together with the reward function they fully specify how the MDP behaves. In model-based RL the agent tries to learn or is given these dynamics and plans against them; in model-free RL it never writes them down and instead learns values or policies directly from sampled experience.