Markov Decision Process

A Markov Decision Process (MDP) consists of five core elements: state space, action space, state transition probability, reward function, and discount factor.

Reinforcement learning learns optimal policies through continuous interaction between an agent and its environment; its mathematical foundation is the Markov Decision Process (MDP), which consists of a state space, action space, transition function, reward function, and discount factor.

A Markov Decision Process (MDP) is mathematically defined by a five-tuple (S, A, P, R, γ).

The Markov Decision Process (MDP) provides a complete mathematical framework for reinforcement learning, with its Markov property holding that future states depend only on the current state and action.

The key assumption of MDP is that the future depends only on the current state and not on the historical path.

Modern deep reinforcement learning methods (such as DQN, PPO, and SAC) can be viewed as function approximation generalizations of classical methods such as value iteration and policy iteration in continuous high-dimensional spaces.

Interaction-induced non-stationarity violates the stationarity assumption of MDPs, invalidating convergence guarantees derived from that assumption.

The research object is a finite Markov decision process (MDP) whose trajectories are generated by a fixed behavior policy, with the state-action chain being irreducible and allowing for periodicity.

In federated reinforcement learning, multiple agents interact with the same Markov decision process, exchange information through a central server, and jointly learn the optimal state-action value function.

强化学习中的状态—动作—奖励框架源自马尔可夫决策过程（MDP）理论

During the mid-training phase, ZGCM-1 reformulates the agent-tool interaction process as a Markov Decision Process (MDP).

Quantum algorithms such as Grover search and quantum amplitude estimation can be used to accelerate the value iteration/policy iteration solving process for MDPs.

An MDP is defined by the 4-tuple (S, A, P, R): the state set S, the action set A, the state transition probability P, and the reward function R.

Reinforcement learning is one of the three major paradigms of machine learning, alongside supervised learning and unsupervised learning; its core framework is derived from Markov Decision Processes (MDP) and consists of five elements: agent, environment, state, action, and reward.