Reinforcement Learning

machine-learning

Definition

Reinforcement Learning

Reinforcement learning is a paradigm of machine learning where an autonomous agent learns to make decisions by interacting with an environment to maximise a cumulative reward signal. Formally, the problem is modelled as a Markov Decision Process (MDP) defined by $(\mathcal{S},\mathcal{A},P,R,\gamma )$.

Formalism

The learning environment is defined by the state space $\mathcal{S}$ and action space $\mathcal{A}$, with transition probabilities $P(s^{\prime }|s,a)$ and an immediate reward function $R(s,a,s^{\prime })$. The learner’s objective is to identify an optimal policy ${\pi }^{\ast }:\mathcal{S}\to \mathcal{A}$ that maximises the expected discounted return $G_t={\sum }_{k=0}^{\infty }{\gamma }^k{r}_{t+k+1}$, where $\gamma \in [0,1]$ is the discount factor.