Expected Return

reinforcement-learning

Definition

Expected Return

Let ${\pi }_{\theta }$ be a parameterised policy and let ${\rho }_0$ be the start-state distribution. The expected return is the objective maximised in reinforcement learning:

$$J(\theta )={\mathbb{E}}_{s_0\sim {\rho }_0,\tau \sim {\pi }_{\theta }}\left[G_0\right]$$

where $G_0={\sum }_{k=0}^{\infty }{\gamma }^{k}R(s_k,a_k)$ is the return from the initial state and $\gamma \in [0,1]$ is the discount factor.