Rewards

In RL literature, rewards at a time instant t are typically denoted as R_t. Thus, the total rewards earned in an episode is given by R = r1+ r2 + ... + r_t, where t is the length of the episode (which can be finite or infinite).

The concept of discounting is used in RL, where a parameter called the discount factor is used, typically represented by γ and 0 ≤ γ ≤ 1 and a power of it multiplies r_t. γ = 0, making the agent myopic, and aiming only for the immediate rewards. γ = 1 makes the agent far-sighted to the point that it procrastinates the accomplishment of the final goal. Thus, a value of γ in the 0-1 range (0 and 1 exclusive) is used to ensure that the agent is neither too myopic nor too far-sighted. γ ensures that the agent prioritizes its actions to maximize the total discounted rewards, R_t, from time instant t, which is given by the following: 

Since 0 ≤ γ ≤ 1, the rewards into the distant future are valued much less than the rewards that the agent can earn in the immediate future. This helps the agent to not waste time and to prioritize its actions. In practice, γ = 0.9-0.99 is typically used in most RL problems.