Summary

### The Setting, Revisited

• The reinforcement learning (RL) framework is characterized by an agent learning to interact with its environment .
• At each time step, the agent receives the environment's state ( the environment presents a situation to the agent) , and the agent must choose an appropriate action in response. One time step later, the agent receives a reward ( the environment indicates whether the agent has responded appropriately to the state ) and a new state .
• All agents have the goal to maximize expected cumulative reward , or the expected sum of rewards attained over all time steps.

### Episodic vs. Continuing Tasks

• A task is an instance of the reinforcement learning (RL) problem.
• Continuing tasks are tasks that continue forever, without end.
• Episodic tasks are tasks with a well-defined starting and ending point.
  • In this case, we refer to a complete sequence of interaction, from start to finish, as an episode .
  • Episodic tasks come to an end whenever the agent reaches a terminal state .

### The Reward Hypothesis

• Reward Hypothesis : All goals can be framed as the maximization of (expected) cumulative reward.

### Goals and Rewards

• (Please see Part 1 and Part 2 to review an example of how to specify the reward signal in a real-world problem.)

### Cumulative Reward

• The return at time step t is G_t := R_{t+1} + R_{t+2} + R_{t+3} + \ldots
• The agent selects actions with the goal of maximizing expected (discounted) return. ( Note: discounting is covered in the next concept. )

### Discounted Return

• The discounted return at time step t is G_t := R_{t+1} + \gamma R_{t+2} + \gamma^2 R_{t+3} + \ldots .
• The discount rate \gamma is something that you set, to refine the goal that you have the agent.
  • It must satisfy 0 \leq \gamma \leq 1 .
  • If \gamma=0 , the agent only cares about the most immediate reward.
  • If \gamma=1 , the return is not discounted.
  • For larger values of \gamma , the agent cares more about the distant future. Smaller values of \gamma result in more extreme discounting, where - in the most extreme case - agent only cares about the most immediate reward.

### MDPs and One-Step Dynamics

• The state space \mathcal{S} is the set of all ( nonterminal ) states.
• In episodic tasks, we use \mathcal{S}^+ to refer to the set of all states, including terminal states.
• The action space \mathcal{A} is the set of possible actions. (Alternatively, \mathcal{A}(s) refers to the set of possible actions available in state s \in \mathcal{S} .)
• (Please see Part 2 to review how to specify the reward signal in the recycling robot example.)
• The one-step dynamics of the environment determine how the environment decides the state and reward at every time step. The dynamics can be defined by specifying p(s',r|s,a) \doteq \mathbb{P}(S_{t+1}=s', R_{t+1}=r|S_{t} = s, A_{t}=a) for each possible s', r, s, \text{and } a .
• A (finite) Markov Decision Process (MDP) is defined by:
  • a (finite) set of states \mathcal{S} (or \mathcal{S}^+ , in the case of an episodic task)
  • a (finite) set of actions \mathcal{A}
  • a set of rewards \mathcal{R}
  • the one-step dynamics of the environment
  • the discount rate \gamma \in [0,1]