Policy and Decision-making

Policy

In reinforcement learning, the policy is an essential component that governs the agent’s behavior. It is a mapping from states to probabilities of selecting each possible action. Formally, the policy at time step t can be denoted as [Tex]\pi_t[/Tex] and [Tex]\pi_t(a|s)[/Tex] which represents the probability that the agent will choose action [Tex]A_t = a[/Tex] when it is in the state [Tex]S_t = s[/Tex]. The reinforcement learning agent’s goal is to learn a policy that typically maximizes the expected cumulative reward over time. The policy in reinforcement learning can be formally expressed as

[Tex]\pi: S \times A \rightarrow [0,1], \\ \pi(s,a) = Pr(A_t = a \mid S_t = s)[/Tex]

where,

• [Tex]\pi: S \times A \rightarrow [0,1][/Tex] indicates the policy function that takes a state s and an action a as input and return the probability [Tex]\pi(s,a)[/Tex] i.e. in the range of [0,1]. This probability shows how likely that the agent takes an action a when it is in the state s.

Types of policies in Reinforcement learning

• Stationary policy: A policy is considered stationary if the distribution of actions it returns depends on the last state visited by the agent, as observed from its history of interactions with the environment. This signifies that regardless of when the agent visits a state, the probability of selecting an action from the state remains the same.
• Deterministic stationary policy: Within the stationary policy, there is a subset known as deterministic stationary policies. These policies are nothing but it select the same action for a given state without considering any probabilities of action. In simple words, the action is solely determined by the current state, and there is no randomness involved. This type of policy can be fully characterized by mapping from the set of states to the set of actions. This mapping specifies the exact action that should be taken in each possible state by the agent, and it uniquely determines the agent’s behavior in every state.

Decision making

Based on the current state of the environment, the agent uses its policy to select an action. This action selection process can be:

• Greedy: The agent chooses the action with the highest expected reward (deterministic or highest probability in a stochastic policy).
• Exploratory: The agent might take a less optimal action with some probability to explore the environment and potentially discover better long-term rewards.

The Learning Process: Refining the Policy

• Reinforcement learning algorithms aim to improve the agent’s policy over time. This is achieved through trial and error interactions with the environment.
• The agent receives rewards (or penalties) based on the chosen actions and the resulting outcomes.
• These rewards are used by the learning algorithm to assess the efficacy of the existing policy and make necessary adjustments. Finding a policy that optimizes the anticipated long-term reward is the aim.

Key Points on Policy and Decision-Making in RL:

• Exploration vs. Exploitation: Finding the right balance between exploration (trying new actions) and exploitation (concentrating on things with high expected rewards) is a major challenge. Too much exploration can delay learning, while insufficient exploration can lead to suboptimal performance.
• Policy Learning Algorithms: Q-learning and Policy Gradient techniques along with other RL algorithms provide frameworks through which an agent learns and improves its policy when interacting with the environment.
• Policy Representation: The policy can be represented in a variety of ways, including a lookup table, neural network, and decision tree. The chosen representation influences how the agent learns and adapts its policy.

The agent-environment interface is a fundamental concept of reinforcement learning. It encapsulates the continuous interaction between an autonomous agent and its surrounding environment that forms the basis of how the agents learn from and adapt to their experiences to achieve specific goals. This article explores the decision-making process of agents, the flexibility of the framework, and the critical distinction between the agent and its environment.