Agent-Environment Interface in AI

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.

Artificial intelligence‘s reinforcement learning field focuses on how agents should behave in environments to maximize cumulative rewards. To accomplish a certain objective, the agent must learn from interactions with the environment in the reinforcement learning problem.

• Agent: The agent is said to be the learner or a decision-maker who is capable of interacting with their surroundings to achieve a specific goal.
• Environment: Everything external to the agent that the agent interacts with is called the environment. This includes all the conditions, contexts, and dynamics that the agent must respond to.

The presence of continuous interaction allows the agent to select the actions while the environment is responsible for responding to those actions thereby presenting a new situation to the agent. The environment grants the rewards typically in numerical values where the agent seeks to maximize it over time. The complete specification of an environment includes all the necessary details for the agent to understand and interact with it. This specification defines the tasks, which is a particular instance of the reinforcement learning problem.

Time steps and continual interaction

The agent-environment interaction in reinforcement learning is structured as a sequence of discrete time steps.

• Discrete-time steps: The interaction occurs at each of a sequence of discrete time steps that is denoted as t. (Where t = 0,1,2,3,… ). At each time step t, a series of events unfolds so that it can dictate the agent’s learning and decision-making process.
• Continual interaction: The continual interaction refers to a scenario in reinforcement learning where the interaction between the agent and the environment does not naturally break down into distinct or separate episodes. Instead, the interaction continues indefinitely without a predefined endpoint.

Perception, Action, and Feedback

• Perception: Perception refers to the process by which the agent gathers all the information about the environment. At each time step t, the agent perceives the current state information of the environment that is denoted as S_t. This state helps to produce all the relevant information to the agent so that it can make a decision based on it. The perception process involves sensing and interpreting data that can be received from various sensors or inputs depending upon the specific tasks.
• Action: Action is the process by which the agent responds to the perceived state of the environment. Based on the state S_t, the agent is capable of choosing an appropriate action At from the set of possible actions A(S_t).
• Feedback: Feedback is the information that the agent receives from the environment after acting. The feedback can be of two forms:
  • New states(S_t+1): After taking an action A_t, the environment transitions to a new state S_t+1. This new state reflects the updated situation in the environment as a result of the agent’s actions.
  • Reward(R_t+1): The agent receives the numerical reward R_t+1, which provides the measure of immediate effect of the action. The reward earned by the agent can be beneficial or it may negative impact. The agent uses these rewards to adjust its policy to maximize the cumulative rewards over time.

Example: Consider a robot in a maze-navigation task. The agent robot aims to find the maze’s exit to earn a positive reward. The perception, action, and feedback for this scenario can be described as follows,

Representation of State, Action and Rewards

• State representation: At each time step t, the agent receives the representation of the environment’s state, thus, this can be denoted as [Tex]S_{t} \epsilon S[/Tex], where the S represents the set of possible states.
• Action selection: Based on the state S_t, the agent now selects an action A_t. The A_t is chosen from the A(S_t), which represents the set of all actions available to the agent when it is in the state S_t.
• Reward and new state: One-time step later, after the agent has taken the action A_t, it now receives a numerical reward R_t+1. This reward indicates the feedback signal for the immediate impact of the action taken by the agent, and it belongs to R that is a subset of real numbers. Meanwhile, the agent finds itself in a new state S_t+1, this new state is obtained as a result of previous action A_t taken by the agent.

Example Scenario: Consider the scenario where the robot’s goal is to learn to walk. The researchers have assigned rewards on each time step proportional to the robot’s forward motion. The robot might receive positive reward for moving forward and negative rewards for bumping into obstacles. The robot’s actions determine whether it receives positive or negative rewards.

The state, action, and reward in this scenario are as follows:

• State(S_t): The robot’s current physical configuration and position
• Action(A_t): Movements or adjustments in the robot’s joints and limbs.
• Reward(R_t+1): Proportional to the robot’s forward motion, encouraging walking. Negative rewards may be given for undesirable actions such as bumping into obstacles.

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.

In reinforcement learning, a critical concept is the Markov property, which defines a specific characteristic of the environment and its state signals. The Markov property ensures that the future state of the environment depends only on the current state and the action taken by the agent but not on the sequence of states and actions that preceded it. This is generally defined as the Markov Decision Process (MDP) framework.

The reinforcement learning framework allows the agent to make decisions based on the state signal received from the environment. This state signal contains all the necessary information about the current situation of the environment that enables the agent to decide what action to take next.

However, the Markov property restricts the state signal to provide only the information that is currently available and it does it necessarily include the hidden or future information that might be useful for the agent to make a decision. For instance, if the agent is playing Blackjack, the agent does not have access to the next card in the deck. This ensures that while there may be hidden state information in the environment that could be beneficial. The agent can only make its decisions based on the information received up to that point.

Thus the Markov property guarantees that the decision-making process remains grounded in the present state and the agent’s immediate perceptions and ensures a manageable and realistic framework for learning and decision-making in uncertain and dynamic environments.

If both the state and action spaces are finite, the MDP is referred to as Finite Markov Decision process(finite MDP). Finite MDP is crucial because they form the foundation for understanding the majority of reinforcement learning theories and applications.

Components of Finite MDP

A finite MDP can be defined as:

• State set (S): All possible states the environment can be in.
• Action set(A): All possible action that the agent can take.
• One-step Dynamics: The probability distribution of the next state and reward given the current state and action.

Dynamics of Finite MDP

At any given state s and action a, the likelihood of each possible combination of next state s’ and reward r can be denoted as

[Tex]p(s’, r| s,a) = Pr\{S_{t+1} = s’, R_{t+1} = r \mid S_t = s, A_t = a\} [/Tex] ……. Equation 1

The above quantities specify the dynamics of finite MDP. Once the dynamics of the environment are defined by the probability distribution p(s’, r| s,a), we can now calculate the various important characteristics of the environment such as expected rewards for state-action pairs, state-transition probabilities and also expected rewards for state-action-next-state triples.

The Expected rewards for the State-Action pairs can be denoted as

[Tex]r(s,a) = \mathbb{E}[R_{t+1} \mid S_t = s, A_t = a] = \sum_{r \in R} r \sum_{s’ \in S} p(s’, r|s,a)[/Tex] ……. Equation 2

The above equation 2 represents the expected reward after taking action a in state s.

The state-transition probabilities can be denoted as,

[Tex]p(s’ | s, a) = Pr\{S_{t+1} = s’ \mid S_t = s, A_t = a\} = \sum_{r \in R} p(s’, r|s,a)[/Tex] ……. Equation 3

The above equation 3 represents the probability of transitioning to state s’ after taking action a in the state s.

The expected rewards for the State-Action-Next-State Triples can be denoted as,

[Tex] r(s,a,s’) = \mathbb{E} [R_{t+1} \mid S_t = s, A_t = a, S_{t+1} = s’] = \frac{\sum_{r \in R} r \cdot p(s’, r|s,a)}{p(s’ | s, a)}[/Tex] ……. Equation 4

The above equation 4 represents the expected reward when the agent transitions from state s to state s’ after taking action a.

The flexibility and abstraction in the reinforcement learning framework enable it to be applied to various problems and contexts such as time steps, action types, and state representation.

• Time steps: Flexible interpretation of time steps can be found in reinforcement learning since it doesn’t need to correspond to fixed-time intervals. Instead they can represent any sequence of decision-making stages.
• Actions: The actions can range from low-level controls to high-level decisions. For instance, the voltages applied to the motors of a robot arm represent the low-level controls. Conversely, high-decision decisions could include choices like whether to pursue a graduate degree or what to have for lunch. These diverse actions demonstrate the flexibility of the reinforcement learning framework in handling various types of decision-making processes.
• States: Similar to actions, states can also be represented in several ways, from low-level sensor readings to high-level abstract descriptions. For example, direct sensor reading represents the low-level sensations and the symbolic representation of objects in a room represents the high-level abstractions.

In reinforcement learning, the boundary between the agent and the environment is not necessarily aligned with the physical boundary of a robot or animal’s body. Typically, this boundary is said to be defined closer to the agent.

For example, components like motors, mechanical linkages, and sensing hardware of a robot are generally considered as a part of the environment rather than part of the agent. Similarly, if we think of a person or animal, the muscles, skeleton, and even sensory organs are considered as a part of the environment.

However, the physical computation of rewards falls inside the system (e.g., within a robot), and the agent in reinforcement learning is treated as if they had gained the rewards from the environment.

The general rule in reinforcement learning that cannot be changed arbitrarily is the role of the agent and environment. The agent is capable of making decisions and taking actions based on the current state and the information it holds. It can typically change its actions and strategy based on the learning from its experiences. In contrast, the environment is responsible for producing the necessary information to the agents about its current state.

The environment does not necessarily restrict the essential information from the agents. Instead, it will produce the essential information for the agents to help them decide on the next action. Even if the environment hides the information from the agents because of Markov’s property, the agents might still know how its rewards are computed as a function and what states they have taken in the past.

In general, the agent-environment boundary can be determined only if one has chosen the particular states, actions, and rewards, and also discovered a particular decision-making task of interest.

In reinforcement learning, the agent-environment interaction forms the core of the learning process. The flexibility and abstraction inherent in this framework that allows it to be applied across various domains from robotics to decision-making in complex environments. By defining the states, actions, and rewards, enables reinforcement learning facilitates goal-oriented behavior and continuous adaption.