Introduction to Reinforcement Learning

Introduction

Reinforcement learning (RL) is a branch of machine learning that focuses on training agents to make decisions and take actions in an environment to maximize a reward signal. The concept is similar to training a pet dog to fetch a ball. Each time the dog successfully retrieves the ball, it receives a treat as a reward. Through repetition, the dog learns that bringing back the ball leads to a positive outcome (the treat) and becomes more likely to repeat the behavior. This feedback-based learning is the core principle of reinforcement learning - an agent (the dog) interacts with an environment (the backyard) and learns to make decisions (fetching the ball) based on the rewards it receives (treats).

Unlike classical machine learning, which relies on pre-existing data for model training, reinforcement learning does not require a dataset. Instead, it can learn from interactions with a designed environment or a world model. This approach aligns with how humans learn certain tasks. For instance, when a person touches a hot surface, they instinctively recoil and learn to avoid doing so in the future. The feedback from the environment helps them acquire knowledge.

Definition

Reinforcement Learning is a framework for solving sequential decision-making problems, where an agent learns to make optimal decisions by interacting with an environment. The agent aims to maximize the cumulative reward it receives over time. The critical components of a reinforcement learning problem are:

Agent: The entity that makes decisions and takes actions in the environment.
Environment: The world in which the agent operates and interacts.
State: The current situation or configuration of the environment.
Action: The choices available to the agent at each state.
Reward: The feedback signal that the agent receives from the environment based on its actions.
Policy: The strategy or mapping that determines the agent's actions in each state.

The agent-environment interaction can be modeled as a Markov Decision Process (MDP), which is defined by the tuple ( $S$ , $A$ , $P$ , $R$ , $γ$ ):

$S$ : The set of states in the environment.
$A$ : The set of actions available to the agent.
$P$ : The state transition probability function, $P(s'|s, a)$ , which represents the probability of transitioning from state $s$ to state $s'$ when taking action $a$ .
$R$ : The reward function, $R(s, a)$ , defines the immediate reward the agent receives for taking action $a$ in state $s$ .
$γ$ : The discount factor determines the importance of future rewards ( $0 ≤ γ ≤ 1$ ).

The goal of reinforcement learning is to find an optimal policy $π^*$ that maximizes the expected cumulative reward:

π^* = \arg\max_π \mathbb{E}\left[\sum_{t=0}^∞ γ^t R(s_t, a_t) | π\right]

Where:

$π$ is a policy,
$t$ is the time step,
$s_t$ and $a_t$ are the state and action at time step $t$ , respectively,
$\mathbb{E}[\cdot]$ denotes the expectation over the trajectories generated by following policy $π$ .

Two fundamental concepts in reinforcement learning are the value function and the action-value function (Q-function):

Value function, $V_π(s)$ , represents the expected cumulative reward starting from state $s$ and following policy $π$ :

V_π(s) = \mathbb{E}\left[\sum_{t=0}^∞ γ^t R(s_t, a_t) | s_0 = s, π\right]

Action-value function, $Q_π(s, a)$ , represents the expected cumulative reward starting from state $s$ , taking action $a$ , and then following policy $π$ :

Q_π(s, a) = \mathbb{E}\left[\sum_{t=0}^∞ γ^t R(s_t, a_t) | s_0 = s, a_0 = a, π\right]

To understand the value function and the action-value function, consider the following examples:

Value Function: Imagine a treasure hunter exploring different rooms in a dungeon. Each room represents a state $(s)$ in the environment. The value function, $V(s)$ , estimates the expected future rewards the treasure hunter can collect from a particular room onwards. It helps evaluate the desirability of being in a specific state, considering the potential future rewards obtainable from that state.
Action-Value Function: Extending the treasure hunter example, suppose he has two possible actions in each room: "search" or "move." The action-value function, $Q(s, a)$ , estimates the expected cumulative reward he can obtain by taking a specific action $(a)$ in a particular state $(s)$ and then following the optimal strategy. It helps determine the best action to take in each state by considering the immediate and expected future rewards resulting from that action.

Learning Value and Action-Value functions is crucial in reinforcement learning because these functions estimate the expected cumulative reward an agent can obtain from a given state or state-action pair. Using those estimates, the agent can make informed decisions about which actions to take in different states to maximize its long-term reward.

Reinforcement learning algorithms aim to estimate these value functions or directly learn the optimal policy through interactions with the environment.

Applications

Feedback control for Defi: Reinforcement Learning can enable PID controllers for DeFi Applications on chain for protocols like OlympusDao, Reflexer Finance, Ampleforth. These PID controllers would take onchain state into account while setting new parameters for the protocol.
Game Playing: Reinforcement learning has achieved significant milestones in game playing, showcasing its ability to master complex strategy games. Notable examples include DeepMind's AlphaGo, which defeated (opens in a new tab) world champion Lee Sedol in 2016 in the game of Go, and OpenAI Five (opens in a new tab), which learned to play the multiplayer game Dota 2 at a high level. These achievements demonstrate the potential of reinforcement learning in solving problems that require long-term planning, decision-making under uncertainty, and adaptation to opponent strategies.
Robotics and Autonomous Systems: Reinforcement learning has been extensively applied in robotics to enable autonomous decision-making and control. Robots can manipulate objects, and perform tasks through trial and error. For example, reinforcement learning has been used to train robotic arms to grasp and manipulate objects, allowing them to adapt to different shapes and sizes.

Conclusion

Reinforcement learning is a powerful paradigm that enables agents to learn and make decisions through interaction with an environment. By receiving rewards and penalties, the agent gradually learns to take actions that maximize its long-term cumulative reward.

By harnessing the power of reinforcement learning, we can develop intelligent agents capable of learning and making decisions in complex and dynamic environments, opening up new possibilities in artificial intelligence and beyond.

Resources

Neural Networks Embeddings