Deep Reinforcement Learning: A Comprehensive Guide

Introduction

Recent advancements in machine learning, exemplified by programs that can defeat humans in complex games like Go, have been propelled by reinforcement learning (RL). Reinforcement learning involves training a program to achieve a goal through trial and error, incentivizing it with rewards and penalties. An agent operates within an environment to maximize its rewards. RL has found applications in various domains, from games to simulating evolution, serving as a tool to explore emergent behavior.

This article provides an overview of reinforcement learning theory, focusing on deep Q-learning. It demonstrates how to use Keras to construct a deep Q-learning network that learns within a simulated video game environment.

Deep Reinforcement Learning Explained

In reinforcement learning, an agent interacts with an environment by taking sequential actions. These environments can be complex and rapidly changing, requiring sophisticated agents capable of adapting to achieve their objectives. Many successful reinforcement learning agents today utilize artificial neural networks, forming deep reinforcement learning algorithms. This chapter will cover the essential theory of reinforcement learning, particularly deep Q-learning, and how to use Keras to build a deep Q-learning network for simulated video game environments. We'll also discuss methods for optimizing deep reinforcement learning agents and introduce other deep RL agent families beyond deep Q-learning.

Essential Theory of Reinforcement Learning

Reinforcement learning is a machine learning paradigm where:

An agent takes an action within an environment (at timestep t).

Read also: Deep Dive into Reinforcement Learning
The environment provides the agent with two pieces of information:
- Reward: A scalar value offering quantitative feedback on the action taken at timestep t. For instance, acquiring cherries in Pac-Man could yield 100 points. The agent aims to maximize accumulated rewards, reinforcing productive behaviors discovered under specific environmental conditions.
- State: How the environment changes in response to the agent's action. These conditions will influence the agent's action choice during the subsequent timestep (t + 1).
The above steps are repeated until a terminal state is reached. This state can be triggered by achieving the maximum reward, attaining a specific desired outcome (e.g., a self-driving car reaching its destination), exhausting allotted time, using all permitted moves in a game, or the agent's demise in a game.

Reinforcement learning problems involve sequential decision-making. Examples include Atari video games (Pac-Man, Pong, Breakout), autonomous vehicles, board games (Go, chess, shogi), robot-arm manipulation tasks, and the Cart-Pole game.

The Cart-Pole Game: A Classic RL Problem

This article uses OpenAI Gym, a popular library of reinforcement learning environments, to train an agent to play Cart-Pole. In this game:

The objective is to balance a pole on top of a cart. The pole is connected to the cart via a pin, allowing rotation along the horizontal axis.
The cart can only move horizontally, either left or right. At each timestep, the cart must move in one direction; it cannot remain stationary.
Each game episode starts with the cart near the screen's center and the pole at a near-vertical angle.
An episode ends when either the pole is no longer balanced (its angle deviates too far from vertical) or the cart touches the screen boundaries.
In the game version used here, an episode has a maximum of 200 timesteps.
One reward point is awarded for each timestep the episode lasts, with a maximum possible reward of 200 points.

The Cart-Pole game is a common introductory problem due to its simplicity. Unlike self-driving cars with their vast sensor data streams, Cart-Pole only has four pieces of state information:

The cart's position along the horizontal axis
The cart's velocity
The angle of the pole
The pole's angular velocity

Similarly, instead of the nuanced actions possible with a self-driving car, the Cart-Pole game offers only two actions at each timestep: move left or move right.

Markov Decision Processes

Reinforcement learning problems can be mathematically defined as Markov decision processes (MDPs). MDPs assume the Markov property: the current timestep contains all relevant information about the environment's state from previous timesteps. In Cart-Pole, this means the agent decides to move right or left at a given timestep t based solely on the cart's and pole's attributes at that time.

An MDP consists of five components:

S: The set of all possible states. Each individual state is represented by s. Even in the simple Cart-Pole game, the number of possible combinations of its four state dimensions is enormous.
A: The set of all possible actions. In Cart-Pole, this set contains only two elements (left and right). Each individual action is denoted as a.
R: The distribution of reward given a state-action pair (s, a). This is a probability distribution, meaning the same (s, a) pair might result in different rewards r on different occasions. The reward distribution's details are hidden from the agent but can be inferred through actions within the environment.
P: A probability distribution representing the probability of the next state (st+1) given a particular state-action pair (s, a) at timestep t. Like R, the P distribution is hidden from the agent, but aspects of it can be inferred by taking actions.
γ (gamma): The discount factor, a hyperparameter. It reflects that immediate rewards are more valuable than distant rewards. The discount factor is analogous to discounted cash flow calculations in accounting. If γ = 0.9, cherries one timestep away are worth 90 points, while cherries 20 timesteps away are worth only 12.2 points.

The Optimal Policy

The goal in an MDP is to find a function that allows an agent to take the appropriate action a (from the set A) when encountering any state s from the set S. This function, denoted by π, is called the policy function. The policy function π dictates the agent's best course of action in any given circumstance to maximize its reward.

The objective function J(π) can be used with machine learning techniques to maximize reward.

Q-Learning: A Model-Free Approach

Q-Learning is a model-free reinforcement learning algorithm. The AI agent doesn't need a model of its environment. Everything is broken down into "states" and "actions." States are observations and samplings from the environment, while actions are the choices the agent makes based on those observations.

This article uses OpenAI's gym, specifically the "MountainCar-v0" environment. To initialize the environment, use gym.make(NAME), then env.reset(), and enter a loop where you perform env.step(ACTION) every iteration.

For different environments, you can query the number of possible actions/moves. In this case, there are 3 possible actions. When you step the environment, you can pass 0, 1, or 2 as the "action" for each step. 0 means push left, 1 is stay still, and 2 means push right. The model only needs to know the options for actions and the reward of performing a chain of those actions given a state.

The observations are returned from resets and steps, like [-0.4826636 0. ], which is the starting observation state. At each step, you get the new state, the reward, whether the environment is done, and extra info. In this environment, the extra info is not used. The reward is simply -1 always. The values are position and velocity.

Q-Learning works by assigning a "Q" value per possible action per state. This creates a table. This table is consulted to determine moves. When "exploiting" the environment, the agent chooses the action with the highest Q value for the current state. To "explore," the agent chooses a random action, which helps the model learn better moves over time.

To learn over time, the Q values need to be updated.

Reinforcement Learning Concepts

Agent: The decision-maker that interacts with its environment.
Environment: The external system with which the agent interacts.
State: A representation of the current situation of the environment.
Action: Choices that the agent can take in a given state.
Reward: Immediate feedback the agent gets after taking an action in a state.
Policy: A set of rules the agent follows to decide its actions based on states.
Value Function: Estimates the expected long-term reward from a specific state under a policy.

Markov Decision Process (MDP)

A Markov Decision Process (MDP) is a mathematical framework defined by the tuple (S,A,T,R,γ).

States (S): A set of all possible states in the environment.
Actions (A): A set of all possible actions the agent can take.
Transition Model (T): The probability of transitioning from one state to another.
Reward Function (R): The immediate reward received after transitioning from one state to another.
Discount Factor (γ): A factor between 0 and 1 that represents the importance of future rewards.

The Bellman equation calculates the value of being in a state or taking an action based on the expected future rewards. It breaks down the expected total reward into the immediate reward and the discounted value of future rewards.

Implementing Reinforcement Learning

Define the Environment: Specify the states, actions, transition rules, and rewards.
Initialize Policies and Value Functions: Set up initial strategies for decision-making and value estimations.
Observe the Initial State: Gather information about the initial conditions of the environment.
Choose an Action: Decide on an action based on current strategies.
Observe the Outcome: Receive feedback in the form of a new state and reward from the environment.
Update Strategies: Adjust decision-making policies and value estimations based on the received feedback.

Deep Q-Networks (DQN) and Other Methods

Q-Learning: A model-free algorithm that learns the value of actions in a state-action space.
Deep Q-Network (DQN): An extension of Q-Learning using deep neural networks to handle large state spaces.
Policy Gradient Methods: Directly optimize the policy by adjusting the policy parameters using gradient ascent.
Actor-Critic Methods: Combine value-based and policy-based methods. The actor updates the policy, and the critic evaluates the action.

Q-Learning in Detail

Q-Learning is a model-free method that learns actions by directly interacting with the environment. The Q-value, denoted as Q(s,a), represents the expected cumulative reward of taking a specific action in a specific state and following the policy thereafter.

A Q-Table stores the Q-value for each state-action pair. This table is continually updated as the agent learns from its experiences. The learning rate (α) determines how much new information overwrites old information. The discount factor (γ) reduces the value of future rewards.

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