Reinforcement Learning: A Journey into Intelligent Decision-Making

In the ever-evolving landscape of artificial intelligence, Reinforcement Learning (RL) has emerged as a powerful paradigm, enabling machines to learn and make decisions through interaction with their environment. Let's dive into the world of reinforcement learning without further ado.

Imagine training a dog named Max using treats as positive reinforcement. When Max successfully follows a command like "sit" or "stay", the owner immediately rewards him with a tasty treat. The positive association between the action and the treat encourages Max to repeat the desired behavior.

Over time, Max learns to associate the specific command with the positive outcome of receiving a treat, reinforcing the training process.

Figure 1. A simple example of Reinforcement Learning

Policy search is a category of reinforcement learning methods that directly optimize the policy and the strategy or behavior that an agent employs to make decisions in an environment. Unlike value-based methods that estimate the value of actions or states, policy search methods focus on finding the optimal policy directly.

Figure 3. Policy Search in Reinforcement Learning

Characteristics:

Exploration: Policy search methods explore the space of possible policies to find the one that maximizes the expected cumulative reward.
Continuous and Discrete Spaces: This can be applied to both continuous and discrete action spaces.
Sample efficiency: can be more sample-efficient in high-dimensional or continuous action spaces.

Policy Space

Policy space refers to the set of all possible policies that an agent can adopt. In reinforcement learning, a policy defines the mapping from states to actions, representing the strategy that the agent follows to interact with its environment.

Characteristics:

Parameterization - policies can be parameterized, and the search for an optimal policy involves finding the best set of parameters.
Complexity - the complexity of the policy space depends on the task, and effective policies may be simple or highly complex.

Genetic algorithm

A genetic algorithm is an optimization technique inspired by the process of natural selection. It involves creating a population of potential solutions, evaluating their fitness, and iteratively evolving the population by selecting individuals with higher fitness to produce the next generation. Genetic algorithms offer a population-based optimization strategy.

Figure 4. Genetic algorithm

Characteristics:

Population-based: Operates on a population of candidate solutions rather than a single solution.
Crossover and mutation: Involves genetic operators like crossover (combining information from two parents) and mutation (introducing random changes).

3. Neural Network Policies

A neural network takes an observation as input, and it will output the action to be executed. More precisely, it will estimate a probability for each action, and then we will select an action randomly according to the estimated probabilities.

Figure 5. A Neural Network Policy

You may wonder why we are picking a random action based on the probabilities given by the neural network, rather than just picking the action with the highest score. This approach lets the agent find the right balance between exploring new actions and exploiting the actions that are known to work well.

Suppose you go to a restaurant for the first time, and all the dishes look equally appealing, so you randomly pick one. If it turns out to be good, you can increase the probability that you'll order it next time, but you shouldn't increase the probability up to 100%, else you will never try out the other dishes, some of which may be even better than the one you try.

Types of Neural Network Policies:

Feedforward Neural Networks

The simplest form of neural network policies is suitable for mapping states to actions.
Limited by the lack of memory of past states.

Recurrent Neural Networks (RNNs)

Introduce memory to the policy, allowing consideration of sequential information.
Suitable for problems with temporal dependencies.

Long Short-Term Memory (LSTM) Networks

A specific type of RNN that addresses the vanishing gradient problem, enabling better handling of long-term dependencies.

4. Evaluating Actions: The Credit Assignment Problem

The credit assignment problem is a fundamental challenge in reinforcement learning, referring to the difficulty of determining which actions taken by an agent contributed to a particular outcome or reward. In other words, it involves assigning credit or blame to the agent's actions based on the observed consequences. Accurately assigning credit is crucial for the learning process because it guides the agent to reinforce good actions and avoid or diminish the impact of bad ones.

To tackle this problem, a common strategy is to evaluate an action based on the sum of all rewards that come after it, usually applying a discount factor γ (gamma) at each step. This sum of discounted rewards is called the action's return. Consider an example in Figure 6. If an agent decides to go right three times in a row and gets +10 reward after the first step, 0 after the second step, and finally -50 after the third step, then assuming we use a discount factor γ = 0.8, the first action will have a return of 10 + γ * 0 + (γ^2) * (-50) = -22. If the discount factor is close to 0, then future rewards won't count for much compared to immediate rewards. Conversely, if the discount factor is close to 1, then rewards far into the future will count almost as much as immediate rewards.

Figure 6. Computing an action's return: the sum of discounted future rewards

Of course, a good action may be followed by several bad actions, resulting in the good action getting a low return (like a good actor may sometimes star in a terrible movie). However, if we run many episodes, on average good actions will get a higher return than bad ones.

Key Aspects of the Credit Assignment Problem:

Temporal Credit Assignment:

There is a temporal gap between taking an action and receiving feedback in the form of a reward or punishment.
Determining which specific actions were responsible for the observed outcome becomes challenging when there is delayed feedback.

Delayed Rewards:

When rewards are delayed, the agent must associate its past actions with future outcomes.
This temporal misalignment complicates the assignment of credit, as the consequences of an action may not be immediately evident.

Exploration vs. Exploitation:

The credit assignment problem is exacerbated by the exploration-exploitation trade-off.
If an agent is exploring new actions, it becomes challenging to assess the impact of those actions on the overall performance.

Credit Blurring:

Credit assignment can become ambiguous when multiple actions contribute to an outcome.
Determining the relative importance of each action in achieving a result is a non-trivial task.

5. Policy Gradients

PG algorithms optimize the parameters of a policy by following the gradients toward higher rewards. One popular class of PG algorithms called REINFORCE algorithms, was introduced back in 1992 by Ronald Williams.

Here is one common variant:

First, let the neural network policy play the game several times, and at each step, compute the gradients that would make the chosen action even more likely - but don't apply these gradients yet.
Once you have run several episodes, compute each action's advantage.
If an action's advantage is positive, it means that the action was probably good, and you want to apply the gradients computed earlier to make the action even more likely to be chosen in the future.
However, if the action's advantage is negative, it means the action was probably bad, and you want to apply the opposite gradients to make this action slightly less likely in the future.
Finally, compute the mean of all the resulting gradient vectors, and use it to perform a Gradient Descent step.

6. Markov Decision Processes

In the early 20th century, the mathematician Andrey Markov studied stochastic processes with no memory, called Markov chains. Such a process has a fixed number of states, and it randomly evolves from one state to another at each step. The probability for it to evolve from a state s to a state s' is fixed, and it depends only on the pair (s, s'), not on past states (this is why we say that the system has no memory).

Figure 7 shows an example of a Markov chain with four states:

Figure 7. Example of a Markov chain

Suppose that the process starts in state s0, and there is a 70% chance that it will remain in that state at the next step. Eventually, it is bound to leave that state and never come back because no other state points back to s0. If it goes to state s1 (20% probability), it will then most likely go to state s2 (90% probability), then immediately back to state s1 (with 100% probability). It may alternate a number of times between these two states, but eventually, it will fall into state s3 and remain there forever (this is a terminal state).

7. Q-Learning

Q-learning is a foundational reinforcement learning algorithm that enables agents to learn optimal strategies in an environment through trial and error. Central to the Q-table, which stores the expected cumulative rewards associated with each state-action pair. The algorithm iteratively updates these Q-values based on the agent's experiences, allowing it to learn a policy that maximizes long-term rewards.

Q-learning employs an exploration-exploitation strategy, striking a balance between trying new actions to discover their outcomes and exploiting known actions for immediate rewards.

Figure 8. Q-Learning

8. Deep Q-Learning

Deep Q-Learning represents a significant advancement in reinforcement learning by leveraging the power of deep neural networks to handle complex, high-dimensional state space. Building upon the foundation of Q-learning, DQN replaces the traditional Q-table with a deep neural network, allowing it to approximate the Q-function for a vast number of state-action pairs. This enables the algorithm to tackle challenging problems, such as playing video games or navigating dynamic environments, where traditional Q-learning might struggle.

DQN incorporates experience replay, a mechanism that stores and randomly samples past experiences, enhancing data efficiency and breaking temporal correlations. The combination of deep neural networks and Q-learning principles in DQN has propelled the field of deep reinforcement learning, opening doors to applications in robotics, autonomous systems, and beyond.

Figure 9. A comparison between Q-Learning and Deep Q-Learning

9. Conclusion:

Reinforcement learning stands at the forefront of AI innovation, unlocking new possibilities for intelligent decision-making in various domains. As researchers continue to overcome challenges and explore novel applications, the future promises a landscape where machines not only learn but adapt and excel in complex, dynamic environments.

The journey to the realm of reinforcement learning is an exciting exploration of the evolving capabilities of artificial intelligence.

Stay tuned for more interesting topics in machine learning!

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