  # What is the difference between V learning and Q-learning?

What is the difference between V learning and Q-learning?

Artificial Intelligence & Machine Learning

More details

###### Diagram showing the components in a typical Reinforcement Learning (RL) system. Thus, an agent takes actions in an environment which is interpreted into a reward and a representation of the state which is fed back into the agent. Incorporates other CC0 work: https://openclipart.org/detail/202735/eye-side-viewhttps://openclipart.org/detail/191072/blue-robot and https://openclipart.org/detail/246662/simple-maze-puzzle

Q-Learning, a form of model-free reinforcement learning (RL), was introduced in 1989 by Christopher Watkins as part of his PhD thesis. It was a significant advancement in the field of machine learning, particularly in the context of RL, where the goal is to learn a policy to act optimally in a Markov Decision Process (MDP) environment.

#### Calculation

Q-Learning seeks to learn a function Q(s, a), representing the quality (or Q-value) of taking an action ‘a’ in a state ‘s’. The Q-values are updated using the Bellman equation:

Where:

#### Usefulness

Q-Learning is useful in scenarios where the model of the environment is unknown. It has been applied in various domains like robotics, game playing, control systems, etc. Its ability to learn optimal policies without requiring a model of the environment makes it a powerful tool in RL.

### V-Learning: History, Calculation, and Usefulness

#### History

Value Iteration is a fundamental method in reinforcement learning and dynamic programming. Moreover, dates back to the early work of Richard Bellman in the 1950s, particularly his development of the Bellman Equation.

The Bellman equation is classified as a functional equation, because solving it means finding the unknown function , which is the value function. Specifically Value Iteration becomes highly useful as a computational method used to find the optimal policy for a Markov decision process (MDP).

##### A Kalman filter as a Hidden Markov model .

A Markov Decision Process (MDP) becomes extensively in decision-making and optimization problems. However, particularly in the field of operations research. It is characterized by its ability to provide a framework for modeling decisions in environments that are both stochastic and dynamic. An MDP is defined by four key components: a set of states (S), a set of actions (A), a transition function (P), and a reward function (R). The states represent different scenarios or configurations that an agent or decision-maker might encounter.

#### Moreover, actions become the choices available to the agent in each state.

The transition function, P, defines the probability of moving from one state to another, given a particular action. This probabilistic nature of state transitions captures the stochastic (random) element of the environment. The reward function, R, assigns a numerical value (reward or cost) to each transition between states, guiding the agent toward favorable outcomes. The goal in an MDP is to find a policy, which is a strategy or a set of rules that specifies the best action to take in each state, such that the cumulative reward over time is maximized. This framework is particularly powerful for modeling complex environments where future outcomes are uncertain and depend on both current decisions and past events, adhering to the Markov property which states that the future is independent of the past given the present.

#### Calculation

Value Iteration involves iteratively updating the value function V(s) for each state ‘s’, which represents the maximum expected cumulative reward starting from state ‘s’. The update rule is:

Where:

#### Usefulness

Value Iteration is particularly useful in environments where the model (transition probabilities and rewards) is known.

### Similarities and Differences between Q-Learning and Value Iteration

#### Similarities

1. Goal: Both aim to find an optimal policy in a reinforcement learning setting.
2. Use of Bellman Equation: Both use forms of the Bellman equation to update their respective functions (Q-function in Q-Learning and Value function in Value Iteration).
3. Learning Type: Value iteration & Q-Learning are both RL methods.

#### Differences?

1. Model Dependency: Q-Learning is model-free (doesn’t require knowledge of the environment’s dynamics), whereas Value Iteration is model-based and requires knowledge of state transition probabilities.
2. Function Type: Q-Learning learns the action-value function (Q-function), which is a function of both states and actions. In contrast, Value Iteration learns the value function (V-function), which is a function of states only.
3. Application: Q-Learning is more applicable in real-world scenarios where the model of the environment is unknown or complex. Value Iteration becomes used when the model of the environment is known and can be defined.
4. Computation: Q-Learning updates Q-values based on actual transitions and rewards observed, making it more suitable for online learning. Value Iteration, on the other hand, relies on the known model to update values. Usually in a batch or offline setting.
##### Agent-Umwelt-Diagram

In conclusion, while Q-Learning and Value Iteration share the common goal of determining optimal actions in a given state. Furthermore, their approaches differ significantly, particularly in terms of their reliance on the environmental model. Q-Learning’s model-free approach makes it more versatile for a wider range of practical applications, whereas Value Iteration’s model-based approach requires a comprehensive understanding of the environment’s dynamics.

Wikipedia

Wikipedia