关于Q Learning中Function Approximation的若干技术疑问

Let's break down your questions one by one—function approximation (FA) can feel abstract when you're only starting with linear examples, so it's totally normal to have these doubts:

1. Do we stop using Q-tables once we use Function Approximation? #

Absolutely. Traditional Q-tables work by explicitly storing a Q-value for every possible (state, action) pair, but this only works when the state space is small and discrete. When you switch to function approximation, you replace that lookup table with a function that computes Q(s,a) on the fly. For linear FA, that function looks like Q(s,a) = w · φ(s,a)—where φ(s,a) is your feature vector for the state-action pair, and w is the weight vector you optimize over. No more storing every (s,a) pair; you just keep the weights, which is way more efficient for large or continuous state spaces.

2. Beyond linear functions: What other types of FA are used? #

Linear FA is the easiest to learn, but it's far from the only option. Common nonlinear alternatives include:

• Deep Neural Networks (DNNs): The most popular choice these days (think DQN, Double DQN, etc.). You can feed raw state data (like pixel values from a game, or high-dimensional sensor readings) directly into a neural network, and it learns both the feature representation and Q-value approximation end-to-end.
• Kernel Methods: Techniques like Kernelized Q-Learning use kernel functions (e.g., RBF kernels) to implicitly map the original state space into a high-dimensional feature space, letting you model nonlinear relationships without manually designing features.
• Decision Trees/Random Forests: These split the state space into regions and assign Q-values to each region. They’re interpretable and work well for tabular or structured state data.

3. How to choose features—hardcoding vs. automatic generation? #

This depends entirely on your problem and the type of FA you’re using:

• Hardcoding features: Makes sense when you understand the problem well and the state space is low-dimensional. For example, in CartPole, you might manually pick features like the cart’s position, velocity, pole angle, and angular velocity. Hardcoding gives you control and is computationally cheap, but it relies on your domain knowledge—miss a critical feature, and your FA will perform poorly.
• Automatic feature generation: This is where nonlinear FA shines. Examples include:
  • Neural networks automatically learn hierarchical features from raw input (e.g., edges → shapes → objects in image-based tasks).
  • Kernel methods implicitly generate high-dimensional features via the kernel function, so you don’t have to define them explicitly.
  • Unsupervised techniques like autoencoders can pre-train feature representations before using them in Q-Learning.

As a general rule: Start with hand-designed features if your problem is simple and you know the key state variables. If your state space is high-dimensional, continuous, or you lack clear domain knowledge, go with an automatic feature learning approach like deep neural networks.

内容的提问来源于stack exchange，提问作者user2505650