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# Questions tagged [function-approximation]

For questions related to the concept of function approximation. For example, questions that involve the use of a neural network (which is a function approximator) in the context of RL in order to approximate a value function or questions that are related to universal approximation theorems.

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### Why does the average-reward estimator for continuing tasks use the TD error?

In Sutton and Barto's RL book, section 10.3 describes how to use average reward $r(\pi)$ to define the quality of a policy, re-defining action-value function $q_\pi(s,a)$ and value function $v_\pi(s)$ ...
• 21
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### Could Softmax Action Selection be useful to solve an episodic task with more than 100000 possible states and 2000 actions?

I am new in the field of RL. I am trying to use tabular methods, Q-Learning for solving a problem that takes a lot of time for computation, so I would like to know if there are more efficient methods ...
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### Knowing the futility of discounting in continuing problems, how can we say discounting has no role in control problems with function approximation?

Sutton-Barto (Section 10.4, page 254): Based on the futility of discounting in continuing problems, how can we conclude that discounting has no role to play in control problems with function ...
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1 vote
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### Why is the step-size $\alpha_t = 1/t$ not appropriate for non-stationary function approximation?

Sutton-Barto (Section: Selecting Step-Size Parameters Manually, page: 222) The classical choice $\alpha_t = 1/t$, which produces sample averages in tabular MC methods, is not appropriate for TD ...
• 149
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### Unclear points for polynomial basis for function approximation [closed]

I have 3 questions for the following box from Sutton-Barto's RL book (page 211) on polynomial basis: Q1- Why is each $x_i$ an "order-n" polynomial? I think this is wrong: in my opinion, ...
• 194
1 vote
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### What is the difference between the $Q_a$ calculated to update delta and those to select next action in the exploitation phase?

As the title suggests, I have a doubt about the computation of the $Q_a$ used to update the delta and the $Q_a$ used to select the next action in the exploitation phase, as shown below (source of ...
62 views

### Watkins' Q(λ) with function approximation: why is gradient not considered when updating eligibility traces for the exploitation phase?

I'm implementing the Watkins' Q(λ) algorithm with function approximation (in 2nd edition of Sutton & Barto). I am very confused about updating the eligibility traces because, at the beginning of ...
33 views

### Alternatives to neural networks for function approximation in Q learning?

I want to know if there is anything other than neural networks (or Deep NNs) that I can effectively use to perform function approximation? I am asking this w.r.t to the use of approximators in Q ...
72 views

### What do we actually 'approximate' when dealing with large state spaces in Q-learning?

I realized that my state space is very large in size. I had planned to use tabular Q-learning (Bellman equation to update the $Q(s, a)$ after each action taken). But this 'large space' realization has ...
56 views

### In TD(0) with linear function approximation, why is the gradient of $\hat v(S^{\prime}, \mathbf w)$ wrt parameters $\mathbf w$ not considered?

I am reading these slides. On page 38, the update for the parameters for the linear function approximation of TD(0) is given. I have a doubt regarding this. The cost function (RMSE) is given on page ...
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1 vote
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### Does there exist functions for which the necessary number of nodes in a shallow neural network tends to infinity as approximation error tends to 0?

The Universal Approximation Theorem states (roughly) that any continuous function can be approximated to within an arbitrary precision $\varepsilon>0$ by a feedforward neural network with one ...
30 views

### Uniform representation of images for machine learning

I'm new to the field of ML so please bear with me while I try to explain what I'm looking for. In most machine learning pipelines that deal with images there is a requirement to "normalize" ...
1 vote
55 views

### Why use sin/cos to give periodicity in time series prediction

In this tutorial https://www.tensorflow.org/tutorials/structured_data/time_series#feature_engineering (scroll down a bit to "Time" heading), they take the sin/cos of the time index, and give ...
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1 vote
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### Is it true that real world data is highly discontinuous?

A function $f$ is said to be continuous at a point $c$ if it satisfies three properties: Should be defined at the point $c$ Left and right-hand limits at $c$ must be equal i.e., the limit must exist ...
• 3,059
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### Is Reinforcement Learning capable of learning complex functions (such as producing a 3d model given an image)?

I want to build an AI that can convert an image of a subject into an anatomically accurate 3D model. To do this, I was thinking of adapting the following code for Deep Deterministic Policy Gradient: ...
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### Can reinforcement learning be used to learn an unknown analytical function (for example, $y = x^2$ )?

Are there any examples for RL to learn analytical functions (for example, $y=x^2$)? What are the considerations when constructing the environment? Are there any literature that analyzes the difficulty/...
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1 vote
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### Recursive Least squares (RLS) for mini batch

For my application I am considering a learning problem where I simulate a bunch of episodes say '$n$' first, and than carry out the recursive least squares update. Similar to $TD(1)$. I know that RLS ...
1 vote
22 views

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1 vote
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### Is there any thumb rule on the cardinality of state space in order to use the parameterized function to estimate value functions?

Value functions for a given MDP can be learned in at least two ways by experience. The first way (tabular calculation) is generally used in the case of state spaces that are small enough. The second ...
• 3,059
1 vote
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### Trying to understand why nonlinearity is important for neural networks by analogy

Is the reason why linear activation functions are usually pretty bad at approximating functions the same reason why combinations of hermitian polynomials or combinations of sines and cosines are ...
• 39
101 views

### Why can a neural network use more than one activation function?

From trying to understand neural networks better, I've come upon a tentative notion that an activation function aims to build a function it's approximating via linear combinations with biases and ...
• 39
282 views

### Why the optimal Bellman operator of a Q-function can be approximated by a single point

I am currently studying reinforcement learning, especially DQN. In DQN, learning proceeds in such a way as to minimize the norm (least-squares, Huber, etc.) of the optimal Bellman equation and the ...
• 97
1 vote
36 views

### How can "any process you can imagine" be thought of as function computation?

I stumbled upon this passage when reading this guide. Universality theorems are a commonplace in computer science, so much so that we sometimes forget how astonishing they are. But it's worth ...
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### How to find good features for a linear function approximation in RL with large discrete state set?

I've recently read much about feature engineering in continuous (uncountable) feature spaces. Now I am interested what methods exist in the setting of large discrete state spaces. For example consider ...
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85 views

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### Is there a possibility that there is no relationship between some inputs and outputs?

I'm doing machine learning projects. I took a look at many datasets I worked with, mostly there are already famous datasets that everyone uses. Let's say I decided to make my own dataset. Is there a ...
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Consider some MDP with no terminal state. We can apply bootstrapping methods (like TD(0)) to learn in these cases no problem, but in policy gradient algorithms that have only a simple monte carlo ...
115 views

### Which neural network can approximate the function $y = x^2 + b$?

I am new to ANN. I am trying out several 'simple' algorithms to see what ANN can (or cannot) be used for and how. I played around with Conv2d once and had it recognize images successfully. Now I am ...
208 views

### Why does reinforcement learning using a non-linear function approximator diverge when using strongly correlated data as input?

While reading the DQN paper, I found that randomly selecting and learning samples reduced divergence in RL using a non-linear function approximator (e.g a neural network). So, why does Reinforcement ...
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I got this slide from CMU's lecture notes. The $x_i$s on the right are inputs and the $w_i$s are weights that get multiplied together then summed up at each hidden layer node. So I'm assuming this is ...