All Questions
Tagged with proofs function-approximation
6 questions
4
votes
1
answer
285
views
Why policy improvement theorem can't be applied in case of function approximation?
Policy improvement theorem is proven as follows:
$$v_\pi(s) = \sum_{a \in A} \pi(a|s)q_\pi(a,s) \leq \max_{a \in A} q_\pi(a,s) = q_\pi(\pi'(s), s)$$
What step of the proof does not hold for function ...
- 143
1
vote
1
answer
178
views
Is there a mathematical proof of the universal approximation theorem for neural networks with binary weights?
Since the Universal approximation theorem shows that standard multilayer feedforward networks with as few as a single hidden layer, sufficient hidden units, and arbitrary bounded and nonconstant ...
- 33
2
votes
2
answers
514
views
Why is the equation $\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{Var} (\epsilon)$ true?
In the book An Introduction to Statistical Learning, the authors claim (equation 2.3, p. 19, chapter 2)
$$\mathbb{E} \left[ (Y - \hat{Y})^2 \right] = \left(f(X) - \hat{f}(X) \right)^2 + \operatorname{...
- 41.4k
2
votes
1
answer
54
views
Equivalence between expected parameter increments in "Off-Policy Temporal-Difference Learning with Function Approximation"
I am having a hard time understanding the proof of theorem 1 presented in the "Off-Policy Temporal-Difference Learning with Function Approximation" paper.
Let $\Delta \theta$ and $\Delta \...
- 23
31
votes
3
answers
18k
views
Where can I find the proof of the universal approximation theorem?
The Wikipedia article for the universal approximation theorem cites a version of the universal approximation theorem for Lebesgue-measurable functions from this conference paper. However, the paper ...
- 473
22
votes
3
answers
6k
views
Why doesn't Q-learning converge when using function approximation?
The tabular Q-learning algorithm is guaranteed to find the optimal $Q$ function, $Q^*$, provided the following conditions (the Robbins-Monro conditions) regarding the learning rate are satisfied
$\...
- 41.4k