# Questions tagged [proofs]

For questions that ask about or call for proofs for specific assertions, whether they be proofs of theorems or corollaries, proofs of concept through working implementation, counter proofs, or counter examples.

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### Why are the Bellman operators contractions?

In these slides, it is written \begin{align} \left\|T^{\pi} V-T^{\pi} U\right\|_{\infty} & \leq \gamma\|V-U\|_{\infty} \tag{9} \label{9} \\ \|T V-T U\|_{\infty} & \leq \gamma\|V-U\|_{\infty} \...
87 views

### Where do the characteristics of self-attention come into play in Linformer's proof that self-attention is low rank?

In Linformer's proof that self-attention is low rank in their paper, I don't see how it doesn't generalize to every matrix. They don't utilize any specifics of self-attention (the entire proof feels ...
903 views

### Is there a simple proof of the convergence of TD(0)?

Does anybody know a simple proof of the convergence of the TD(0) value function prediction algorithm?
122 views

### What is the proof that the branch and bound algorithm always finds optimal path in a graph?

I've been studying Branch and Bound's graph algorithm and I hear it always finds the optimal path because it uses previously found solutions to find others However, I haven't been able to find a ...
40 views

### Why does TD (0) converge to the MLE solution of the Markov model?

Why does TD (0) converge to the MLE solution of the Markov model? Let's take the Example 6.4 in Sutton and Barto's book as an example. Example 6.4: You are the Predictor Place yourself now in the ...
1k views

### Is there a proof to explain why XOR cannot be linearly separable?

Can someone explain to me with a proof or example why you can't linearly separate XOR (and therefore need a neural network, the context I'm looking at it in)? I understand why it's not linearly ...
17 views

### proof of convergence for the random forest algorithm

I am looking for the proof of convergence of the random forest algorithm. A cursory google search shows many, but I do not understand which version (original?) of the algorithm this is. Can you kindly ...
31 views

### How to show $\rho > 0$ when $\rho$ be minimum attainable from $y_n(W^{*T}X_n)$, where $W^*$ the vector that separates the data?

In the book Learning from Data written (by Abu Mostafa), we have the following exercise: Let $\rho$ be minimum attainable from $y_n(W^{*T}X_n)$ where $W^*$ is the vector that separates the data. Show ...
57 views

### What is the derivative of equation 1 in the paper "Conservative Q-Learning for Offline Reinforcement Learning"?

I am looking at the paper Conservative Q-Learning for Offline Reinforcement Learning, but I'm not sure how they proved theorem 3.1. Here is a screenshot of theorem 3.1. In the proof of theorem 3.1 ...
31 views

### How to prove importance sampling ratio is uncorrelated with action-value (or state-value) estimate?

In Sutton & Barto (2nd edition), the following is mentioned on page 150 (p. 172 of the pdf), section 7.4: the importance sampling ratio has expected value one (Section 5.9) and is uncorrelated ...
469 views

### Why does Q-learning converge to the optimal policy, even if the agent acts sub-optimally?

In Q-learning, during training, it doesn't matter how the agent selects actions. The algorithm always converges to the optimal policy. Why does this happen? What's the intuition?
31 views

101 views

### How to prove the formula of eligibility traces operator in reinforcement learning?

I don't understand how the formula in the red circle is derived. The screenshot is taken from this paper