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1 vote
0 answers
69 views

Curve fitting with "rough" loss functions

Many real-valued classification and regression problems can be framed as minimization in the following way. Setup: Let $\Theta \in \mathbb{R}^p$ be the parameter space that we are searching over. For ...
Simon Kuang's user avatar
1 vote
0 answers
98 views

Limit cycles or stable solutions for k-dimensional piece-wise linear ODEs

As a branch of reinforcement learning, restless multi-armed bandits have been shown PSPACE-HARD but Whittle has offered an implementable solution called the Whittle Index Policy. Weber and Weiss ...
Keqin Liu 'Kevin''s user avatar
9 votes
1 answer
2k views

Is There an Induction-Free Proof of the 'Be The Leader' Lemma?

This lemma is used in the context of online convex optimisation. It is sometimes called the 'Be the Leader Lemma'. Lemma: Suppose $f_1,f_2,\ldots,f_N$ are real valued functions with the same ...
Daron's user avatar
  • 1,915
7 votes
1 answer
914 views

Universal approximation theorem for whole $\mathbb{R}^d$

The well-known universal approximation theorem states that neural network with one hidden layer can approximate any continuous function on every compact subset of $\mathbb{R}^d$. My question is ...
almnagako's user avatar
  • 361
18 votes
0 answers
303 views

Profiles of very high dimensional functions

This question comes from trying to understand the recent success of deep neural nets. Neural networks just (crudely speaking) create a very complicated function of very many variables, and then ...
Igor Rivin's user avatar
  • 95.9k