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Algorithm
arXiv (Cornell University)
Random Function Descent
2023
Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. We establish a connection between Bayesian Optimization (i.e. average case optimization theory) and classical…
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Algorithm

Sequence of operations for a task

In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning).

In contrast, a heuristic is an approach to solving problems without well- defined correct or optimal results. For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation.

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arXiv (Cornell University)
Random Function Descent
2023
Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. We establish a connection between Bayesian Optimization (i.e. average case optimization theory) and classical optimization using a 'stochastic Taylor approximation' to rediscover gradient descent. This rediscovery yields a step size schedule we call Random Function Descent (RFD), which, in contrast to classical derivations, is scale invariant. Furthermore, our analys…
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