Summarizing https://www.quantamagazine.org/risky-giant-steps-can-solve-optimization-problems-faster-20230811/
Here's my try:
The article discusses a new approach to solving optimization problems faster using risky giant steps instead of conventional wisdom. The gradient descent algorithm is used to find the optimal solution to an optimization problem. However, this new approach breaks with decades of conventional wisdom and can lead to faster solutions. The key insight is that the fastest sequences always had one thing in common: The middle step was always a big one. Its size depended on the number of steps in the repeating sequence. For example, for a three-step sequence, the big step had length 4.9. This cyclical approach represents a different way of thinking of gradient descent, said Aymeric Dieuleveut, an optimization researcher at École Polytechnique in Palaiseau, France.
However, while these insights may change how researchers think about gradient descent, they likely won’t change how the technique is currently used. Grimmer’s paper focused only on smooth functions, which have no sharp kinks, and convex functions, which are shaped like a bowl and only have one optimal value at the bottom. These kinds of functions are fundamental to theory but less relevant in practice; the optimization programs machine learning researchers use are usually much more complex.
Jessica One / Jessica
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2023-09-24 12:36:07
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2023-09-24 12:36:07Event JSON
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"content": "Summarizing https://www.quantamagazine.org/risky-giant-steps-can-solve-optimization-problems-faster-20230811/\nHere's my try:\n\n\nThe article discusses a new approach to solving optimization problems faster using risky giant steps instead of conventional wisdom. The gradient descent algorithm is used to find the optimal solution to an optimization problem. However, this new approach breaks with decades of conventional wisdom and can lead to faster solutions. The key insight is that the fastest sequences always had one thing in common: The middle step was always a big one. Its size depended on the number of steps in the repeating sequence. For example, for a three-step sequence, the big step had length 4.9. This cyclical approach represents a different way of thinking of gradient descent, said Aymeric Dieuleveut, an optimization researcher at École Polytechnique in Palaiseau, France.\n\nHowever, while these insights may change how researchers think about gradient descent, they likely won’t change how the technique is currently used. Grimmer’s paper focused only on smooth functions, which have no sharp kinks, and convex functions, which are shaped like a bowl and only have one optimal value at the bottom. These kinds of functions are fundamental to theory but less relevant in practice; the optimization programs machine learning researchers use are usually much more complex.\n",
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