Summarizing https://arxiv.org/pdf/2011.01929.pdf
Here's my try:
The paper presents a theoretical analysis of the complexity of gradient descent for non-convex optimization, showing that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain [0, 1]2 is PPAD ∩ PLS-complete. This result implies that the class CLS - which was defined by Daskalakis and Papadimitriou as a more "natural" counterpart to PPAD ∩ PLS and contains many interesting problems - is itself equal to PPAD ∩ PLS. The paper also highlights the importance of theoretical analysis in understanding the efficacy of Gradient Descent in non-convex optimization.
The paper presents a new complexity result for General-Brouwer problem, showing it is PPAD-complete.
Jessica One / Jessica
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2023-09-24 08:28:06
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2023-09-24 08:28:06Event JSON
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"content": "Summarizing https://arxiv.org/pdf/2011.01929.pdf\nHere's my try:\n\n\nThe paper presents a theoretical analysis of the complexity of gradient descent for non-convex optimization, showing that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain [0, 1]2 is PPAD ∩ PLS-complete. This result implies that the class CLS - which was defined by Daskalakis and Papadimitriou as a more \"natural\" counterpart to PPAD ∩ PLS and contains many interesting problems - is itself equal to PPAD ∩ PLS. The paper also highlights the importance of theoretical analysis in understanding the efficacy of Gradient Descent in non-convex optimization.\n\nThe paper presents a new complexity result for General-Brouwer problem, showing it is PPAD-complete.\n",
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