5 papers
Finding Simple Proofs for First-Order Optimization
Daniel Berg Thomsen, Manu Upadhyaya, Baptiste Goujaud +2
Progress in mathematics often requires more than a certificate of truth: it requires proof structures that are transparent, checkable, and reusable. Automated systems can increasin…
Provable non-accelerations of the heavy-ball method
Baptiste Goujaud, Adrien Taylor, Aymeric Dieuleveut
In this work, we show that the heavy-ball ($\HB$) method provably does not reach an accelerated convergence rate on smooth strongly convex problems. More specifically, we show that…
Gradient Descent on Logistic Regression: Do Large Step-Sizes Work with Data on the Sphere?
Si Yi Meng, Baptiste Goujaud, Antonio Orvieto +1
Gradient descent (GD) on logistic regression has many fascinating properties. When the dataset is linearly separable, it is known that the iterates converge in direction to the max…
Open Problem: Two Riddles in Heavy-Ball Dynamics
Baptiste Goujaud, Adrien Taylor, Aymeric Dieuleveut
This short paper presents two open problems on the widely used Polyak's Heavy-Ball algorithm. The first problem is the method's ability to exactly \textit{accelerate} in dimension…
Counter-examples in first-order optimization: a constructive approach
Baptiste Goujaud, Aymeric Dieuleveut, Adrien Taylor
While many approaches were developed for obtaining worst-case complexity bounds for first-order optimization methods in the last years, there remain theoretical gaps in cases where…