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A Strengthened Conjecture on the Minimax Optimal Constant Stepsize for Gradient Descent
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Drori and Teboulle [4] conjectured that the minimax optimal constant stepsize for N steps of gradient descent is given by the stepsize that balances performance on Huber and quadra…
Scalable Projection-Free Optimization Methods via MultiRadial Duality Theory
Thabo Samakhoana, Benjamin Grimmer
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be che…
Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps
Benjamin Grimmer, Kevin Shu, Alex L. Wang
This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered…
Accelerated Gradient Descent via Long Steps
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent's textbook convergence guarantees can be improved by c…