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Vincent Roulet
Integration Methods and Optimization Algorithms
Damien Scieur, Vincent Roulet, Francis Bach, Alexandre d'Aspremont
Neural Information Processing Systems http://nips.cc/
Sharpness, Restart and Acceleration
Vincent Roulet, Alexandre d'Aspremont
The ลojasiewicz inequality shows that sharpness bounds on the minimum of convex optimization problems hold almost generically. Sharpness directly controls the performance of restart schemes, as observed by Nemirovskii and Nesterov [1985]. The constants quantifying error bounds are of course unobservable, but we show that optimal restart strategies are robust, and searching for the best scheme only increases the complexity by a logarithmic factor compared to the optimal bound. Overall then, restart schemes generically accelerate accelerated methods.
A Smoother Way to Train Structured Prediction Models
Venkata Krishna Pillutla, Vincent Roulet, Sham M. Kakade, Zaid Harchaoui
Neural Information Processing Systems http://nips.cc/
A Smoother Way to Train Structured Prediction Models
Venkata Krishna Pillutla, Vincent Roulet, Sham M. Kakade, Zaid Harchaoui
Neural Information Processing Systems http://nips.cc/
Integration Methods and Optimization Algorithms
Damien Scieur, Vincent Roulet, Francis Bach, Alexandre d'Aspremont
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. Compared with recent advances in this vein, the differential equation considered here is the basic gradient flow, and we derive a class of multi-step schemes which includes accelerated algorithms, using classical conditions from numerical analysis. Multi-step schemes integrate the differential equation using larger step sizes, which intuitively explains the acceleration phenomenon.
Sharpness, Restart and Acceleration
Vincent Roulet, Alexandre d'Aspremont
Neural Information Processing Systems http://nips.cc/