We lay the theoretical foundation for automating optimizer design in gradient-based learning. Based on the greedy principle, we formulate the problem of designing optimizers and their hyperparameters as maximizing the instantaneous decrease in loss. By treating an optimizer as a function that translates loss gradient signals into parameter motions, the problem reduces to a family of convex optimization problems over the space of optimizers. Solving these problems under various constraints not only recovers a wide range of popular optimizers as closed-form solutions, but also produces the optimal hyperparameters of these optimizers with respect to the problems at hand. This enables a systematic approach to design optimizers and tune their hyperparameters dynamically according to the gradient statistics that are collected during the training process. Furthermore, this optimization of optimization can be performed dynamically during training.
Quantitative mode stability for the wave equation on the Kerr-Newman spacetime
Risk-Aware Objective-Based Forecasting in Inertia Management
Chainalysis: Geography of Cryptocurrency 2023
Periodicity in Cryptocurrency Volatility and Liquidity
Impact of Geometric Uncertainty on the Computation of Abdominal Aortic Aneurysm Wall Strain
Simulation-based Bayesian inference with ameliorative learned summary statistics -- Part I