Adaptive Gradient Methods for Constrained Convex Optimization and Variational Inequalities
This work provides incremental improvements in optimization algorithms for machine learning and related fields by automating learning rate adjustments and handling constraints.
The authors introduced adaptive first-order methods, including AdaACSA and AdaAGD+, for constrained convex optimization and variational inequalities, achieving nearly-optimal convergence rates for smooth and non-smooth functions with stochastic gradients without prior knowledge of function parameters.
We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both smooth and non-smooth functions, even when they only have access to stochastic gradients. In addition, they do not require any prior knowledge on how the objective function is parametrized, since they automatically adjust their per-coordinate learning rate. These can be seen as truly accelerated Adagrad methods for constrained optimization. We complement them with a simpler algorithm AdaGrad+ which enjoys the same features, and achieves the standard non-accelerated convergence rate. We also present a set of new results involving adaptive methods for unconstrained optimization and monotone operators.