Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methods
This provides a noise-adaptive accelerated optimization method for machine learning and AI practitioners, offering a first universal algorithm with global guarantees in second-order optimization.
The paper tackles the problem of minimizing second-order smooth, convex functions by proposing a universal and adaptive second-order method that achieves O(σ/√T) convergence with stochastic oracles and O(1/T^3) with deterministic oracles, without prior knowledge of oracle type or parameters.
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(σ/ \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $σ^2$, and improves its convergence to $O( 1 / T^3)$ with deterministic oracles, where $T$ is the number of iterations. Our method also interpolates these rates without knowing the nature of the oracle apriori, which is enabled by a parameter-free adaptive step-size that is oblivious to the knowledge of smoothness modulus, variance bounds and the diameter of the constrained set. To our knowledge, this is the first universal algorithm with such global guarantees within the second-order optimization literature.