2020/02/21 by Filip Hanzely, Nikita Doikov, Hanzely, Filip +5 · 6 citations
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2002.09526
openalex publication_date 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function f. Our method can be seen both as a \em stochastic extension of the cubically-regularized Newton method of Nesterov and Polyak (2006), and a \em second-order enhancement of stochastic subspace descent of Kozak et al. (2019). We prove that as we vary the minibatch size, the global convergence rate of SSCN interpolates between the rate of stochastic coordinate descent (CD) and the rate of cubic regularized Newton, thus giving new insights into the connection between first and second-order methods. Remarkably, the local convergence rate of SSCN matches the rate of stochastic subspace descent applied to the problem of minimizing the quadratic function \frac12 (x-x^*)^\top ∇2f(x^*)(x-x^*), where x^* is the minimizer of f, and hence depends on the properties of f at the optimum only. Our numerical experiments show that SSCN outperforms non-accelerated first-order CD algorithms while being competitive to their accelerated variants.