Random directions stochastic approximation with deterministic perturbations
This work addresses optimization challenges in machine learning by enhancing RDSA methods, though it appears incremental as it builds on existing techniques.
The authors tackled the problem of improving random directions stochastic approximation (RDSA) by introducing deterministic perturbation schemes, resulting in new first-order and second-order algorithms with provable convergence and derived convergence rates for specific optimization cases.
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate deterministic perturbations. We show that the gradient and/or Hessian estimates in the resulting algorithms with deterministic perturbations are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results.