# Random directions stochastic approximation with deterministic perturbations

arXiv: https://arxiv.org/abs/1808.02871 · HTML: https://mlsanity.com/paper/1808.02871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Generalized Random Direction Newton Algorithms for Stochastic Optimization](https://mlsanity.com/paper/2602.19893/) (2026)

## Abstract (arXiv)

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.