# Adaptive Sequential Stochastic Optimization

arXiv: https://arxiv.org/abs/1610.01970 · HTML: https://mlsanity.com/paper/1610.01970/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2016.

## Built on by (most cited first, 8 of 8)

- [Stochastic Optimization under Distributional Drift](https://mlsanity.com/paper/2108.07356/) (2021)
- [An Accelerated Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothness](https://mlsanity.com/paper/2409.19212/) (2024)
- [A Nearly Optimal Single Loop Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothness](https://mlsanity.com/paper/2412.20017/) (2024)
- [Maximum Likelihood With a Time Varying Parameter](https://mlsanity.com/paper/2302.14529/) (2023)
- [A Novel Theoretical Framework for Exponential Smoothing](https://mlsanity.com/paper/2403.04345/) (2024)
- [Distributed Fractional Bayesian Learning for Adaptive Optimization](https://mlsanity.com/paper/2404.11354/) (2024)
- [Rate Analysis of Coupled Distributed Stochastic Approximation for Misspecified Optimization](https://mlsanity.com/paper/2404.13669/) (2024)
- [Simultaneous Learning and Optimization via Misspecified Saddle Point Problems](https://mlsanity.com/paper/2510.05241/) (2025)

## Abstract (arXiv)

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are solved by sequentially applying a selected optimization algorithm, such as stochastic gradient descent (SGD), based on drawing a number of samples in order to carry the iterations. Two tracking criteria are introduced to evaluate approximate minimizer quality: one based on being accurate with respect to the mean trajectory, and the other based on being accurate in high probability (IHP). An estimate of a bound on the minimizers' change, combined with properties of the chosen optimization algorithm, is used to select the number of samples needed to meet the desired tracking criterion. A technique to estimate the change in minimizers is provided along with analysis to show that eventually the estimate upper bounds the change in minimizers. This estimate of the change in minimizers provides sample size selection rules that guarantee that the tracking criterion is met for sufficiently large number of time steps. Simulations are used to confirm that the estimation approach provides the desired tracking accuracy in practice, while being efficient in terms of number of samples used in each time step.