# Stochastic Optimization Algorithms for Problems with Controllable Biased Oracles

arXiv: https://arxiv.org/abs/2306.07810 · HTML: https://mlsanity.com/paper/2306.07810/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles](https://mlsanity.com/paper/2408.11084/) (2024)

## Abstract (arXiv)

Motivated by emerging applications in machine learning, we consider an optimization problem in a general setting in which the gradient of the objective function is available via a biased stochastic oracle. We assume a bias-control parameter can reduce the bias magnitude; however, a lower bias requires more computation/samples. For instance, in two applications on stochastic composition optimization and policy optimization for infinite-horizon Markov decision processes, we show that the bias follows a power law and exponential decay, respectively, as functions of their corresponding bias control parameters. For problems with such gradient oracles, the paper proposes stochastic algorithms that adjust the bias-control parameter throughout the iterations. We analyze the nonasymptotic performance of the proposed algorithms in the nonconvex regime and establish their sample or bias-control computation complexities to obtain a stationary point in expectation or with high probability. Finally, we numerically evaluate the performance of the proposed algorithms over three applications.