# PPI-SVRG: Unifying Prediction-Powered Inference and Variance Reduction for Semi-Supervised Optimization

arXiv: https://arxiv.org/abs/2601.21470 · HTML: https://mlsanity.com/paper/2601.21470/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient](https://mlsanity.com/paper/1703.00102/) (2017)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Don't Jump Through Hoops and Remove Those Loops: SVRG and Katyusha are Better Without the Outer Loop](https://mlsanity.com/paper/1901.08689/) (2019)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Improved SVRG for Non-Strongly-Convex or Sum-of-Non-Convex Objectives](https://mlsanity.com/paper/1506.01972/) (2015)
- [DeepOBS: A Deep Learning Optimizer Benchmark Suite](https://mlsanity.com/paper/1903.05499/) (2019)
- [Prediction-Guided Active Experiments](https://mlsanity.com/paper/2411.12036/) (2024)

## Built on by (most cited first, 4 of 4)

- [OptiRepair: Closed-Loop Diagnosis and Repair of Supply Chain Optimization Models with LLM Agents](https://mlsanity.com/paper/2602.19439/) (2026)
- [Beyond the Training Distribution: Evaluating Predictions Under Distribution Shift and Selection Bias](https://mlsanity.com/paper/2606.14506/) (2026)
- [The Value of Information in Resource-Constrained Pricing](https://mlsanity.com/paper/2603.24974/) (2026)
- [ABC-Align: Prediction-Powered Alignment with Adaptive Bias Control](https://mlsanity.com/paper/2609.34374/) (2026)

## Abstract (arXiv)

We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates -- PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the neighborhood size. When predictions are perfect, we recover SVRG exactly. When predictions degrade, convergence remains stable but reaches a larger neighborhood. Experiments confirm the theory: PPI-SVRG reduces MSE by 43--52% under label scarcity on mean estimation benchmarks and improves test accuracy by 2.7--2.9 percentage points on MNIST with only 10% labeled data.