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

ArXiv.org · 2026-01-29

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.

Privacy-Preserving Reinforcement Learning from Human Feedback via Decoupled Reward Modeling

arXiv (Cornell University) · 2026-03-23

Preference-based fine-tuning has become an important component in training large language models, and the data used at this stage may contain sensitive user information. A central question is how to design a differentially private pipeline that is well suited to the distinct structure of reinforcement learning from human feedback. We propose a privacy-preserving framework that imposes differential privacy only on reward learning and derives the final policy from the resulting private reward model. Theoretically, we study the suboptimality gap and show that privacy contributes an additional additive term beyond the usual non-private statistical error. We also establish a minimax lower bound and show that the dominant term changes with sample size and privacy level, which in turn characterizes regimes in which the upper bound is rate-optimal up to logarithmic factors. Empirically, synthetic experiments confirm the scaling predicted by the theory, and experiments on the Anthropic HH-RLHF dataset using the Gemma-2B-IT model show stronger private alignment performance than existing differentially private baseline methods across privacy budgets.

Privacy-Preserving Reinforcement Learning from Human Feedback via Decoupled Reward Modeling

arXiv (Cornell University) · 2026-03-23

Preference-based fine-tuning has become an important component in training large language models, and the data used at this stage may contain sensitive user information. A central question is how to design a differentially private pipeline that is well suited to the distinct structure of reinforcement learning from human feedback. We propose a privacy-preserving framework that imposes differential privacy only on reward learning and derives the final policy from the resulting private reward model. Theoretically, we study the suboptimality gap and show that privacy contributes an additional additive term beyond the usual non-private statistical error. We also establish a minimax lower bound and show that the dominant term changes with sample size and privacy level, which in turn characterizes regimes in which the upper bound is rate-optimal up to logarithmic factors. Empirically, synthetic experiments confirm the scaling predicted by the theory, and experiments on the Anthropic HH-RLHF dataset using the Gemma-2B-IT model show stronger private alignment performance than existing differentially private baseline methods across privacy budgets.

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

SSRN Electronic Journal · 2026-01-01

Online Tensor Inference

Operations Research · 2026-02-09

From Big Data to Real-Time Decisions: Online Tensor Inference Modern digital platforms, from e-commerce and online advertising to mobile health, generate massive streams of high-dimensional data that must be analyzed in real time. In their paper “Online Tensor Inference,” Xin Wen, Will Wei Sun, and Yichen Zhang develop a new statistical framework that enables both efficient learning and rigorous inference for streaming tensor data. The authors propose an online low-rank tensor estimation method based on stochastic gradient descent that processes observations sequentially without storing historical data, overcoming the memory and scalability limitations of traditional offline approaches. Beyond estimation, the paper introduces a novel online debiasing technique that delivers valid confidence intervals and hypothesis tests on the fly without data splitting. Theoretical results establish near-minimax-optimal convergence rates and asymptotic normality for general linear functionals of tensors. Together, these advances provide a principled foundation for real-time, statistically grounded decision making in fast-changing, data-rich environments.

Policy-Aware Design of Large-Scale Factorial Experiments

ArXiv.org · 2026-04-09

Digital firms routinely run many online experiments on shared user populations. When product decisions are compositional, such as combinations of interface elements, flows, messages, or incentives, the number of feasible interventions grows combinatorially, while available traffic remains limited. Overlapping experiments can therefore generate interaction effects that are poorly handled by decentralized A/B testing. We study how to design large-scale factorial experiments when the objective is not to estimate every treatment effect, but to identify a high-performing policy under a fixed experimentation budget. We propose a two-stage design that centralizes overlapping experiments into a single factorial problem and models expected outcomes as a low-rank tensor. In the first stage, the platform samples a subset of intervention combinations, uses tensor completion to infer performance on untested combinations, and eliminates weak factor levels using estimated marginal contributions. In the second stage, it applies sequential halving to the surviving combinations to select a final policy. We establish gap-independent simple-regret bounds and gap-dependent identification guarantees showing that the relevant complexity scales with the degrees of freedom of the low-rank tensor and the separation structure across factor levels, rather than the full factorial size. In an offline evaluation based on a product-bundling problem constructed from 100 million Taobao interactions, the proposed method substantially outperforms one-shot tensor completion and unstructured best-arm benchmarks, especially in low-budget and high-noise settings. These results show how centralized, policy-aware experimentation can make combinatorial product design operationally feasible at platform scale.

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

Open MIND · 2026-01-29

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.

Do More Predictions Improve Statistical Inference? Filtered Prediction-Powered Inference

Open MIND · 2026-02-11

Recent advances in artificial intelligence have enabled the generation of large-scale, low-cost predictions with increasingly high fidelity. As a result, the primary challenge in statistical inference has shifted from data scarcity to data reliability. Prediction-powered inference methods seek to exploit such predictions to improve efficiency when labeled data are limited. However, existing approaches implicitly adopt a use-all philosophy, under which incorporating more predictions is presumed to improve inference. When prediction quality is heterogeneous, this assumption can fail, and indiscriminate use of unlabeled data may dilute informative signals and degrade inferential accuracy. In this paper, we propose Filtered Prediction-Powered Inference (FPPI), a framework that selectively incorporates predictions by identifying a data-adaptive filtered region in which predictions are informative for inference. We show that this region can be consistently estimated under a margin condition, achieving fast rates of convergence. By restricting the prediction-powered correction to the estimated filtered region, FPPI adaptively mitigates the impact of biased or noisy predictions. We establish that FPPI attains strictly improved asymptotic efficiency compared with existing prediction-powered inference methods. Numerical studies and a real-data application to large language model evaluation demonstrate that FPPI substantially reduces reliance on expensive labels by selectively leveraging reliable predictions, yielding accurate inference even in the presence of heterogeneous prediction quality.

Do More Predictions Improve Statistical Inference? Filtered Prediction-Powered Inference

ArXiv.org · 2026-02-11

Recent advances in artificial intelligence have enabled the generation of large-scale, low-cost predictions with increasingly high fidelity. As a result, the primary challenge in statistical inference has shifted from data scarcity to data reliability. Prediction-powered inference methods seek to exploit such predictions to improve efficiency when labeled data are limited. However, existing approaches implicitly adopt a use-all philosophy, under which incorporating more predictions is presumed to improve inference. When prediction quality is heterogeneous, this assumption can fail, and indiscriminate use of unlabeled data may dilute informative signals and degrade inferential accuracy. In this paper, we propose Filtered Prediction-Powered Inference (FPPI), a framework that selectively incorporates predictions by identifying a data-adaptive filtered region in which predictions are informative for inference. We show that this region can be consistently estimated under a margin condition, achieving fast rates of convergence. By restricting the prediction-powered correction to the estimated filtered region, FPPI adaptively mitigates the impact of biased or noisy predictions. We establish that FPPI attains strictly improved asymptotic efficiency compared with existing prediction-powered inference methods. Numerical studies and a real-data application to large language model evaluation demonstrate that FPPI substantially reduces reliance on expensive labels by selectively leveraging reliable predictions, yielding accurate inference even in the presence of heterogeneous prediction quality.

Policy-Aware Design of Large-Scale Factorial Experiments

arXiv (Cornell University) · 2026-04-09

Digital firms routinely run many online experiments on shared user populations. When product decisions are compositional, such as combinations of interface elements, flows, messages, or incentives, the number of feasible interventions grows combinatorially, while available traffic remains limited. Overlapping experiments can therefore generate interaction effects that are poorly handled by decentralized A/B testing. We study how to design large-scale factorial experiments when the objective is not to estimate every treatment effect, but to identify a high-performing policy under a fixed experimentation budget. We propose a two-stage design that centralizes overlapping experiments into a single factorial problem and models expected outcomes as a low-rank tensor. In the first stage, the platform samples a subset of intervention combinations, uses tensor completion to infer performance on untested combinations, and eliminates weak factor levels using estimated marginal contributions. In the second stage, it applies sequential halving to the surviving combinations to select a final policy. We establish gap-independent simple-regret bounds and gap-dependent identification guarantees showing that the relevant complexity scales with the degrees of freedom of the low-rank tensor and the separation structure across factor levels, rather than the full factorial size. In an offline evaluation based on a product-bundling problem constructed from 100 million Taobao interactions, the proposed method substantially outperforms one-shot tensor completion and unstructured best-arm benchmarks, especially in low-budget and high-noise settings. These results show how centralized, policy-aware experimentation can make combinatorial product design operationally feasible at platform scale.