Title: Prediction-Powered Semi-Supervised Learning with Online Power Tuning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Semi-Supervised Learning

Pseudo-Labeling

Online Learning

Prediction-Powered Inference

Debiasing
Abstract: Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator.
In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. 
This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models.
To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. 
We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes Prediction-Powered Semi-Supervised Learning (PP-SSL), which is a fresh direction for dealing with the classic challenge in semi-supervised learning: how to get the most out of many unlabeled samples when the labeled ones are scarce and expensive. Traditional approaches, for example simple pseudo-labeling or teacher-student frameworks, often run into trouble when the teacher model makes mistakes—especially for minority groups. Such errors in pseudo-labels can bias the learning process, causing the trained model to perform worse than one would expect, or even worse than using only the labeled data.\n\nThe authors build on the Prediction-Powered Inference (PPI) principle, where pseudo-labels are used both for labeled and unlabeled data in a way that the expected bias cancels out. In earlier work, the weighting between real and pseudo-labels—this λ parameter—was set offline, based on quantities like the variance of the labeled data and the accuracy of the teacher model. But these are usually unknown in practice.\n\nWhat makes PP-SSL special is the automatic, online adjustment of λ during training, using the AdaGrad algorithm. With this, the method finds a good balance between using real labels and pseudo-labels on the fly, without needing prior knowledge or manual tuning. The paper provides a theoretical analysis, showing that the new gradient estimator is unbiased and can achieve lower variance than the standard supervised gradients, leading to faster and more stable training, especially as the accuracy of the teacher improves or more unlabeled data becomes available.\n\nThe authors give thorough experiments, both on synthetic datasets (with carefully designed group imbalances) and on real-world datasets like California Housing and UTKFace for age estimation. The results show that PP-SSL consistently matches or outperforms standard SSL and previous PPI-based methods, especially in difficult cases where the teacher model is weak for certain subgroups. The approach also proves more robust in situations with distribution shifts between groups.\n\nFinally, the paper openly discusses limitations, such as the assumption that labeled and unlabeled samples are from the same distribution, and the current focus on fixed (not self-updating) teacher models. There is also attention to broader societal impacts, including fairness and robustness, and the need for further work to handle distributional shifts or to apply the method to more task types.\n\nIn summary, PP-SSL gives a principled, practical improvement for semi-supervised learning, making better use of unlabeled data while protecting against the classic pitfall of pseudo-label bias, especially in real-world, unbalanced datasets.\n\nSTRENGTHS AND WEAKNESSES:\nThe method reduces bias from bad pseudo-labels by tuning the λ parameter automatically during training, so you do not have to guess the right value beforehand. It works well even if the teacher model is not perfect, especially for smaller groups that often get ignored. The approach is backed by clear theoretical results, and also shows strong improvements in practical experiments with real and synthetic data. The algorithm is simple to use with existing optimizers like AdaGrad, so implementation is straightforward.\n\nThe main weakness, as the auhtors themselves note, is that the method assumes the labeled and unlabeled data are coming from the same distribution. As a minor weakness imo, most experiments are in regression settings. Considering classification tasks too would make the results stronger.\n\nQUESTIONS:\n1. The authors briefly mention self-training as an alternative to the teacher-student approach in SSL. Given that they propose an *online* learning approach within the teacher-student paradigm, onw wonders whether they can transfer their ideas to self-training (which is online by conceptualizatoin)? In particular, could you use the same model for both labeled and pseudo-labeled data, but iteratively update pseudo-labeled data only, while dynamically tuning λ as in PP-SSL to continuously adapt how much weight to give to pseudo-labels. In this case, could some of the convergence results be translated to self-training?\n\n2. \"A key limitation of our method, shared by many SSL methods, is the assumption that labeled and unlabeled data are drawn from the same distribution. ..... Extending our framework to handle such shifts is a natural direction for future work.\" Can the authros share some ideas of how thery are aiming to do that in the PP-SSL framework? https://www.jmlr.org/papers/v23/22-0541.html or (more general) https://arxiv.org/pdf/2505.07367 might be starting points for the iterative/online case.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes using prediction-powered inference (PPI) with online power tuning as a method for training models in a semi-supervised fashion. The basic idea is to optimize the PPI++ loss while running an online learning algorithm to set the power tuning parameter. This method is shown to outperform natural baselines on several datasets.\n\nSTRENGTHS AND WEAKNESSES:\nOnline power tuning is a very reasonable idea and finding ways to leverage it in a learning context (in combination with PPI debiasing techniques) is a great direction.\n\nMy main concern is about whether the empirical evaluation is sufficient. Semi-supervised learning is a very vast literature, with many methods and tricks developed over the years. The paper doesn't compare to any baselines developed for semi-supervised learning. Also, two of three experiments are with a simple linear model, so I'm guessing the pseudo-labels can't be that good. It would be convincing to see a comparison with state-of-the-art semi-supervised learning methods, with state-of-the-art predictive models, and with challenging datasets. I was also wondering why there was no comparison to Zhu et al. [14], since that paper operates in the same setting?\n\nSee \"questions\" for further comments.\n\nQUESTIONS:\n- In line 4: What do you mean by a factor of 4 being asymptotically equivalent? Having the same dependence on n? Also, where does the factor 4 come from?\n\n- In line 180: \"In contrast, PP-SSL provides a principled mechanism for leveraging unlabeled data that improves statistical efficiency without compromising correctness.\" What is correctness here? Don't we just care about optimizing the loss? If so, why do we care about not introducing bias?\n\n- Why did you decide to use AdaGrad (as opposed to a different stochastic optimization method)? Did you try any others?\n\n- I don't fully understand what the baseline methods are. What is \"teacher model f used for pseudo-labeling\"? Is this using f to label all unlabeled data and training a model on everything? Also, what is $\\lambda_{\\mathrm{PP}}^*$, seeing that your gradients depend on the current iterate (suggesting the tuning parameter should change at every step), unlike in PPI++ where there is a single distribution?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes Prediction-Powered Semi-Supervised Learning (PP-SSL), which incorporates the bias-correction principle of Prediction-Powered Inference (PPI) into the training process of semi-supervised learning (SSL). The method addresses the bias introduced by inaccurate pseudo-labels using an unbiased gradient estimator, and dynamically integrates it into training via an online learning algorithm. Theoretical analysis establishes finite-time convergence guarantees, and empirical results on synthetic, tabular, and image-based regression tasks demonstrate that PP-SSL outperforms both classical SSL methods and previous PPI-style approaches under distributional shift.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper presents an insightful extension of the Prediction-Powered Inference (PPI) framework from inference to optimization, specifically tailored for semi-supervised learning. Unlike prior work, it directly addresses the practical issue of pseudo-label bias during training and introduces a principled mechanism to mitigate it. The paper is generally well-organized, with clear motivation, formulation, and theoretical analysis.\n\nNevertheless, several questions remain regarding the generality of the datasets, the explanation of the teacher model, and the analysis of the learned λ. Please refer to the questions.\n\nQUESTIONS:\n1. The explanation of the teacher model is not clear. If I understand correctly, the paper focuses exclusively on fixed teacher models. It is unclear how the method would adapt to self-training or evolving pseudo-label generators, which are more common in modern SSL pipelines. I would appreciate it if the authors could clarify this point.\n\n2. While the online λ tuning is theoretically well-justified, there is limited qualitative analysis or visualization. Can the authors provide qualitative visualizations of λ values during training and how they correlate with pseudo-label error over time?\n\n3. Are there comparisons between online λ and fixed λ values to better illustrate the benefits of adaptive tuning?\n\n4. Have the authors considered extending PP-SSL to image classification tasks like CIFAR-10 or STL-10? The absence of popular benchmark datasets may limit direct comparison with standard SSL baselines. It would be helpful to demonstrate how PP-SSL behaves in more common classification settings.\n\nLIMITATIONS:\nThe authors assume that labeled and unlabeled data come from the same distribution, which can be a practical limitation. It would be helpful if the paper included a more discussion of this limitation.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes PPI-SSL, which extends the Prediction-Powered Inference (PPI) framework to the semi-supervised learning (SSL) setting. It introduces a way to balance the contributions of labeled and pseudo-labeled data by adaptively tuning a weighting parameter $\\lambda$, updated via AdaGrad.\n\nSTRENGTHS AND WEAKNESSES:\n## Strength\n- The paper is clearly written and well organized.\n- The proposed adaptive mechanism for $\\lambda$ is intuitive and practically motivated.\n\n## Weakness\n- I am not an expert in this area and not a theory person, but as far as I understand, the formulation of Eq. (3) has already appeared in prior works like PPI and Doubly-Robust Self-Training. So it is not accurate to say this paper newly “extends its core idea to semi-supervised learning (SSL) for model training.” At least that part is not new. The relatively novel contribution seems to be the AdaGrad-based update of $\\lambda$, which deserves clearer emphasis.\n- Lemma 3.1 assumes the gradient function is Lipschitz, which seems like a very strong assumption. I’m wondering how realistic this is for modern networks, and whether any regularization is applied to enforce it. (In practice, it’s more common to assume the model is Lipschitz rather than the gradient itself.)\n- It would be helpful to empirically verify Corollary 3.3 in a toy experiment, e.g., using a simple MLP where the bound involving $\\sigma$ can be computed. Also, is this bound used in practice to initialize $\\lambda$? If so, please clarify.\n\nQUESTIONS:\n- Please clarify what is truly novel in the paper beyond the AdaGrad update of \\lambda.\n- How realistic is the Lipschitz assumption in Lemma 3.1, and how is it enforced in practice?\n- Could you verify Corollary 3.3 empirically on a synthetic setting, and is it used to initialize \\lambda in real experiments?\n\nLIMITATIONS:\nLimitations are discussed in the paper, and there are no obvious societal concerns.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}