We provide the first sharp characterization of the optimal first-order query complexity of agnostic active learning, and propose a new general active learning algorithm which achieves it. Remarkably, the optimal query complexity admits a leading term which is always strictly smaller than the sample complexity of passive supervised learning (by a factor proportional to the best-in-class error rate). This was not previously known to be possible. For comparison, in all previous general analyses, the leading term exhibits an additional factor, such as the disagreement coefficient or related complexity measures, and therefore only provides improvements over passive learning in restricted cases. The present work completely removes such factors from the leading term, implying that every concept class benefits from active learning in the non-realizable case. Whether such benefits are possible has been the driving question underlying the past two decades of research on the theory of agnostic active learning. This work finally settles this fundamental question.

Active learning (AL) reduces annotation costs by selecting the most informative samples based on both model sensitivity and predictive uncertainty. While sensitivity can be measured through parameter gradients in an unsupervised manner, predictive uncertainty can hardly be estimated without true labels especially for regression tasks, reducing the informativeness of actively selected samples. This paper proposes the concept of auxiliary data to aid the uncertainty estimation for regression tasks. With detailed theoretical analysis, we reveal that auxiliary data, despite potential distribution shifts, can provide a promising uncertainty surrogate when properly weighted. Such finding inspires our design of AGBAL, a novel AL framework that recalibrates auxiliary data losses through density ratio weighting to obtain reliable uncertainty estimates for sample selection. Extensive experiments show that AGBAL consistently outperforms existing approaches without auxiliary data across diverse synthetic and real-world datasets.

In recent developments in scientific machine learning (SciML), neural surrogate solvers for partial differential equations (PDEs) have become powerful tools for accelerating scientific computation for various science and engineering applications. However, training neural PDE solvers often demands a large amount of high-fidelity PDE simulation data, which are expensive to generate. Active learning (AL) offers a promising solution by adaptively selecting training data from the PDE settings-including parameters, initial and boundary conditions-that are expected to be most informative to help reduce this data burden. In this work, we introduce PaPQS, a Plug-and-Play Query Synthesis AL framework that synthesizes informative PDE settings directly in the continuous design space.

Virtual Screening (VS) is vital for drug discovery but struggles with low hit rates and high computational costs. While Active Learning (AL) has shown promise in improving the efficiency of VS, traditional methods rely on inflexible and handcrafted heuristics, limiting adaptability in complex chemical spaces, particularly in balancing molecular diversity and selection accuracy. To overcome these challenges, we propose GLARE1, a reinforced active learning framework that reformulates VS as a Markov Decision Process (MDP). Using Group Relative Policy Optimization (GRPO), GLARE dynamically balances chemical diversity, biological relevance, and computational constraints, eliminating the need for inflexible heuristics. Experiments show GLARE outperforms state-of-the-art AL methods, with a 64.8% average improvement in Enrichment Factors (EF). Additionally, GLARE enhances the performance of VS foundation models like DrugCLIP, achieving up to an 8-fold improvement in EF0.5% with as few as 15 active molecules.

Virtual Screening (VS) is vital for drug discovery but struggles with low hit rates and high computational costs. While Active Learning (AL) has shown promise in improving the efficiency of VS, traditional methods rely on inflexible and handcrafted heuristics, limiting adaptability in complex chemical spaces, particularly in balancing molecular diversity and selection accuracy. To overcome these challenges, we propose GLARE, a reinforced active learning framework that reformulates VS as a Markov Decision Process (MDP). Using Group Relative Policy Optimization (GRPO), GLARE dynamically balances chemical diversity, biological relevance, and computational constraints, eliminating the need for inflexible heuristics. Experiments show GLARE outperforms state-of-the-art AL methods, with a 64.8% average improvement in Enrichment Factors (EF). Additionally, GLARE enhances the performance of VS foundation models like DrugCLIP, achieving up to an 8-fold improvement in EF$_{0.5\\%}$

Active learning for continuous regression has lacked an acquisition function that targets epistemic uncertainty when the predictive distribution is multimodal: variance misses modal disagreement, and information-theoretic targets like BALD are designed for discrete outputs. We introduce a Two-Index framework that makes this separation explicit: one stochastic index selects among competing model hypotheses (epistemic source), while a second governs within-hypothesis randomness (aleatoric source). An entropy decomposition within the framework identifies the mutual information between the output and the epistemic index as a principled acquisition objective, and we prove this quantity vanishes as the model is trained on growing datasets, confirming that it captures exactly the uncertainty data can resolve. Because this mutual information is intractable for continuous outputs, we derive the Mutual Information Lower Bound (MI-LB) acquisition function, a closed-form approximation for Mixture Density Network ensembles. On benchmarks featuring multimodal systems, MI-LB matches or beats every baseline evaluated and is the only method to do so consistently -- geometric and Fisher-based baselines compete only when the input space already encodes the multimodality, and collapse otherwise.

Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations. For sequential decision-making, such as active learning and Bayesian optimization, acquisition should prioritize epistemic uncertainty about the latent signal rather than irreducible aleatoric observation noise. We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone, even when that distribution is known exactly. We then exploit a distinctive advantage of PFNs: because the synthetic data-generating process is under our control, each task can contain an explicit latent signal and noise function, and the generator can provide query-level labels for both the noiseless target and the observation-noise variance. We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads. The observation-level predictive is induced by convolving the latent signal distribution with the learned noise model. Empirically, epistemic-only acquisition mitigates the failure mode of total-variance exploration in noisy and heteroscedastic settings. In matched comparisons, decoupled models usually improve over tuned observation-level baselines, with the clearest gains in HPO; in broader sweeps, a decoupled model obtains the best average rank in both HPO and synthetic BO.

We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms for this problem with both modular and non-modular cost functions. In both cases, we prove that two simple greedy algorithms are not near-optimal but the best between them is near-optimal if the utility function satisfies pointwise submodularity and pointwise cost-sensitive submodularity respectively. This implies a combined algorithm that is near-optimal with respect to the optimal algorithm that uses half of the budget. We discuss applications of our theoretical results and also report experiments comparing the greedy algorithms on the active learning problem.

Progress in the field of machine learning has been fueled by the introduction of benchmark datasets pushing the limits of existing algorithms. Enabling the design of datasets to test specific properties and failure modes of learning algorithms is thus a problem of high interest, as it has a direct impact on innovation in the field. In this sense, we introduce Synbols -- Synthetic Symbols -- a tool for rapidly generating new datasets with a rich composition of latent features rendered in low resolution images. Synbols leverages the large amount of symbols available in the Unicode standard and the wide range of artistic font provided by the open font community. Our tool's high-level interface provides a language for rapidly generating new distributions on the latent features, including various types of textures and occlusions. To showcase the versatility of Synbols, we use it to dissect the limitations and flaws in standard learning algorithms in various learning setups including supervised learning, active learning, out of distribution generalization, unsupervised representation learning, and object counting.