Conventional wisdom holds that large-batch training is fundamentally incompatible with Reinforcement Learning (RL) - beyond a modest threshold, increasing batch sizes typically yields diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. We challenge this view by observing that non-stationarity is not a fixed property of RL, but evolves throughout training: early stages exhibit rapid behavioral shifts that demand small batches for plasticity, whereas late stages approach a quasi-stationary regime where large batches enable precise convergence. Motivated by this observation, we propose Adaptive Batch Scaling (ABS), that dynamically adjusts the effective batch size according to the stability of the learning policy. Central to ABS is Behavioral Divergence, a novel metric that quantifies policy non-stationarity by measuring action-level shifts between consecutive updates, which we use to scale batch size inversely to policy volatility. Integrated with the Parallelised Q-Network (PQN) algorithm and evaluated on the ALE benchmark, ABS seamlessly reconciles early-stage plasticity with late-stage stable convergence. Strikingly, contrary to conventional wisdom, our results reveal that the combination of larger networks and larger batch sizes achieves the best performance - a scaling behavior previously thought to be unattainable in RL, now unlocked through adaptive batch control.

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a single trajectory of the slow component, while the fast dynamics remain unobserved, making statistical learning challenging. Approaches based on partial differential equations (PDE), such as Fokker-Planck formulations, aim to characterize the evolution of probability densities, typically requiring dense space-time data or grid-based solvers. In contrast, we adopt a trajectory-based perspective and develop a data-driven framework for learning effective stochastic dynamics from a single observed path. We model the dynamics by coupled multiscale stochastic differential equations (SDEs) and first obtain a principled model reduction through stochastic averaging. Unlike generic model reduction techniques such as PCA, this respects the dynamical structure of the original system and explicitly incorporates the interaction between slow and fast scales. A central challenge, however, is that the reduced model depends on the invariant distribution of the fast process, which is a solution to an intractable and often unknown PDE. We introduce a novel learning framework that parameterizes the invariant distribution using normalizing flows, enabling expressive density modeling in the latent fast-variable space. The flow is trained end-to-end by optimizing a penalized likelihood objective induced by the reduced stochastic dynamics. Furthermore, we develop a Bayesian variational inference procedure for uncertainty quantification, employing a second normalizing flow to approximate the posterior distribution over model parameters. This yields a scalable approach to capturing epistemic uncertainty in multiscale systems.

As such, we prevent policies from merely exploiting heuristic rewards without improving the task reward.

Attribution maps are one of the most established tools to explain the functioning of computer vision models. They assign importance scores to input features, indicating how relevant each feature is for the prediction of a deep neural network.

For infinite-dimensional Gaussian process models, the prior draws almost surely fall out of the corresponding RKHS.

Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts improves reliability, while routing simpler queries to smaller, distilled models enhances efficiency. This motivates the problem of learning with multiple-expert deferral. This thesis presents a comprehensive study of this problem and the related problem of learning with abstention, supported by strong consistency guarantees. First, for learning with abstention (a special case of deferral), we analyze score-based and predictor-rejector formulations in multi-class classification. We introduce new families of surrogate losses and prove strong non-asymptotic, hypothesis set-specific consistency guarantees, resolving two existing open questions. We analyze both single-stage and practical two-stage settings, with experiments on CIFAR-10, CIFAR-100, and SVHN demonstrating the superior performance of our algorithms. Second, we address general multi-expert deferral in classification. We design new surrogate losses for both single-stage and two-stage scenarios and prove they benefit from strong $H$-consistency bounds. For the two-stage scenario, we show that our surrogate losses are realizable $H$-consistent for constant cost functions, leading to effective new algorithms. Finally, we introduce a novel framework for regression with deferral to address continuous label spaces. Our versatile framework accommodates multiple experts and various cost structures, supporting both single-stage and two-stage methods. It subsumes recent work on regression with abstention. We propose new surrogate losses with proven $H$-consistency and demonstrate the empirical effectiveness of the resulting algorithms.

Part qualification is crucial in additive manufacturing (AM) because it ensures that additively manufactured parts can be consistently produced and reliably used in critical applications. Part qualification aims at verifying that an additively manufactured part meets performance requirements; therefore, predicting the complex stress-strain behaviors of additively manufactured parts is critical. We develop a dynamic time warping (DTW)-transfer learning (TL) framework for additive manufacturing part qualification by transferring knowledge of the stress-strain behaviors of additively manufactured low-cost polymers to metals. Specifically, the framework employs DTW to select a polymer dataset as the source domain that is the most relevant to the target metal dataset. Using a long short-term memory (LSTM) model, four source polymers (i.e., Nylon, PLA, CF-ABS, and Resin) and three target metals (i.e., AlSi10Mg, Ti6Al4V, and carbon steel) that are fabricated by different AM techniques are utilized to demonstrate the effectiveness of the DTW-TL framework. Experimental results show that the DTW-TL framework identifies the closest match between polymers and metals to select one single polymer dataset as the source domain. The DTW-TL model achieves the lowest mean absolute percentage error of 12.41% and highest coefficient of determination of 0.96 when three metals are used as the target domain, respectively, outperforming the vanilla LSTM model without TL as well as the TL model pre-trained on four polymer datasets as the source domain.

Reasoning reinforcement learning (RL) has recently revealed a new scaling effect: test-time scaling. Thinking models such as R1 and o1 improve their reasoning accuracy at test time as the length of the reasoning context increases. However, compared with training-time scaling, test-time scaling is fundamentally limited by the limited context length of base models, which remains orders of magnitude smaller than the amount of tokens consumed during training. We revisit test-time enhancement techniques through the lens of scaling effect and introduce a unified framework of multi-dimensional test-time scaling to extend the capacity of test-time reasoning. Beyond conventional context-length scaling, we consider two additional dimensions: batch scaling, where accuracy improves with parallel sampling, and turn scaling, where iterative self-refinement enhances reasoning quality. Building on this perspective, we propose 3D test-time scaling, which integrates context, batch, and turn scaling. We show that: (1) each dimension demonstrates a test-time scaling effect, but with a bounded capacity; (2) combining all three dimensions substantially improves the reasoning performance of challenging testbeds, including IOI, IMO, and CPHO, and further benefits from human preference feedback; and (3) the human-in-the-loop framework naturally extends to a more open-ended domain, i.e., embodied learning, which enables the design of humanoid control behaviors.