Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks mechanisms for uncertainty quantification, leading to overconfident and poorly calibrated models. Bayesian variants of LoRA address this limitation, but at the cost of a significantly increased number of trainable parameters, partially offsetting the original efficiency gains. Additionally, these models are harder to train and may suffer from unstable convergence. In this work, we propose a novel parameter-efficient Bayesian LoRA, demonstrating that effective uncertainty quantification can be achieved in very low-dimensional parameter spaces. The proposed method achieves strong performance with improved calibration and generalization while maintaining computational efficiency. Our empirical findings show that, with the appropriate projection of the weight space: (1) uncertainty can be effectively modeled in a low-dimensional space, and (2) weight covariances exhibit low ranks.

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly through the connection to PAC-Bayes analysis. A second line of work has provided algorithm-specific generalization bounds through stability arguments or using mutual information bounds, and has shown that the bounds are tight in practice, but unfortunately these bounds do not directly apply to approximate Bayesian algorithms. This paper fills this gap by developing algorithm-specific stability based generalization bounds for a class of approximate Bayesian algorithms that includes VI, specifically when using stochastic gradient descent to optimize their objective. As in the non-Bayesian case, the generalization error is bounded by by expected parameter differences on a perturbed dataset. The new approach complements PAC-Bayes analysis and can provide tighter bounds in some cases. An experimental illustration shows that the new approach yields non-vacuous bounds on modern neural network architectures and datasets and that it can shed light on performance differences between variant approximate Bayesian algorithms.

Recent advances in imitation learning, particularly using generative modelling techniques like diffusion, have enabled policies to capture complex multi-modal action distributions. However, these methods often require large datasets and multiple inference steps for action generation, posing challenges in robotics where the cost for data collection is high and computation resources are limited. To address this, we introduce IMLE Policy, a novel behaviour cloning approach based on Implicit Maximum Likelihood Estimation (IMLE). IMLE Policy excels in low-data regimes, effectively learning from minimal demonstrations and requiring 38\% less data on average to match the performance of baseline methods in learning complex multi-modal behaviours. Its simple generator-based architecture enables single-step action generation, improving inference speed by 97.3\% compared to Diffusion Policy, while outperforming single-step Flow Matching. We validate our approach across diverse manipulation tasks in simulated and real-world environments, showcasing its ability to capture complex behaviours under data constraints. Videos and code are provided on our project page: https://imle-policy.github.io/.

Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling, but, in practice, suffers from error amplification, where errors in the model compound and generation quality degrades as sequence length $H$ increases. From a theoretical perspective, this phenomenon should not appear in well-specified settings, and, indeed, a growing body of empirical work hypothesizes that misspecification, where the learner is not sufficiently expressive to represent the target distribution, may be the root cause. Under misspecification -- where the goal is to learn as well as the best-in-class model up to a multiplicative approximation factor $C\geq 1$ -- we confirm that $C$ indeed grows with $H$ for next-token prediction, lending theoretical support to this empirical hypothesis. We then ask whether this mode of error amplification is avoidable algorithmically, computationally, or information-theoretically, and uncover inherent computational-statistical tradeoffs. We show: (1) Information-theoretically, one can avoid error amplification and achieve $C=O(1)$. (2) Next-token prediction can be made robust so as to achieve $C=\tilde O(H)$, representing moderate error amplification, but this is an inherent barrier: any next-token prediction-style objective must suffer $C=\Omega(H)$. (3) For the natural testbed of autoregressive linear models, no computationally efficient algorithm can achieve sub-polynomial approximation factor $C=e^{(\log H)^{1-\Omega(1)}}$; however, at least for binary token spaces, one can smoothly trade compute for statistical power and improve on $C=\Omega(H)$ in sub-exponential time. Our results have consequences in the more general setting of imitation learning, where the widely-used behavior cloning algorithm generalizes next-token prediction.

The horseshoe prior, a widely used handy alternative to the spike-and-slab prior, has proven to be an exceptional default global-local shrinkage prior in Bayesian inference and machine learning. However, designing tests with frequentist false discovery rate (FDR) control using the horseshoe prior or the general class of global-local shrinkage priors remains an open problem. In this paper, we propose a frequentist-assisted horseshoe procedure that not only resolves this long-standing FDR control issue for the high dimensional normal means testing problem but also exhibits satisfactory finite-sample FDR control under any desired nominal level for both large-scale multiple independent and correlated tests. We carry out the frequentist-assisted horseshoe procedure in an easy and intuitive way by using the minimax estimator of the global parameter of the horseshoe prior while maintaining the remaining full Bayes vanilla horseshoe structure. The results of both intensive simulations under different sparsity levels, and real-world data demonstrate that the frequentist-assisted horseshoe procedure consistently achieves robust finite-sample FDR control. Existing frequentist or Bayesian FDR control procedures can lose finite-sample FDR control in a variety of common sparse cases. Based on the intimate relationship between the minimax estimation and the level of FDR control discovered in this work, we point out potential generalizations to achieve FDR control for both more complicated models and the general global-local shrinkage prior family.

In this paper, we propose an improved online confidence bound for multinomial logistic (MNL) models and apply this result to MNL bandits, achieving variance-dependent optimal regret. Recently, Lee & Oh (2024) established an online confidence bound for MNL models and achieved nearly minimax-optimal regret in MNL bandits. However, their results still depend on the norm-boundedness of the unknown parameter $B$ and the maximum size of possible outcomes $K$. To address this, we first derive an online confidence bound of $O\left(\sqrt{d \log t} + B \right)$, which is a significant improvement over the previous bound of $O (B \sqrt{d} \log t \log K )$ (Lee & Oh, 2024). This is mainly achieved by establishing tighter self-concordant properties of the MNL loss and introducing a novel intermediary term to bound the estimation error. Using this new online confidence bound, we propose a constant-time algorithm, OFU-MNL++, which achieves a variance-dependent regret bound of $O \Big( d \log T \sqrt{ \smash[b]{\sum_{t=1}^T} \sigma_t^2 } \Big) $ for sufficiently large $T$, where $\sigma_t^2$ denotes the variance of the rewards at round $t$, $d$ is the dimension of the contexts, and $T$ is the total number of rounds. Furthermore, we introduce a Maximum Likelihood Estimation (MLE)-based algorithm, OFU-MN$^2$L, which achieves an anytime poly(B)-free regret of $O \Big( d \log (BT) \sqrt{ \smash[b]{\sum_{t=1}^T} \sigma_t^2 } \Big) $.

In this paper, we consider the risk-sensitive cost criterion with exponentiated costs for Markov decision processes and develop a model-free policy gradient algorithm in this setting. Unlike additive cost criteria such as average or discounted cost, the risk-sensitive cost criterion is less studied due to the complexity resulting from the multiplicative structure of the resulting Bellman equation. We develop an actor-critic algorithm with function approximation in this setting and provide its asymptotic convergence analysis. We also show the results of numerical experiments that demonstrate the superiority in performance of our algorithm over other recent algorithms in the literature.

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods assume fixed but unknown hypotheses, relying on estimators like maximum likelihood. While extensive research has compared these approaches, the frequentist paradigm of obtaining point estimates has become predominant in deep learning, as Bayesian inference is challenging due to the computational complexity and the approximation gap of posterior estimation methods. However, a good understanding of trade-offs between the two approaches is lacking in the regime of amortized estimators, where in-context learners are trained to estimate either point values via maximum likelihood or maximum a posteriori estimation, or full posteriors using normalizing flows, score-based diffusion samplers, or diagonal Gaussian approximations, conditioned on observations. To help resolve this, we conduct a rigorous comparative analysis spanning diverse problem settings, from linear models to shallow neural networks, with a robust evaluation framework assessing both in-distribution and out-of-distribution generalization on tractable tasks. Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems, and we further discuss why this might be the case.

The foundation model enables general-purpose problem-solving and enjoys desirable rapid adaptation due to its adopted cross-task generalization paradigms, e.g., pretraining, meta-training, and finetuning. Recent advances in these paradigms show the crucial role of challenging tasks' prioritized sampling in enhancing adaptation robustness. However, ranking task difficulties exhausts massive task queries to evaluate, thus computation and annotation intensive, which is typically unaffordable in practice. This work underscores the criticality of both adaptation robustness and learning efficiency, especially in scenarios where tasks are risky or costly to evaluate, e.g., policy evaluations in Markov decision processes (MDPs) or inference with large models. To this end, we present Model Predictive Task Sampling (MPTS) to establish connections between the task space and adaptation risk landscape to form a theoretical guideline in robust active task sampling. MPTS characterizes the task episodic information with a generative model and directly predicts task-specific adaptation risk values from posterior inference. The developed risk learner can amortize expensive evaluation and provably approximately rank task difficulties in the pursuit of task robust adaptation. MPTS can be seamlessly integrated into zero-shot, few-shot, and many-shot learning paradigms. Extensive experimental results are conducted to exhibit the superiority of the proposed framework, remarkably increasing task adaptation robustness and retaining learning efficiency in contrast to existing state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

Accurate prediction of urban spatiotemporal dynamics is essential for enhancing urban management and decision-making. Existing spatiotemporal prediction models are predominantly deterministic, focusing on primary spatiotemporal patterns. However, those dynamics are highly complex, exhibiting multi-modal distributions that are challenging for deterministic models to capture. In this paper, we highlight the critical role of probabilistic prediction in capturing the uncertainties and complexities inherent in spatiotemporal data. While mainstream probabilistic models can capture uncertainty, they struggle with accurately learning primary patterns and often suffer from computational inefficiency. To address these challenges, we propose CoST, which collaborates deterministic and probabilistic models to improve both predictive accuracy and the ability to handle uncertainty. To achieve this, we design a mean-residual decomposition framework, where the mean value is modeled by a deterministic model, and the residual variations are learned by a probabilistic model, specifically diffusion models. Moreover, we introduce a scale-aware diffusion process, which better accounts for spatially heterogeneous dynamics across different regions. Extensive experiments on eight real-world datasets demonstrate that CoST significantly outperforms existing methods in both deterministic and probabilistic metrics, achieving a 20% improvement with low computational cost. CoST bridges the gap between deterministic precision and probabilistic uncertainty, making a significant advancement in the field of urban spatiotemporal prediction.