Stochastic Natural Gradient Variational Inference (NGVI) is a widely used method for approximating posterior distribution in probabilistic models. Despite its empirical success and foundational role in variational inference, its theoretical underpinnings remain limited, particularly in the case of non-conjugate likelihoods. While NGVI has been shown to be a special instance of Stochastic Mirror Descent, and recent work has provided convergence guarantees using relative smoothness and strong convexity for conjugate models, these results do not extend to the nonconjugate setting, where the variational loss becomes non-convex and harder to analyze. In this work, we focus on mean-field parameterization and advance the theoretical understanding of NGVI in three key directions. First, we derive sufficient conditions under which the variational loss satisfies relative smoothness with respect to a suitable mirror map. Second, leveraging this structure, we propose a modified NGVI algorithm incorporating non-Euclidean projections and prove its global non-asymptotic convergence to a stationary point. Finally, under additional structural assumptions about the likelihood, we uncover hidden convexity properties of the variational loss and establish fast global convergence of NGVI to a global optimum. These results provide new insights into the geometry and convergence behavior of NGVI in challenging inference settings.

Incontrast,our work is concerned with an overall limit on the total amount of information an agent may acquire fromtheenvironment and,inturn,howthattranslates intoitsselection ofafeasible learning target.

Although actor-critic methods have been successful in practice, their theoretical analyses have several limitations. Specifically, existing theoretical work either sidesteps the exploration problem by making strong assumptions or analyzes impractical methods with complicated algorithmic modifications. Moreover, the actor-critic methods analyzed for linear MDPs often employ natural policy gradient and construct "implicit" policies without explicit parameterization. Such policies are computationally expensive to sample from, making the environment interactions inefficient. To that end, we focus on the finite-horizon linear MDPs and propose an optimistic actor-critic framework that uses parametric log-linear policies. In particular, we introduce a tractable $\textit{logit-matching}$ regression objective for the actor. For the critic, we use approximate Thompson sampling via Langevin Monte Carlo to obtain optimistic value estimates. We prove that the resulting algorithm achieves $\widetilde{\mathcal{O}}(ε^{-4})$ and $\widetilde{\mathcal{O}}(ε^{-2})$ sample complexity in the on-policy and off-policy setting, respectively. Our results match prior theoretical work in achieving the state-of-the-art sample complexity, while our algorithm is more aligned with practice.

In many classification problems, the costs of misclassifying observations from different classes can be highly unequal. The Neyman-Pearson multiclass classification (NPMC) framework addresses this issue by minimizing a weighted misclassification risk while imposing upper bounds on class-specific error probabilities. Existing NPMC methods typically assume that training labels are correctly observed. In practice, however, labels are often corrupted due to measurement error or annotation, and the effect of such label noise on NPMC procedures remains largely unexplored. We study the NPMC problem when only noisy labels are available in the training data. We propose an empirical likelihood (EL)-based method that relates the distributions of noisy and true labels through an exponential tilting density ratio model. The resulting maximum EL estimators recover the class proportions and posterior probabilities of the clean labels required for error control. We establish consistency, asymptotic normality, and optimal convergence rates for these estimators. Under mild conditions, the resulting classifier satisfies NP oracle inequalities with respect to the true labels asymptotically. An expectation-maximization algorithm computes the maximum EL estimators. Simulations show that the proposed method performs comparably to the oracle classifier under clean labels and substantially improves over procedures that ignore label noise.

The exponential mechanism is a general method to construct a randomized estimator that satisfies (ε,0)-differential privacy. Recently, Wang et al. showed that the Gibbs posterior, which is a data-dependent probability distribution that contains the Bayesian posterior, is essentially equivalent to the exponential mechanism under certain boundedness conditions on the loss function. While the exponential mechanism provides a way to build an (ε,0)-differential private algorithm, it requires boundedness of the loss function, which is quite stringent for some learning problems. In this paper, we focus on (ε,δ)-differential privacy of Gibbs posteriors with convex and Lipschitz loss functions. Our result extends the classical exponential mechanism, allowing the loss functions to have an unbounded sensitivity.

Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on experimental feedback data collected from human annotators under controlled and costly conditions. In this work, we introduce observational reward modeling -- learning reward models with observational user feedback (e.g., clicks, copies, and upvotes) -- as a scalable and cost-effective alternative. We identify two fundamental challenges in this setting: (1) observational feedback is noisy due to annotation errors, which deviates it from true user preference; (2) observational feedback is biased by user preference, where users preferentially provide feedback on responses they feel strongly about, which creats a distribution shift between training and inference data. To address these challenges, we propose CausalRM, a causal-theoretic reward modeling framework that aims to learn unbiased reward models from observational feedback. To tackle challenge (1), CausalRM introduces a noise-aware surrogate loss term that is provably equivalent to the primal loss under noise-free conditions by explicitly modeling the annotation error generation process. To tackle challenge (2), CausalRM uses propensity scores -- the probability of a user providing feedback for a given response -- to reweight training samples, yielding a loss function that eliminates user preference bias. Extensive experiments across diverse LLM backbones and benchmark datasets validate that CausalRM effectively learns accurate reward signals from noisy and biased observational feedback and delivers substantial performance improvements on downstream RLHF tasks -- including a 49.2% gain on WildGuardMix and a 32.7% improvement on HarmBench. Code is available on our project website.

While the inverse sensitivity mechanism was shown to be instance optimal, it was only with respect to a class of unbiased mechanisms such that the most likely outcome matches the underlying data.

Furthermore, weprovethat, under mild assumptions, a slight variation of WQL enjoys desirable theoretical properties in the tabular setting.

Furthermore, we obtain exactp-values, which are easily computed in terms of the Tulap random variable. We show that our results also apply to distribution-free hypothesis testsforcontinuous data.

These datasets enable large-scale study of abuse detection for these languages. Anonymized comments: To further address privacy concerns, we anonymize our dataset. We combine thehate and offensivecategories in these datasets for training a binary classification model. We showthepercentage (%)ofemoticons present inourdatasetMACDinTable12. Infuture work,we will investigate in detail about the impact of emoticons on abuse detection. However,duetothe limited scale and diversity of abuse detection datasets in Indic languages, development of these models for Indic languages has been severely impeded.