Fine-tuning a pretrained language model on a curated dataset can produce spurious correlations between the fine-tuning task and unintended latent factors -- such as misaligned personas or political slant -- that the curation procedure has entangled with the task. The model can latch onto these spurious correlations, leading to bias and reduced out-of-distribution generalisation. We prove that under reasonable assumptions on task complexity and the spurious correlation, such latent factors can be identified, without supervision, from the weights of a naive LoRA fine-tune. Existing approaches to removing bias, such as activation steering, remove identified factors from residual-stream activations, either at inference or during training. We argue, however, that the goal should be to remove the spurious correlation, not the latent factor itself, as the pretrained model may rely on it for genuine task signal. To enable this, we propose GRASP, GRadient projection of Associated Spurious Patterns, which prevents the model from acquiring new reliance on the identified latent factor while preserving any pretrained content along it. We validate on three fine-tuning tasks. The first two involve emergent misalignment, where fine-tuning on a narrow task -- in our case, writing insecure code and giving bad medical advice -- leads to misaligned responses on unrelated topics. Here our method completely removes misalignment in the insecure code case and reduces them by ~5x in the bad medical advice case, beating all baselines in the trade-off between misalignment-reduction and task-preservation. The last is a novel political-bias experiment, where fine-tuning on right-skewed Reddit financial-advice data causes political-lean drift on unrelated topics. Here our method reduces drift by more than half, while improving financial task performance, beating all baselines.

This paper studies adaptive targeting under network interference in a bandit setting, where treatments applied to one individual may affect others through spillover effects. We consider a linear model in a sparse regime, where each individual's outcome can be affected by at most a few others. We first establish a regret lower bound showing that ignoring the network structure and reducing the problem to a standard linear bandit inevitably leads to inefficient learning, particularly in large populations. To understand how structural information can be leveraged, we analyze regimes with varying levels of knowledge of the interference structure: (1) full support knowledge, (2) knowledge of the column support sizes, and (3) no prior knowledge. For each regime, we establish regret lower bounds characterizing the fundamental limits of learning, and develop algorithms that achieve near-optimal regret. Together, our results provide a unified view of how knowledge of the interference structure governs the efficiency of online learning under interference, and offer practical adaptive targeting algorithms in each setting. Numerical experiments on synthetic and real-world data demonstrate the practical benefits of our algorithms.

Expert demonstrations, such as those from car drivers, help navigate environments with unknown rewards, but are often collected in controlled settings, such as closed-course test tracks, while learned control policies must be deployed in new environments, such as city streets. We can imitate experts to perform well in the same source environment where demonstrations are observed, and we may even use inverse reinforcement learning (IRL) to improve on simple behavior cloning (Ng and Russell, 2000; Abbeel and Ng, 2004; Ziebart et al., 2008; Fu et al., 2018; Geng et al., 2020). But the target environment may have a different transition law, discount factor, or soft-control regularization. For this, IRL is crucial: we can learn a reward from demonstrations in the source environment and transfer it to the target environment, learning a policy that optimizes the same reward function in a new setting (Fu et al., 2018; Schlaginhaufen and Kamgarpour, 2024). In this paper, we characterize how well this transfer can be done and which approaches are preferable. In particular, we show the value in a coupled approach that takes the target environment into account even when learning from the source. In ordinary offline control, the Bellman equation uses a known reward, so the main statistical error comes from target transitions.

Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in the over-parameterized regime by showing that the prediction induced by continuous-time neural tangent kernel (NTK) gradient flow is exactly equivalent to that from a classical random-effects model. In this framework, training time acts as a variance component, or equivalently an empirical Bayes covariance hyperparameter, governing the allocation of variation from noise to structured signal. This equivalence reveals an optimization-inference duality: the gradient-flow path is both an optimization trajectory and an empirical Bayes random-effects inference path. Conditional on training time, the network output is the posterior mean of the latent signal, and estimating training time by restricted maximum likelihood (REML) turns early stopping into likelihood-based empirical Bayes inference rather than external tuning. This perspective yields a two-stage inferential procedure. First, a variance-component test determines whether DNN training captures statistically significant structure beyond initialization. Second, conditional on training being warranted, REML provides a likelihood-based early stopping rule. The resulting stopping time admits a spectral interpretation in the NTK eigenbasis, where training proceeds until spectral loss decorrelation is achieved. We further establish that REML-guided early stopping achieves asymptotically optimal prediction error for fixed-design in-sample prediction and, under additional random-design regularity conditions, for out-of-sample prediction. This work reframes DNN training as statistical inference and provides a principled foundation for deciding whether and how long to train deep neural networks.

We design a class of additive noise mechanisms that satisfy \((\varepsilon, δ)\)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for \((\varepsilon, δ)\)-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes (\(l_1\)-loss) and variances (\(l_2\)-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.

We study the problem of learning to bid when the bidder's value is dynamic, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the time elapsed since their last successful bid, with auctions arriving in continuous time and only aggregated feedback revealed at the end of the horizon. Such a bidder must (1) balance the immediate benefit of winning the current auction against its impact on future values and (2) learn unknown environmental parameters. We derive regret bounds for a class of learning methods that combine plug-in estimators with a differential-equation characterization of the optimal policy, and show that a specific confidence bound algorithm learns the optimal policy with a near optimal regret of $\widetilde{O}(\log N)$ for piecewise linear primitives, and $\widetilde{O}(N^{1/3})$ for general, smooth primitives, achieving these regrets without explicit randomization. These theoretical results are supported by numerical experiments.

Fairness-accuracy trade-offs are a central concern in the deployment of fairness-aware machine learning methods. When sensitive attributes are unavailable at inference time-the so called unawareness setting, principled methods for obtaining accurate predictions under relaxed fairness constraints are largely missing. In this work, we address this gap by formulating regression under a demographic parity penalty as an optimal transport problem. Our framework unifies both the \emph{aware} and \emph{unaware} settings and characterizes optimal prediction functions via optimal transport maps, under both squared Wasserstein-2 and Total Variation penalties. These results reveal that the choice of penalty reflects fundamentally different fairness philosophies: the Wasserstein penalty induces a smooth, population-wide compromise, while Total Variation enforces exact parity for a subset of individuals. Building on these theoretical characterizations, we propose an algorithm that is simple to implement, computationally efficient, and consistently matches or outperforms state-of-the-art baselines on real-world benchmarks.

We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new post-processing estimator. We begin by showing that counterfactual fairness is equivalent to satisfying demographic parity conditional on the latent variable. This allows us to provide a closed-form expression of the optimal fair regressor via a barycentric quantile map. In order to handle continuous latent variables, we propose a discretized post-processing method. Then, under mild regularity assumptions, we prove high-probability finite-sample fairness guarantees for our estimator, providing an unfairness decay at rate $\tilde O(n^{-1/3})$, and establishing a matching risk bound of order $\tilde O(n^{-1/3})$. We provide a matching lower bound on the excess risk of almost fair predictions. Finally, we extend our results to the setting of relaxed counterfactual fairness. We validate our approach on real-world and synthetic data.

We study bandit learning in matching markets, where players and arms constitute the two market sides, and the players' utilities are linear in the arm contexts. In each round, new arms arrive with observable contexts. Then, the algorithm matches them to players, aiming to minimize each player's regret against a stable matching benchmark. This contextual structure creates significant complexity: subtle context shifts can slightly alter one player's utility while completely reconfiguring the underlying benchmark, causing large regret spikes for others. We address this in two settings: stochastic contexts, drawn from a latent distribution, and adversarial contexts, which may be arbitrary. For the stochastic case, we introduce a novel minimum preference gap to capture learning difficulty and provide a fully adaptive algorithm with an instance-dependent poly-logarithmic regret upper bound. We also establish matching instance-independent regret upper and lower bounds under a mild distributional assumption. For the adversarial setting, we propose a tractable regret notion that remains valid under arbitrary contexts and achieves an instance-independent sublinear regret bound via an adaptive algorithm.

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space and yields variance reduction compared to the classical inverse propensity score estimator. Building on these value estimates, we investigate policy optimization and present two practical approaches for computing optimal pricing rules: an interpretable data-shared Lasso formulation and a flexible policy parameterization based on neural networks. Using a controlled synthetic travel insurance environment, we empirically confirm the theoretical results and show that neural networks outperform existing techniques for policy optimization.