Domain adaptation faces a fundamental paradox in the cold-start regime. When target data is scarce, statistical methods fail to distinguish relevant source domains from irrelevant ones, which often leads to negative transfer. In this paper, we address this challenge by leveraging expert textual descriptions of the target domain, a resource that is often available but overlooked. We propose a probabilistic framework that translates these semantic descriptions into a choice model, namely a Language-Induced Prior (LIP), that learns the preferences from a pretrained Large Language Model (LLM). The LIP is then integrated into an Expectation-Maximization algorithm to identify source relevance. Methodologically, this framework is compatible with any parametric model where a likelihood is available. It allows the LIP to guide the selection of sources when target signals are weak, while gradually refining these choices as samples accumulate. Theoretically, we prove that the estimator roughly matches an oracle cold-start MSE under a correct prior, while remaining asymptotically consistent regardless of the quality of the LIP. Empirically, we validated the framework on a descriptive (Gaussian estimation), a predictive (C-MAPSS dataset), and a prescriptive task (MuJoCo hopper).

We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate $\mathcal{O}(n^{-1})$, where $n$ is the number of expert trajectories. Our guarantees apply under misspecification and require no exploration assumptions. We further extend reward-identifiability results to general Borel spaces and derive novel results on the derivatives of the soft-optimal value function with respect to reward parameters.

We study inventory control with decision-dependent censoring, focusing on the censored or repeated newsvendor (R-NV), where each order quantity determines whether demand is fully observed or censored by sales. Existing approaches based on parametric Thompson sampling (TS) can be brittle under prior mismatch, while offline imputation methods need not transfer to online learning. Motivated by the predictive view of decision making, we combine these ideas by taking oracle actions on learned completions of latent demand. We propose in-context generative posterior sampling (ICGPS), which uses modern generative models that are meta-trained offline and deployed online by in-context autoregressive generation. Theoretically, we show that the Bayesian regret of ICGPS with a learned completion kernel is bounded by the Bayesian regret of a TS benchmark with the ideal completion kernel plus a deployment penalty scaling as $\sqrt{T}$ times the square root of the completion mismatch. This yields a plug-in template for operational problems with known TS regret bounds. For R-NV, we derive sublinear Bayesian regret by reducing censored feedback to bandit convex optimization feedback. We also show that, under reasonable coverage and stability assumptions, the online completion mismatch is controlled by the offline censored predictive mismatch, so offline predictive quality transfers to online performance. Practically, we instantiate ICGPS with ChronosFlow, which combines a frozen time-series transformer backbone with a trainable conditional normalizing-flow head for fast censoring-consistent sampling. In benchmark experiments, ChronosFlow-ICGPS matches correctly specified TS, outperforms myopic and UCB-style baselines, and is robust to prior mismatch and distribution shift. ChronosFlow-ICGPS also performs well for the real-world SuperStore dataset, especially under heavy censoring.

Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often yields accurate predictive distributions, but cheap variational families such as mean-field (MF) can produce over-concentrated approximations that miss posterior dependence. We propose variational predictive resampling (VPR), a scalable posterior sampling method that exploits VI's predictive strength within a predictive-resampling framework to better approximate the Bayesian posterior. Given a prior-likelihood pair, VPR repeatedly imputes future observations from the current variational predictive, updates the variational approximation after each imputation, and records the parameter value implied by the completed sample. We establish conditions under which the law of the parameter returned by VPR is well defined and show that its finite-horizon approximation converges to this limit. In a tractable Gaussian location model, we show that VPR with MF variational predictives converges to the exact Bayesian posterior, whereas the optimal MF-VI approximation retains a non-vanishing asymptotic gap. Experiments on linear regression, logistic regression, and hierarchical linear mixed-effects models demonstrate that VPR substantially improves posterior uncertainty quantification and recovers posterior dependence missed by MF-VI, while remaining computationally competitive with, and often more efficient than, MCMC.

Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with fully interpretable, user-configurable parameters and modular topology, demand process, and control rules. The simulator advances a directed routing graph in discrete time: demand arrives at the destination, is served from stock or recorded as backlog, and triggers replenishment through the network. The state vector tracks per-node on-hand inventory with outstanding orders, in-transit shipments, and a smoothed demand estimate, so the dynamics close as a Markov chain on a tractable state space whose transition kernel acts linearly on the empirical distribution of the state. The released data reproduces the bullwhip effect at empirically consistent magnitudes, and three conservation laws encoded in the Markov chain serve as verification tools when users extend the simulator. We release datasets at two catalogue scales ($C=50$ and $C=200$) with six scenario sweeps producing 30 additional rollouts and 20 Latin-hypercube perturbations, exhibiting dynamics absent from fixed TSF benchmarks: variance amplification, cascading bottlenecks, regime shifts, and cross-channel coupling through shared macro shocks. Zero-shot evaluation of four foundation models (Chronos, Moirai, TimesFM, Lag-Llama) shows MASE values exceeding public GIFT-Eval references at low-to-moderate horizons, supporting incorporation into existing benchmarks. The same pairing produces forecast confidence bands via Latin-hypercube perturbation of demand-side knobs, forward UQ from parameter uncertainty unavailable on standard TSF datasets, demonstrating that foundation models can serve as fast surrogates for the digital twin's forward UQ. Code (MIT): https://github.com/tuhinsahai/ISOMORPH.

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity guarantee for finding an $ε$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact $k$-gram ansatz} in place of transformers with context length $k$, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the \emph{Ising broadcast process} (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian -- both deviating from the true language for any sublinear context. For the \emph{coloring broadcast process} (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with \emph{any} valid coloring of the underlying tree. Together these results imply an $Ω(n)$ lower bound on the context length required to faithfully sample length-$n$ sequences. In contrast, we prove that an autoregressive \emph{reasoning} model with only $Θ(\log n)$ working memory can sample exactly from the true language -- an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

Many three-dimensional spatial fields are anisotropic, with directions of rapid and slow variation that need not align with the coordinate axes. Standard Gaussian process kernels with Automatic Relevance Determination (ARD) capture only axis-aligned anisotropy, while generic full symmetric positive definite (SPD) metrics can represent rotated anisotropy but do not parameterise principal length-scales and directions directly. We introduce an interpretable rotationally anisotropic GP kernel that parameterises a three-dimensional SPD covariance metric using three principal length-scales and an explicit SO(3) rotation. The rotation is represented by an axis-angle vector and mapped to SO(3) via the Lie-algebra exponential map, giving unconstrained Euclidean coordinates for inference while always inducing a valid SPD metric. The construction spans the same family of three-dimensional SPD covariance metrics as a generic full-SPD parameterisation, but exposes the geometry differently: length-scales and orientation are explicit, interpretable, and directly available for prior specification and posterior summaries. We perform Bayesian inference on these quantities using Markov Chain Monte Carlo (MCMC), and characterise the resulting symmetries and weakly identified regimes. On synthetic data with rotated anisotropy, the posterior recovers the generating metric and improves prediction relative to an axis-aligned ARD baseline, while matching the predictive performance of a generic full SPD baseline. When the ground truth is axis-aligned, posterior mass concentrates near the identity rotation and predictive performance matches ARD. On a material-density dataset from a laboratory-fabricated nano-brick, the inferred metric reveals rotated anisotropy that is not captured by axis-aligned kernels.