We study safe linear bandits (SLBs), where an agent selects actions from a convex set to maximize an unknown linear objective subject to unknown linear constraints in each round. Existing methods for SLBs provide strong regret guarantees, but require solving expensive optimization problems. To address this, we propose Constrained Linear Thompson Sampling (COLTS), a sampling-based framework that selects actions by solving perturbed linear programs, which significantly reduces computational costs while matching the regret and risk of prior methods. We develop two main variants: S-COLTS, which ensures zero risk and eO( d3T) regret given a safe action, and R-COLTS, which achieves eO( d3T)regret and risk with no instance information. In simulations, these methods match or outperform state of the art SLB approaches while substantially improving scalability. On the technical front, we introduce a novel coupled noise design that ensures frequent'local optimism' about the true optimum, and a scaling-based analysis to handle the per-round variability of constraints.

Contextual Markov Decision Processes (cMDP) model this challenge, but existing methods often require explicit context variables (e.g., friction, gravity), limiting their use when contexts are latent or hard to measure. We introduce Dynamics-Aligned Latent Imagination (DALI), a framework integrated within the Dreamer architecture that infers latent context representations from agent-environment interactions. By training a self-supervised encoder to predict forward dynamics, DALI generates actionable representations conditioning the world model and policy, bridging perception and control. We theoretically prove this encoder is essential for efficient context inference and robust generalization. DALI's latent space enables counterfactual consistency: Perturbing a gravity-encoding dimension alters imagined rollouts in physically plausible ways. On challenging cMDP benchmarks, DALI achieves significant gains over contextunaware baselines, often surpassing context-aware baselines in extrapolation tasks, enabling zero-shot generalization to unseen contextual variations.

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs) with unobserved confounding. Recent advances have introduced bridge-function to circumvent unmeasured confounding and develop estimators for the policy value, yet the statistical error bounds of them related to the length of horizon T and the size of the state-action space |O||A| remain largely unexplored. In this paper, we systematically investigate the finite-sample error bounds of OPE estimators in finite-horizon tabular confounded POMDPs. Specifically, we show that under certain rank conditions, the estimation error for policy value can achieve a rate of O(T1.5/ n), excluding the cardinality of the observation space |O| and the action space |A|. With an additional mild condition on the concentrability coefficients in confounded POMDPs, the rate of estimation error can be improved to O(T/ n).

We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV--an Adaptive, Multiply-Robust estimator for Instrumental-Variable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.

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.

LLM-enabled AI workflows increasingly produce outputs through iterative generate-evaluate-revise loops. Each iteration can improve the candidate, but it also creates a release decision: when to stop and output the current result? This raises a statistical challenge because deployment-time evaluator scores are adaptively generated and repeatedly monitored, yet the likelihood models or exchangeability assumptions typically used for calibration are unavailable. We propose an always-valid release wrapper for existing generator-evaluator pipelines. The wrapper builds a hard-negative reference pool of high-scoring failures, calibrates deployment-time evaluator scores against this pool, and accumulates the resulting evidence with an e-process. This separates two roles: the reference pool turns black-box scores into conservative evidence, while the e-process provides validity under optional stopping. In theory, we show that a conservative reference pool yields finite-sample control of the probability of releasing on infeasible tasks, that is, tasks for which the given workflow is not capable of producing a reliable solution. We also characterize conditions under which the same conservative rule still achieves nontrivial release on feasible tasks. In an MBPP+ coding-agent case study, the wrapper reduces premature incorrect release relative to baseline stopping rules while still releasing on tasks for which the workflow repeatedly accumulates moderate supporting evidence.

Information-theoretic generalization bounds based on the supersample construction are a central tool for algorithm-dependent generalization analysis in the batch i.i.d.~setting. However, existing supersample conditional mutual information (CMI) bounds do not directly apply to sequential decision-making problems such as online learning, streaming active learning, and bandits, where data are revealed adaptively and the learner evolves along a causal trajectory. To address this limitation, we develop a sequential supersample framework that separates the learner filtration from a proof-side enlargement used for ghost-coordinate comparisons. Under a row-wise exchangeability assumption, the sequential generalization gap is controlled by sequential CMI, a sum of roundwise selector--loss information terms. We also establish a Bernstein-type refinement that yields faster rates under suitable variance conditions. The selector-SCMI proof strategy applies to online learning, streaming active learning with importance weighting, and stochastic multi-armed bandits.

We study the $(\varepsilon, δ)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high computational cost, rendering them hard to implement, and also suffer from suboptimal dependence on $\log(1/δ)$. We propose a randomized and computationally efficient algorithm for best policy identification that combines posterior sampling with an online learning algorithm to guide exploration in the MDP. Our method achieves asymptotic optimality in sample complexity, also in terms of posterior contraction rate, and runs in $O(S^2AH)$ per episode, matching standard model-based approaches. Unlike prior algorithms such as MOCA and PEDEL, our guarantees remain meaningful in the asymptotic regime and avoid sub-optimal polynomial dependence on $\log(1/δ)$. Our results provide both theoretical insights and practical tools for efficient policy identification in tabular MDPs.

Bandit algorithms are increasingly used in real-world sequential decision-making problems. Associated with this is an increased desire to be able to use the resulting datasets to answer scientific questions like: Did one type of ad lead to more purchases? In which contexts is a mobile health intervention effective? However, classical statistical approaches fail to provide valid confidence intervals when used with data collected with bandit algorithms. Alternative methods have recently been developed for simple models (e.g., comparison of means). Yet there is a lack of general methods for conducting statistical inference using more complex models on data collected with (contextual) bandit algorithms; for example, current methods cannot be used for valid inference on parameters in a logistic regression model for a binary reward. In this work, we develop theory justifying the use of M-estimators--which includes estimators based on empirical risk minimization as well as maximum likelihood--on data collected with adaptive algorithms, including (contextual) bandit algorithms. Specifically, we show that M-estimators, modified with particular adaptive weights, can be used to construct asymptotically valid confidence regions for a variety of inferential targets.

To foster their reliable use in real-world scenarios, it is crucial to augment their transparency.