We study policy optimization for online episodic tabular Markov decision processes with unknown transition kernels, aiming for best-of-both-worlds guarantees together with data-dependent regret bounds. Recent work (Dann et al., 2023; Li et al., 2026) has shown that policy optimization can adapt to both adversarial and stochastic losses with first-order, second-order, and path-length bounds, but only under known transitions, leaving open whether such data-dependent guarantees are achievable by policy optimization when the transition kernel is unknown. We resolve this by developing a new algorithm based on optimistic follow-the-regularized-leader that attains these guarantees under unknown transitions. The key ingredient is a new design of optimistic $Q$-function estimators together with a data-dependent transition bonus that controls estimator bias through the loss-prediction error. Our analysis further identifies an unavoidable transition-dependent complexity term that captures the intrinsic cost of estimating the transition kernel. As a result, we obtain first-order, second-order, and path-length bounds with the transition-dependent complexity term while simultaneously achieving gap-dependent $\mathrm{polylog}(T)$ regret in the stochastic regime.

The problem of contextual dueling bandits is central to reinforcement learning with human feedback (RLHF), a widely used approach in AI alignment for incorporating human preferences into learning systems. Despite its importance, existing methods are constrained either by strong preference modeling assumptions or by applicability only to finite action spaces. Moreover, prior algorithms typically rely on online optimization oracles, which are computationally infeasible for complex function classes, limiting their practical effectiveness. In this work, we present the first fundamental theoretical study of general contextual dueling bandits over continuous action spaces. Our key contribution is a novel algorithm based on a regularized min-max optimization framework that achieves a regret bound of O( dT)--the first such guarantee for this general setting. By leveraging offline oracles instead of online ones, our method further improves computational efficiency.

Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these high-dimensional treatments without losing their semantic meaning or rendering analysis intractable. Here we address this problem by focusing on learning low-dimensional representations that capture the underlying structure of such treatments. These representations enable downstream applications such as guiding generative models to produce meaningful treatment variants and facilitating adaptive assignment in online experiments. We propose double kernel representation learning, which models the causal effect through the inner product of kernel-based representations of treatments and user covariates. We develop an alternating-minimization algorithm that learns these representations efficiently from data and provide convergence guarantees under a low-rank factor model. As an application of this framework, we introduce an adaptive design strategy for online experimentation and demonstrate the method's effectiveness through numerical experiments.

We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.

We study contextual online pricing with biased offline data. For the scalar price elasticity case, we identify the instance-dependent quantity δ2 that measures how far the offline data lies from the (unknown) online optimum. We show that the time length T, bias bound V, size N and dispersion λmin(ˆΣ) of the offline data, and δ2 jointly determine the statistical complexity.

Efficient online decision-making in contextual bandits is challenging, as methods without informative priors often suffer from computational or statistical inefficiencies. In this work, we leverage pre-trained diffusion models as expressive priors to capture complex action dependencies and develop a practical algorithm that efficiently approximates posteriors under such priors, enabling both fast updates and sampling. Empirical results demonstrate the effectiveness and versatility of our approach across diverse contextual bandit settings.

In this work, we study the federated multi-armed bandit (FMAB) problem, where a set of agents collaboratively aim to minimize cumulative regret. Unlike traditional centralized bandit models, agents in FMAB settings are connected via a communication graph and cannot share data freely due to bandwidth limitations or privacy constraints. This raises a fundamental challenge: how to achieve optimal learning performance under stringent communication budgets. We propose a novel communication-efficient algorithm containing two points: one for eliminating suboptimal arms through early and frequent communication of key decisions, and the other for refining global estimates using incremental epoch, quantized, and differentially transmitted statistics. Incremental Epoch-based Successive Elimination Algorithm (EpoInc-SE) is presented by carefully balancing communication frequency and precision of global estimates. Theoretically, we derive tight upper bounds on both individual cumulative regret and group regret, and prove that our method asymptotically matches the lower bound of regret in federated settings.

Contextual bandit algorithms have transformed modern experimentation by enabling real-time adaptation for personalized treatment. Yet these advantages create challenges for statistical inference due to adaptivity. We study inference with contextual-bandit data without assuming a well-specified outcome model. In this setting, we show a previously overlooked issue: standard algorithms such as LinUCB may fail to stabilize under misspecified working models, leading to non-Gaussian estimator behavior and invalid inference. This issue is practically important, as misspecified working models -- such as approximations of complex dynamical systems -- are often employed by online agents in real-world adaptive experiments to balance reward, computational tractability, and robustness. We develop an inverse-probability-weighted Z-estimation framework for a broad class of marginal moment targets, including projection parameters, structural parameters with noisy contexts, and off-policy values. We identify a stability condition tailored to this framework, scaled inverse-propensity convergence, under which the IPW-Z estimator is consistent and asymptotically normal with a consistent sandwich variance estimator. We further establish sufficient conditions for scaled inverse-propensity convergence for several policy classes, including multi-armed bandit algorithms and smooth contextual allocation policies. Simulations and a HeartSteps V1 real-data-calibrated application show reliable coverage and competitive performance across multiple targets. Overall, our results highlight the importance of stability-aware adaptive design for valid post-experiment inference.

Many ranking-and-selection (R&S) problems arise in settings where information is noisy, structured, and expensive. In multi-fidelity experimentation, one can query cheap but biased proxies or expensive high-fidelity measurements; in dueling bandits, feedback arrives only through pairwise comparisons rather than direct rewards. These models are increasingly natural in engineering design, simulation optimization, preference learning for LLMs, and human-in-the-loop evaluation, where absolute scores are often unavailable or prohibitively costly and decisions must be made with a prescribed level of confidence. What makes these settings especially challenging is that the usual single-winner template is no longer sufficient. First, the answer map may be set-valued: in good-alternative or subset-selection problems, several answers can be simultaneously correct. Second, even when the true instance is answerable, a noisy estimate may temporarily fall outside the answerable set.

We study online preference-based reinforcement learning (PbRL) with the goal of improving sample efficiency. While a growing body of theoretical work has emerged--motivated by PbRL's recent empirical success, particularly in aligning large language models (LLMs)--most existing studies focus only on pairwise comparisons. A few recent works [93, 49, 76] have explored using multiple comparisons and ranking feedback, but their performance guarantees fail to improve--and can even deteriorate--as the feedback length increases, despite the richer information available. To address this gap, we adopt the Plackett-Luce (PL) model for ranking feedback over action subsets and propose M-AUPO, an algorithm that selects multiple actions by maximizing the average uncertainty within the offered subset.