The Combinatorial Multi-Armed Bandit (CMAB) framework extends classical multi-armed bandit theory to complex decision-making settings where agents select super arms to maximize a collective reward. While Thompson Sampling (TS) is widely favored for its robust empirical performance in these settings, its theoretical guarantees have historically suffered from a significant bottleneck: standard Combinatorial Thompson Sampling (\texttt{CTS}) incurs a regret bound with an exponential dependence on the size $k^*$ of the optimal super-arm. This exponential term arises because standard independent posterior sampling fails to coordinate optimism across the base arms of the optimal super arm, causing the probability of exploration to vanish as $k^*$ increases. Although recent advances have achieved polynomial regret for \emph{linear} rewards, designing an efficient TS algorithm for general, non-linear CMABs remains an open challenge. In this paper, we resolve this open question by proposing \emph{Combinatorial Thompson Sampling with a Single Seed} (\texttt{CTS$^3$}). Unlike standard approaches that sample base arms independently, \texttt{CTS$^3$} employs a comonotonic coupling strategy: it generates parameters for all base arms using a single shared random seed via the inverse CDF transform. This mechanism synchronizes sampling fluctuations across arms, ensuring concerted optimism and preventing the exploration probability from decaying exponentially. We prove that \texttt{CTS$^3$} achieves a regret bound of ${O}\left( \frac{m kk^*B^2}{\Delta_{\min}}\poly(\log(T,m,\Delta_{\max}/\Delta_{\min}))\right)$ for general reward functions satisfying monotonicity and bounded smoothness, where $m$ is the number of total base arms, $k$ is the largest super arm size, and $k^*$ is size of the optimal arm. To the best of our knowledge, this is the first polynomial regret bound for Thompson Sampling in general CMAB settings. Empirical evaluations confirm that \texttt{CTS$^3$} significantly outperforms standard independent TS, particularly in regimes with large super arms.

Accurate medical image segmentation relies on collaborative modeling of local details and global semantics, especially in small-volume structures, blurred boundaries, and fine-grained anatomical regions under low signal-to-noise conditions. However, existing transformer-based methods typically suffer from feature redundancy problems caused by inaccurate attention mechanism focus and nonlinear modeling defects caused by insufficient expression ability of feedforward networks, which leads to attention bias and nonlinear modeling bias, and ultimately degrades segmentation performance. To address these challenges, we propose CGCA-KAN, a novel transformer-based framework that employs a collaborative correction mechanism (CCM) to jointly mitigate attention bias and nonlinear modeling bias. Specifically, we introduce a cluster-aware self-attention module (CASAM) to mitigate attention bias by refining semantic focus and suppressing redundancy through token group compression, thereby enhancing attention to small-volume structures. Additionally, we design a Kolmogorov-Arnold Network enhanced feedforward network (KAN-EFFN) to mitigate nonlinear modeling bias through adaptive nonlinear transformations, thereby improving the model's ability to delineate blurred boundaries. Extensive experiments on LiTS2017, Synapse, and BraTS2020 datasets demonstrate state-of-the-art performance in fine-grained segmentation of ambiguous lesions in the liver, complex structures of multiple organs, and brain tumors. Our results highlight CGCA-KAN as a promising solution for addressing modeling biases in medical image segmentation.

Imitation learning is a central problem in reinforcement learning where the goal is to learn a policy that mimics the expert's behavior. In practice, it is often challenging to learn the expert policy from a limited number of demonstrations accurately due to the complexity of the state space. Moreover, it is essential to explore the environment and collect data to achieve beyond-expert performance. To overcome these challenges, we propose a novel imitation learning algorithm called Imitation Learning with Double Exploration (ILDE), which implements exploration in two aspects: (1) optimistic policy optimization via an exploration bonus that rewards state-action pairs with high uncertainty to potentially improve the convergence to the expert policy, and (2) curiosity-driven exploration of the states that deviate from the demonstration trajectories to potentially yield beyond-expert performance. Empirically, we demonstrate that ILDE outperforms the state-of-the-art imitation learning algorithms in terms of sample efficiency and achieves beyond-expert performance on Atari and MuJoCo tasks with fewer demonstrations than in previous work. We also provide a theoretical justification of ILDE as an uncertainty-regularized policy optimization method with optimistic exploration, leading to a regret growing sublinearly in the number of episodes.

Recent advances in Reinforcement Learning from Human Feedback (RLHF) have shown that KL-regularization plays a pivotal role in improving the efficiency of RL fine-tuning for large language models (LLMs). Despite its empirical advantage, the theoretical difference between KL-regularized RL and standard RL remains largely under-explored. While there is a recent line of work on the theoretical analysis of KL-regularized objective in decision making (Xiong et al., 2024a; Xie et al., 2024; Zhao et al., 2024), these analyses either reduce to the traditional RL setting or rely on strong coverage assumptions. In this paper, we propose an optimism-based KL-regularized online contextual bandit algorithm, and provide a novel analysis of its regret. By carefully leveraging the benign optimization landscape induced by the KL-regularization and the optimistic reward estimation, our algorithm achieves an $\mathcal{O}\big(\eta\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big)$ logarithmic regret bound, where $\eta, N_{\mathcal R},T,d_{\mathcal R}$ denote the KL-regularization parameter, the cardinality of the reward function class, number of rounds, and the complexity of the reward function class. Furthermore, we extend our algorithm and analysis to reinforcement learning by developing a novel decomposition over transition steps and also obtain a similar logarithmic regret bound.

Reverse-Kullback-Leibler (KL) regularization has emerged to be a predominant technique to enhance policy optimization in reinforcement learning (RL) and reinforcement learning from human feedback (RLHF), which forces the learned policy to stay close to a reference policy. While the effectiveness of KL-regularization has been empirically demonstrated in various practical scenarios, current theoretical analyses of KL-regularized RLHF still yield the same $\mathcal{O}(1 / \epsilon^2)$ sample complexity as ones without KL-regularization. To understand the fundamental distinction between objectives with KL-regularization and ones without KL-regularization, we are the first to theoretically demonstrate the power of KL-regularization by providing a sharp analysis for KL-regularized contextual bandits and RLHF, revealing an $\mathcal{O}(1 / \epsilon)$ sample complexity when $\epsilon$ is sufficiently small. We also prove matching lower bounds for both settings. More specifically, we study how the coverage of the reference policy affects the sample complexity of KL-regularized online contextual bandits and RLHF. We show that with sufficient coverage from the reference policy, a simple two-stage mixed sampling algorithm can achieve an $\mathcal{O}(1 / \epsilon)$ sample complexity with only an additive dependence on the coverage coefficient, thus proving the benefits of online data even without explicit exploration. Our results provide a comprehensive understanding of the roles of KL-regularization and data coverage in online decision making, shedding light on the design of more efficient algorithms.

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $\tilde O\big(d\sqrt{\sum_{t=1}^T\sigma_t^2} + d\big)$, where $\sigma_t$ is the variance of the pairwise comparison at round $t$, $d$ is the dimension of the context vectors, and $T$ is the time horizon. Our regret bound naturally aligns with the intuitive expectation — in scenarios where the comparison is deterministic, the algorithm only suffers from an $\tilde O(d)$ regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework. To the best of our knowledge, this is the first statistically optimal algorithm for nonlinear offline RL.

Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i.e., $\tilde{\mathcal{O}}(d\sqrt T)$, where $d$ is the model dimension and $T$ is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS.CDB outperforms existing algorithms by a large margin.

The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation. Our key algorithmic design includes (1) a general deterministic policy-switching strategy that achieves low switching cost, (2) a monotonic value function structure with carefully controlled function class complexity, and (3) a variance-weighted regression scheme that exploits historical trajectories with high data efficiency. MQL-UCB achieves minimax optimal regret of $\tilde{O}(d\sqrt{HK})$ when $K$ is sufficiently large and near-optimal policy switching cost of $\tilde{O}(dH)$, with $d$ being the eluder dimension of the function class, $H$ being the planning horizon, and $K$ being the number of episodes. Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.

Recently, several studies \citep{zhou2021nearly, zhang2021variance, kim2021improved, zhou2022computationally} have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime and the deterministic reward regime. However, these algorithms are either computationally intractable or unable to handle unknown variance of the noise. In this paper, we present a novel solution to this open problem by proposing the \emph{first computationally efficient} algorithm for linear bandits with heteroscedastic noise. Our algorithm is adaptive to the unknown variance of noise and achieves an $\tilde{O}(d \sqrt{\sum_{k = 1}^K \sigma_k^2} + d)$ regret, where $\sigma_k^2$ is the \emph{variance} of the noise at the round $k$, $d$ is the dimension of the contexts and $K$ is the total number of rounds. Our results are based on an adaptive variance-aware confidence set enabled by a new Freedman-type concentration inequality for self-normalized martingales and a multi-layer structure to stratify the context vectors into different layers with different uniform upper bounds on the uncertainty. Furthermore, our approach can be extended to linear mixture Markov decision processes (MDPs) in reinforcement learning. We propose a variance-adaptive algorithm for linear mixture MDPs, which achieves a problem-dependent horizon-free regret bound that can gracefully reduce to a nearly constant regret for deterministic MDPs. Unlike existing nearly minimax optimal algorithms for linear mixture MDPs, our algorithm does not require explicit variance estimation of the transitional probabilities or the use of high-order moment estimators to attain horizon-free regret. We believe the techniques developed in this paper can have independent value for general online decision making problems.

We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear function of a given feature mapping, we propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $\tilde O(d\sqrt{H^3K})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $K$ is the number of episodes. Our algorithm is based on a weighted linear regression scheme with a carefully designed weight, which depends on a new variance estimator that (1) directly estimates the variance of the *optimal* value function, (2) monotonically decreases with respect to the number of episodes to ensure a better estimation accuracy, and (3) uses a rare-switching policy to update the value function estimator to control the complexity of the estimated value function class. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for $\sigma$-sub-Gaussian label noise, our analysis provides a regret upper bound of $O(\sigma^2 d \log T) + o(\log T)$, where $d$ is the dimension of the input vector, $T$ is the total number of rounds. We also prove an $\Omega(\sigma^2d\log(T/d))$ lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heterogeneous noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.