Recent advances in large language model (LLM) post-training have leveraged two distinct paradigms to enhance reasoning capabilities: reinforcement learning (RL) and knowledge distillation (KD). While RL enables the emergence of complex reasoning behaviors, it often suffers from low sample efficiency when the initial policy struggles to explore high-reward trajectories. Conversely, KD improves learning efficiency via mimicking the teacher model but tends to generalize poorly to out-of-domain scenarios. In this work, we present \textbf{KDRL}, a \textit{unified post-training framework} that jointly optimizes a reasoning model through teacher supervision (KD) and self-exploration (RL). Specifically, KDRL leverages policy gradient optimization to simultaneously minimize the reverse Kullback-Leibler divergence (RKL) between the student and teacher distributions while maximizing the expected rule-based rewards. We first formulate a unified objective that integrates GRPO and KD, and systematically explore how different KL approximations, KL coefficients, and reward-guided KD strategies affect the overall post-training dynamics and performance. Empirical results on multiple reasoning benchmarks demonstrate that KDRL outperforms GRPO and various KD baselines while achieving a favorable balance between performance and reasoning token efficiency. These findings indicate that integrating KD and RL serves as an effective and efficient strategy to train reasoning LLMs.

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance. However, this comes at the cost of significant computational overhead. In this paper, we show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, such as Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, and Qwen2.5-Math-7B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation.

--Effective agent exploration remains a core challenge in reinforcement learning (RL) for complex discrete state-space environments, particularly under partial observability. This paper presents a decoupled hierarchical RL framework integrating state abstraction (DcHRL-SA) to address this issue. The proposed method employs a dual-level architecture, consisting of a high-level RL-based actor and a low-level rule-based policy, to promote effective exploration. Additionally, state abstraction method is incorporated to cluster discrete states, effectively lowering state dimensionality. Experiments conducted in two discrete customized grid environments demonstrate that the proposed approach consistently outperforms PPO in terms of exploration efficiency, convergence speed, cumulative reward, and policy stability. These results demonstrate a practical approach for integrating decoupled hierarchical policies and state abstraction in discrete grids with large-scale exploration space. Code will be available at https://github.com/XQY169/DcHRL-SA. Index T erms --Reinforcement learning, decoupled hierarchical decision-making, state abstraction, discrete grid environment.

With the rapid development of vision tasks and the scaling on datasets and models, redundancy reduction in vision datasets has become a key area of research. To address this issue, dataset distillation (DD) has emerged as a promising approach to generating highly compact synthetic datasets with significantly less redundancy while preserving essential information. However, while DD has been extensively studied for image datasets, DD on video datasets remains underexplored. Video datasets present unique challenges due to the presence of temporal information and varying levels of redundancy across different classes. Existing DD approaches assume a uniform level of temporal redundancy across all different video semantics, which limits their effectiveness on video datasets. In this work, we propose Dynamic-Aware Video Distillation (DAViD), a Reinforcement Learning (RL) approach to predict the optimal Temporal Resolution of the synthetic videos. A teacher-in-the-loop reward function is proposed to update the RL agent policy. To the best of our knowledge, this is the first study to introduce adaptive temporal resolution based on video semantics in video dataset distillation. Our approach significantly outperforms existing DD methods, demonstrating substantial improvements in performance. This work paves the way for future research on more efficient and semantic-adaptive video dataset distillation research.

Humanoid locomotion faces a critical scalability challenge: traditional reinforcement learning (RL) methods require task-specific rewards and struggle to leverage growing datasets, even as more training terrains are introduced. We propose DreamPolicy, a unified framework that enables a single policy to master diverse terrains and generalize zero-shot to unseen scenarios by systematically integrating offline data and diffusion-driven motion synthesis. At its core, DreamPolicy introduces Humanoid Motion Imagery (HMI) - future state predictions synthesized through an autoregressive terrain-aware diffusion planner curated by aggregating rollouts from specialized policies across various distinct terrains. Unlike human motion datasets requiring laborious retargeting, our data directly captures humanoid kinematics, enabling the diffusion planner to synthesize "dreamed" trajectories that encode terrain-specific physical constraints. These trajectories act as dynamic objectives for our HMI-conditioned policy, bypassing manual reward engineering and enabling cross-terrain generalization. DreamPolicy addresses the scalability limitations of prior methods: while traditional RL fails to exploit growing datasets, our framework scales seamlessly with more offline data. As the dataset expands, the diffusion prior learns richer locomotion skills, which the policy leverages to master new terrains without retraining. Experiments demonstrate that DreamPolicy achieves average 90% success rates in training environments and an average of 20% higher success on unseen terrains than the prevalent method. It also generalizes to perturbed and composite scenarios where prior approaches collapse. By unifying offline data, diffusion-based trajectory synthesis, and policy optimization, DreamPolicy overcomes the "one task, one policy" bottleneck, establishing a paradigm for scalable, data-driven humanoid control.

Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial attacks. While numerous adversarial learning methods have been proposed, fundamental questions about their statistical optimality in robust loss remain largely unanswered. In particular, the minimax rate of convergence and the construction of rate-optimal estimators under future $X$-attacks are yet to be worked out. In this paper, we address this issue in the context of nonparametric regression, under suitable assumptions on the smoothness of the regression function and the geometric structure of the input perturbation set. We first establish the minimax rate of convergence under adversarial $L_q$-risks with $1 \leq q \leq \infty$ and propose a piecewise local polynomial estimator that achieves the minimax optimality. The established minimax rate elucidates how the smoothness level and perturbation magnitude affect the fundamental limit of adversarial learning under future $X$-attacks. Furthermore, we construct a data-driven adaptive estimator that is shown to achieve, within a logarithmic factor, the optimal rate across a broad scale of nonparametric and adversarial classes.

Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces, where function approximation is required for sample-efficient learning. This thesis addresses this gap by rigorously examining the statistical complexity of RL with function approximation from a learning theoretic perspective. Departing from a long history of prior work, we consider the weakest form of function approximation, called agnostic policy learning, in which the learner seeks to find the best policy in a given class $Π$, with no guarantee that $Π$ contains an optimal policy for the underlying task. We systematically explore agnostic policy learning along three key axes: environment access -- how a learner collects data from the environment; coverage conditions -- intrinsic properties of the underlying MDP measuring the expansiveness of state-occupancy measures for policies in the class $Π$, and representational conditions -- structural assumptions on the class $Π$ itself. Within this comprehensive framework, we (1) design new learning algorithms with theoretical guarantees and (2) characterize fundamental performance bounds of any algorithm. Our results reveal significant statistical separations that highlight the power and limitations of agnostic policy learning.

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics and reward functions are linear in the same feature space-limits its applicability in real-world domains, where rewards often exhibit nonlinear or discrete structures. Motivated by applications such as healthcare and e-commerce, where data is scarce and reward signals can be binary or count-valued, we propose the Generalized Linear MDP (GLMDP) framework-an extension of the linear MDP framework-that models rewards using generalized linear models (GLMs) while maintaining linear transition dynamics. We establish the Bellman completeness of GLMDPs with respect to a new function class that accommodates nonlinear rewards and develop two offline RL algorithms: Generalized Pessimistic Value Iteration (GPEVI) and a semi-supervised variant (SS-GPEVI) that utilizes both labeled and unlabeled trajectories. Our algorithms achieve theoretical guarantees on policy suboptimality and demonstrate improved sample efficiency in settings where reward labels are expensive or limited.

In this paper we analyze the sample complexities of learning the optimal state-action value function $Q^*$ and an optimal policy $π^*$ in a discounted Markov decision process (MDP) where the agent has recursive entropic risk-preferences with risk-parameter $β\neq 0$ and where a generative model of the MDP is available. We provide and analyze a simple model based approach which we call model-based risk-sensitive $Q$-value-iteration (MB-RS-QVI) which leads to $(ε,δ)$-PAC-bounds on $\|Q^*-Q^k\|$, and $\|V^*-V^{π_k}\|$ where $Q_k$ is the output of MB-RS-QVI after k iterations and $π_k$ is the greedy policy with respect to $Q_k$. Both PAC-bounds have exponential dependence on the effective horizon $\frac{1}{1-γ}$ and the strength of this dependence grows with the learners risk-sensitivity $|β|$. We also provide two lower bounds which shows that exponential dependence on $|β|\frac{1}{1-γ}$ is unavoidable in both cases. The lower bounds reveal that the PAC-bounds are both tight in $\varepsilon$ and $δ$ and that the PAC-bound on $Q$-learning is tight in the number of actions $A$, and that the PAC-bound on policy-learning is nearly tight in $A$.

We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications naturally exhibit random (potentially trajectory-dependent) stopping times. Since those stopping times typically depend on the policy, their randomness has an effect on policy gradient formulas, which we (mostly for the first time) derive rigorously in this work both for stochastic and deterministic policies. We present two complementary perspectives, trajectory or state-space based, and establish connections to optimal control theory. Our numerical experiments demonstrate that using the proposed formulas can significantly improve optimization convergence compared to traditional approaches.