UAV Trajectory Optimization via Improved Noisy Deep Q-Network

This paper proposes an Improved Noisy Deep Q-Network (Noisy DQN) to enhance the exploration and stability of Unmanned Aerial Vehicle (UAV) when applying deep reinforcement learning in simulated environments. This method enhances the exploration ability by combining the residual NoisyLinear layer with an adaptive noise scheduling mechanism, while improving training stability through smooth loss and soft target network updates. Experiments show that the proposed model achieves faster convergence and up to $+40$ higher rewards compared to standard DQN and quickly reach to the minimum number of steps required for the task 28 in the 15 * 15 grid navigation environment set up. The results show that our comprehensive improvements to the network structure of NoisyNet, exploration control, and training stability contribute to enhancing the efficiency and reliability of deep Q-learning.

EMA Policy Gradient: Taming Reinforcement Learning for LLMs with EMA Anchor and Top-k KL

Reinforcement Learning (RL) has enabled Large Language Models (LLMs) to acquire increasingly complex reasoning and agentic behaviors. In this work, we propose two simple techniques to improve policy gradient algorithms for LLMs. First, we replace the fixed anchor policy during RL with an Exponential Moving Average (EMA), similar to a target network in deep Q-learning. Second, we introduce Top-k KL estimator, which allows for flexible interpolation between exact KL and sampled KL. We derive the stability conditions for using EMA anchor; moreover, we show that our Top-k KL estimator yields both unbiased KL values and unbiased gradients at any k, while bringing the benefits of exact KL. When combined with GRPO, the two techniques (EMA-PG) lead to a significant performance boost. On math reasoning, it allows R1-distilled Qwen-1.5B to reach 53.9% on OlympiadBench compared to 50.8% by GRPO. On agentic RL domains, with Qwen-3B base, EMA-PG improves GRPO by an average of 33.3% across 7 datasets of Q&A with search engines, including 29.7% $\rightarrow$ 44.1% on HotpotQA, 27.4% $\rightarrow$ 40.1% on 2WikiMultiHopQA. Overall, we show that EMA-PG is a simple, principled, and powerful approach to scaling RL for LLMs. Code: https://github.com/LunjunZhang/ema-pg

Periodic Regularized Q-Learning

In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this limitation, a significant line of research has introduced regularization techniques to ensure stable convergence under function approximation. In this work, we propose a new algorithm, periodic regularized Q-learning (PRQ). We first introduce regularization at the level of the projection operator and explicitly construct a regularized projected value iteration (RP-VI), subsequently extending it to a sample-based RL algorithm. By appropriately regularizing the projection operator, the resulting projected value iteration becomes a contraction. By extending this regularized projection into the stochastic setting, we establish the PRQ algorithm and provide a rigorous theoretical analysis that proves finite-time convergence guarantees for PRQ under linear function approximation.

The Role of Target Update Frequencies in Q-Learning

The target network update frequency (TUF) is a central stabilization mechanism in (deep) Q-learning. However, their selection remains poorly understood and is often treated merely as another tunable hyperparameter rather than as a principled design decision. This work provides a theoretical analysis of target fixing in tabular Q-learning through the lens of approximate dynamic programming. We formulate periodic target updates as a nested optimization scheme in which each outer iteration applies an inexact Bellman optimality operator, approximated by a generic inner loop optimizer. Rigorous theory yields a finite-time convergence analysis for the asynchronous sampling setting, specializing to stochastic gradient descent in the inner loop. Our results deliver an explicit characterization of the bias-variance trade-off induced by the target update period, showing how to optimally set this critical hyperparameter. We prove that constant target update schedules are suboptimal, incurring a logarithmic overhead in sample complexity that is entirely avoidable with adaptive schedules. Our analysis shows that the optimal target update frequency increases geometrically over the course of the learning process.

Structuring Value Representations via Geometric Coherence in Markov Decision Processes

Geometric properties can be leveraged to stabilize and speed reinforcement learning. Existing examples include encoding symmetry structure, geometry-aware data augmentation, and enforcing structural restrictions. In this paper, we take a novel view of RL through the lens of order theory and recast value function estimates into learning a desired poset (partially ordered set). We propose \emph{GCR-RL} (Geometric Coherence Regularized Reinforcement Learning) that computes a sequence of super-poset refinements -- by refining posets in previous steps and learning additional order relationships from temporal difference signals -- thus ensuring geometric coherence across the sequence of posets underpinning the learned value functions. Two novel algorithms by Q-learning and by actor--critic are developed to efficiently realize these super-poset refinements. Their theoretical properties and convergence rates are analyzed. We empirically evaluate GCR-RL in a range of tasks and demonstrate significant improvements in sample efficiency and stable performance over strong baselines.

Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.

Choice-Model-Assisted Q-learning for Delayed-Feedback Revenue Management

We study reinforcement learning for revenue management with delayed feedback, where a substantial fraction of value is determined by customer cancellations and modifications observed days after booking. We propose \emph{choice-model-assisted RL}: a calibrated discrete choice model is used as a fixed partial world model to impute the delayed component of the learning target at decision time. In the fixed-model deployment regime, we prove that tabular Q-learning with model-imputed targets converges to an $O(\varepsilon/(1-γ))$ neighborhood of the optimal Q-function, where $\varepsilon$ summarizes partial-model error, with an additional $O(t^{-1/2})$ sampling term. Experiments in a simulator calibrated from 61{,}619 hotel bookings (1{,}088 independent runs) show: (i) no statistically detectable difference from a maturity-buffer DQN baseline in stationary settings; (ii) positive effects under in-family parameter shifts, with significant gains in 5 of 10 shift scenarios after Holm--Bonferroni correction (up to 12.4\%); and (iii) consistent degradation under structural misspecification, where the choice model assumptions are violated (1.4--2.6\% lower revenue). These results characterize when partial behavioral models improve robustness under shift and when they introduce harmful bias.

CRoSS: A Continual Robotic Simulation Suite for Scalable Reinforcement Learning with High Task Diversity and Realistic Physics Simulation

Continual reinforcement learning (CRL) requires agents to learn from a sequence of tasks without forgetting previously acquired policies. In this work, we introduce a novel benchmark suite for CRL based on realistically simulated robots in the Gazebo simulator. Our Continual Robotic Simulation Suite (CRoSS) benchmarks rely on two robotic platforms: a two-wheeled differential-drive robot with lidar, camera and bumper sensor, and a robotic arm with seven joints. The former represent an agent in line-following and object-pushing scenarios, where variation of visual and structural parameters yields a large number of distinct tasks, whereas the latter is used in two goal-reaching scenarios with high-level cartesian hand position control (modeled after the Continual World benchmark), and low-level control based on joint angles. For the robotic arm benchmarks, we provide additional kinematics-only variants that bypass the need for physical simulation (as long as no sensor readings are required), and which can be run two orders of magnitude faster. CRoSS is designed to be easily extensible and enables controlled studies of continual reinforcement learning in robotic settings with high physical realism, and in particular allow the use of almost arbitrary simulated sensors. To ensure reproducibility and ease of use, we provide a containerized setup (Apptainer) that runs out-of-the-box, and report performances of standard RL algorithms, including Deep Q-Networks (DQN) and policy gradient methods. This highlights the suitability as a scalable and reproducible benchmark for CRL research.

Q-ShiftDP: A Differentially Private Parameter-Shift Rule for Quantum Machine Learning

Quantum Machine Learning (QML) promises significant computational advantages, but preserving training data privacy remains challenging. Classical approaches like differentially private stochastic gradient descent (DP-SGD) add noise to gradients but fail to exploit the unique properties of quantum gradient estimation. In this work, we introduce the Differentially Private Parameter-Shift Rule (Q-ShiftDP), the first privacy mechanism tailored to QML. By leveraging the inherent boundedness and stochasticity of quantum gradients computed via the parameter-shift rule, Q-ShiftDP enables tighter sensitivity analysis and reduces noise requirements. We combine carefully calibrated Gaussian noise with intrinsic quantum noise to provide formal privacy and utility guarantees, and show that harnessing quantum noise further improves the privacy-utility trade-off. Experiments on benchmark datasets demonstrate that Q-ShiftDP consistently outperforms classical DP methods in QML.

Causal Flow Q-Learning for Robust Offline Reinforcement Learning

Expressive policies based on flow-matching have been successfully applied in reinforcement learning (RL) more recently due to their ability to model complex action distributions from offline data. These algorithms build on standard policy gradients, which assume that there is no unmeasured confounding in the data. However, this condition does not necessarily hold for pixel-based demonstrations when a mismatch exists between the demonstrator's and the learner's sensory capabilities, leading to implicit confounding biases in offline data. We address the challenge by investigating the problem of confounded observations in offline RL from a causal perspective. We develop a novel causal offline RL objective that optimizes policies' worst-case performance that may arise due to confounding biases. Based on this new objective, we introduce a practical implementation that learns expressive flow-matching policies from confounded demonstrations, employing a deep discriminator to assess the discrepancy between the target policy and the nominal behavioral policy. Experiments across 25 pixel-based tasks demonstrate that our proposed confounding-robust augmentation procedure achieves a success rate 120\% that of confounding-unaware, state-of-the-art offline RL methods.