We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based algorithm that uses clipping to constrain the span of the value function for improved statistical efficiency. However, the clipping procedure requires computing the minimum of the value function over the entire state space, which is prohibitive since the state space in linear MDP setting can be large or even infinite. In this paper, we introduce a value iteration method with efficient clipping operation that only requires computing the minimum of value functions over the set of states visited by the algorithm. Our algorithm enjoys the same regret bound as the previous work while being computationally efficient, with computational complexity that is independent of the size of the state space.

An uneven shell surface enables steering by using only the movement of the pendulum, allowing for mechanically simple designs that may be feasible to scale to large quantities or small sizes. We train a control policy using reinforcement learning in simulation and deploy it onto the robot to complete a rectangular trajectory. I. INTRODUCTION A. Motivation Existing spherical robot designs require two to four actuators for steering and jumping capabilities [1], increasing cost, power use, maintenance, and size. Reducing the number of actuators can alleviate these challenges, making it easier to scale to greater numbers and smaller sizes. This work investigates ROCK, a robot with an internal pendulum controlled by a single motor capable of rolling, steering, and jumping.

Motivated by collaborative reinforcement learning (RL) and optimization with time-correlated data, we study a generic federated stochastic approximation problem involving $M$ agents, where each agent is characterized by an agent-specific (potentially nonlinear) local operator. The goal is for the agents to communicate intermittently via a server to find the root of the average of the agents' local operators. The generality of our setting stems from allowing for (i) Markovian data at each agent and (ii) heterogeneity in the roots of the agents' local operators. The limited recent work that has accounted for both these features in a federated setting fails to guarantee convergence to the desired point or to show any benefit of collaboration; furthermore, they rely on projection steps in their algorithms to guarantee bounded iterates. Our work overcomes each of these limitations. We develop a novel algorithm titled \texttt{FedHSA}, and prove that it guarantees convergence to the correct point, while enjoying an $M$-fold linear speedup in sample-complexity due to collaboration. To our knowledge, \emph{this is the first finite-time result of its kind}, and establishing it (without relying on a projection step) entails a fairly intricate argument that accounts for the interplay between complex temporal correlations due to Markovian sampling, multiple local steps to save communication, and the drift-effects induced by heterogeneous local operators. Our results have implications for a broad class of heterogeneous federated RL problems (e.g., policy evaluation and control) with function approximation, where the agents' Markov decision processes can differ in their probability transition kernels and reward functions.

Reinforcement learning (RL) has emerged as a powerful paradigm for solving decision-making problems in dynamic environments. In this research, we explore the application of Double DQN (DDQN) and Dueling Network Architectures, to financial trading tasks using historical SP500 index data. Our focus is training agents capable of optimizing trading strategies while accounting for practical constraints such as transaction costs. The study evaluates the model performance across scenarios with and without commissions, highlighting the impact of cost-sensitive environments on reward dynamics. Despite computational limitations and the inherent complexity of financial time series data, the agent successfully learned meaningful trading policies. The findings confirm that RL agents, even when trained on limited datasets, can outperform random strategies by leveraging advanced architectures such as DDQN and Dueling Networks. However, significant challenges persist, particularly with a sub-optimal policy due to the complexity of data source.

Reward comparisons are vital for evaluating differences in agent behaviors induced by a set of reward functions. Most conventional techniques utilize the input reward functions to learn optimized policies, which are then used to compare agent behaviors. However, learning these policies can be computationally expensive and can also raise safety concerns. Direct reward comparison techniques obviate policy learning but suffer from transition sparsity, where only a small subset of transitions are sampled due to data collection challenges and feasibility constraints. Existing state-of-the-art direct reward comparison methods are ill-suited for these sparse conditions since they require high transition coverage, where the majority of transitions from a given coverage distribution are sampled. When this requirement is not satisfied, a distribution mismatch between sampled and expected transitions can occur, leading to significant errors. This paper introduces the Sparsity Resilient Reward Distance (SRRD) pseudometric, designed to eliminate the need for high transition coverage by accommodating diverse sample distributions, which are common under transition sparsity. We provide theoretical justification for SRRD's robustness and conduct experiments to demonstrate its practical efficacy across multiple domains.

This paper proposes SafeGPT, a two-tiered framework that integrates generative pretrained transformers (GPTs) with reinforcement learning (RL) for efficient and reliable unmanned aerial vehicle (UAV) last-mile deliveries. In the proposed design, a Global GPT module assigns high-level tasks such as sector allocation, while an On-Device GPT manages real-time local route planning. An RL-based safety filter monitors each GPT decision and overrides unsafe actions that could lead to battery depletion or duplicate visits, effectively mitigating hallucinations. Furthermore, a dual replay buffer mechanism helps both the GPT modules and the RL agent refine their strategies over time. Simulation results demonstrate that SafeGPT achieves higher delivery success rates compared to a GPT-only baseline, while substantially reducing battery consumption and travel distance. These findings validate the efficacy of combining GPT-based semantic reasoning with formal safety guarantees, contributing a viable solution for robust and energy-efficient UAV logistics.

Progress in offline reinforcement learning (RL) has been impeded by ambiguous problem definitions and entangled algorithmic designs, resulting in inconsistent implementations, insufficient ablations, and unfair evaluations. Although offline RL explicitly avoids environment interaction, prior methods frequently employ extensive, undocumented online evaluation for hyperparameter tuning, complicating method comparisons. Moreover, existing reference implementations differ significantly in boilerplate code, obscuring their core algorithmic contributions. We address these challenges by first introducing a rigorous taxonomy and a transparent evaluation protocol that explicitly quantifies online tuning budgets. To resolve opaque algorithmic design, we provide clean, minimalistic, single-file implementations of various model-free and model-based offline RL methods, significantly enhancing clarity and achieving substantial speed-ups. Leveraging these streamlined implementations, we propose Unifloral, a unified algorithm that encapsulates diverse prior approaches within a single, comprehensive hyperparameter space, enabling algorithm development in a shared hyperparameter space. Using Unifloral with our rigorous evaluation protocol, we develop two novel algorithms - TD3-AWR (model-free) and MoBRAC (model-based) - which substantially outperform established baselines. Our implementation is publicly available at https://github.com/EmptyJackson/unifloral.

Risk-averse reinforcement learning (RARL) is critical for decision-making under uncertainty, which is especially valuable in high-stake applications. However, most existing works focus on risk measures, e.g., conditional value-at-risk (CVaR), while measures of variability remain underexplored. In this paper, we comprehensively study nine common measures of variability, namely Variance, Gini Deviation, Mean Deviation, Mean-Median Deviation, Standard Deviation, Inter-Quantile Range, CVaR Deviation, Semi_Variance, and Semi_Standard Deviation. Among them, four metrics have not been previously studied in RARL. We derive policy gradient formulas for these unstudied metrics, improve gradient estimation for Gini Deviation, analyze their gradient properties, and incorporate them with the REINFORCE and PPO frameworks to penalize the dispersion of returns. Our empirical study reveals that variance-based metrics lead to unstable policy updates. In contrast, CVaR Deviation and Gini Deviation show consistent performance across different randomness and evaluation domains, achieving high returns while effectively learning risk-averse policies. Mean Deviation and Semi_Standard Deviation are also competitive across different scenarios. This work provides a comprehensive overview of variability measures in RARL, offering practical insights for risk-aware decision-making and guiding future research on risk metrics and RARL algorithms.

We introduce Kimina-Prover Preview, a large language model that pioneers a novel reasoning-driven exploration paradigm for formal theorem proving, as showcased in this preview release. Trained with a large-scale reinforcement learning pipeline from Qwen2.5-72B, Kimina-Prover demonstrates strong performance in Lean 4 proof generation by employing a structured reasoning pattern we term \textit{formal reasoning pattern}. This approach allows the model to emulate human problem-solving strategies in Lean, iteratively generating and refining proof steps. Kimina-Prover sets a new state-of-the-art on the miniF2F benchmark, reaching 80.7% with pass@8192. Beyond improved benchmark performance, our work yields several key insights: (1) Kimina-Prover exhibits high sample efficiency, delivering strong results even with minimal sampling (pass@1) and scaling effectively with computational budget, stemming from its unique reasoning pattern and RL training; (2) we demonstrate clear performance scaling with model size, a trend previously unobserved for neural theorem provers in formal mathematics; (3) the learned reasoning style, distinct from traditional search algorithms, shows potential to bridge the gap between formal verification and informal mathematical intuition. We open source distilled versions with 1.5B and 7B parameters of Kimina-Prover

Hindsight Experience Replay (HER) is widely regarded as the state-of-the-art algorithm for achieving sample-efficient multi-goal reinforcement learning (RL) in robotic manipulation tasks with binary rewards. HER facilitates learning from failed attempts by replaying trajectories with redefined goals. However, it relies on a heuristic-based replay method that lacks a principled framework. To address this limitation, we introduce a novel replay strategy, "Next-Future", which focuses on rewarding single-step transitions. This approach significantly enhances sample efficiency and accuracy in learning multi-goal Markov decision processes (MDPs), particularly under stringent accuracy requirements -- a critical aspect for performing complex and precise robotic-arm tasks. We demonstrate the efficacy of our method by highlighting how single-step learning enables improved value approximation within the multi-goal RL framework. The performance of the proposed replay strategy is evaluated across eight challenging robotic manipulation tasks, using ten random seeds for training. Our results indicate substantial improvements in sample efficiency for seven out of eight tasks and higher success rates in six tasks. Furthermore, real-world experiments validate the practical feasibility of the learned policies, demonstrating the potential of "Next-Future" in solving complex robotic-arm tasks.