Humanoid table tennis (TT) demands rapid perception, proactive whole-body motion, and agile footwork under strict timing -- capabilities that remain difficult for unified controllers. We propose a reinforcement learning framework that maps ball-position observations directly to whole-body joint commands for both arm striking and leg locomotion, strengthened by predictive signals and dense, physics-guided rewards. A lightweight learned predictor, fed with recent ball positions, estimates future ball states and augments the policy's observations for proactive decision-making. During training, a physics-based predictor supplies precise future states to construct dense, informative rewards that lead to effective exploration. The resulting policy attains strong performance across varied serve ranges (hit rate $\geq$ 96% and success rate $\geq$ 92%) in simulations. Ablation studies confirm that both the learned predictor and the predictive reward design are critical for end-to-end learning. Deployed zero-shot on a physical Booster T1 humanoid with 23 revolute joints, the policy produces coordinated lateral and forward-backward footwork with accurate, fast returns, suggesting a practical path toward versatile, competitive humanoid TT.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Abstract-- Reliable autonomous navigation across the unstructured terrains of distant planetary surfaces is a critical enabler for future space exploration. However, the deployment of learning-based controllers is hindered by the inherent sim-to-real gap, particularly for the complex dynamics of wheel interactions with granular media. This work presents a complete sim-to-real framework for developing and validating robust control policies for dynamic waypoint tracking on such challenging surfaces. We leverage massively parallel simulation to train reinforcement learning agents across a vast distribution of procedurally generated environments with randomized physics. These policies are then transferred zero-shot to a physical wheeled rover operating in a lunar-analogue facility. Our experiments systematically compare multiple reinforcement learning algorithms and action smoothing filters to identify the most effective combinations for real-world deployment. Crucially, we provide strong empirical evidence that agents trained with procedural diversity achieve superior zero-shot performance compared to those trained on static scenarios. We also analyze the trade-offs of fine-tuning with high-fidelity particle physics, which offers minor gains in low-speed precision at a significant computational cost. T ogether, these contributions establish a validated workflow for creating reliable learning-based navigation systems, marking a substantial step towards deploying autonomous robots in the final frontier .

Numerous heuristics and advanced approaches have been proposed for exploration in different settings for deep reinforcement learning. Noise-based exploration generally fares well with dense-shaped rewards and bonus-based exploration with sparse rewards. However, these methods usually require additional tuning to deal with undesirable reward settings by adjusting hyperparameters and noise distributions. Rewards that actively discourage exploration, i.e., with an action cost and no other dense signal to follow, can pose a major challenge. We propose a novel exploration method, Stable Error-seeking Exploration (SEE), that is robust across dense, sparse, and exploration-adverse reward settings. To this endeavor, we revisit the idea of maximizing the TD-error as a separate objective. Our method introduces three design choices to mitigate instability caused by far-off-policy learning, the conflict of interest of maximizing the cumulative TD-error in an episodic setting, and the non-stationary nature of TD-errors. SEE can be combined with off-policy algorithms without modifying the optimization pipeline of the original objective. In our experimental analysis, we show that a Soft-Actor Critic agent with the addition of SEE performs robustly across three diverse reward settings in a variety of tasks without hyperparameter adjustments.

A key challenge in reinforcement learning (RL) is reward (mis)specification, whereby imprecisely defined reward functions can result in unintended, possibly harmful, behaviours. Indeed, reward functions in RL are typically treated as black-box mappings from state-action pairs to scalar values. While effective in many settings, this approach provides no information about why rewards are given, which can hinder learning and interpretability. Reward Machines address this issue by representing reward functions as finite state automata, enabling the specification of structured, non-Markovian reward functions. However, their ex-pressivity is typically bounded by regular languages, leaving them unable to capture more complex behaviours such as counting or parametrised conditions. In this work, we build on the Runtime Monitoring Language (RML) to develop a novel class of language-based Reward Machines. By leveraging the built-in memory of RML, our approach can specify reward functions for non-regular, non-Markovian tasks. We demonstrate the expressiveness of our approach through experiments, highlighting additional advantages in flexible event-handling and task specification over existing Reward Machine-based methods.

Reinforcement learning (RL) has emerged as an effective paradigm for enhancing model reasoning. However, existing RL methods like GRPO often rely on unstructured self-sampling to fit scalar rewards, often producing inefficient rollouts that fail to capture transferable problem-solving strategies. To address these limitations, we propose **TemplateRL**, a structured template-guided RL framework that augments policy optimization with explicit template guidance. Our approach first constructs a problem-solving template library via MCTS on a small seed set, then seamlessly integrates this high-level structured guidance into RL training. By guiding rollout generation to align with proven template structures, TemplateRL significantly improves high-quality trajectory hit rates while reducing ineffective exploration. This structure-guided design steers the policy toward validated strategic patterns, stabilizing training dynamics, and enhancing RL sampling efficiency. Notably, the explicit template library is interpretable, editable, and supports online updates-enabling continuous updates during both training and inference. Extensive experiments demonstrate that TemplateRL outperforms GRPO by 99% on AIME and 41% on AMC, with superior stability on weak models and remarkable cross-domain generalization, highlighting its potential for broader tasks.

We study the emergence of tacit collusion between adaptive trading agents in a stochastic market with endogenous price formation. Using a two-player repeated game between a market maker and a market taker, we characterize feasible and collusive strategy profiles that raise prices beyond competitive levels. We show that, when agents follow simple learning algorithms (e.g., gradient ascent) to maximize their own wealth, the resulting dynamics converge to collusive strategy profiles, even in highly liquid markets with small trade sizes. By highlighting how simple learning strategies naturally lead to tacit collusion, our results offer new insights into the dynamics of AI-driven markets.

We train humanoid policies that compliantly respond to external forces while tracking a reference motion. The desired force-displacement relationship is modulated by a'stiffness' input at deployment time, and a single policy learns to realize a wide range of stiffnesses. In the images, the reference motion is visualized in blue, and the approximate external force on the robot is illustrated by the red arrows. Abstract-- We introduce SoftMimic, a framework for learning compliant whole-body control policies for humanoid robots from example motions. Imitating human motions with reinforcement learning allows humanoids to quickly learn new skills, but existing methods incentivize stiff control that aggressively corrects deviations from a reference motion, leading to brittle and unsafe behavior when the robot encounters unexpected contacts. In contrast, SoftMimic enables robots to respond compliantly to external forces while maintaining balance and posture. Our approach leverages an inverse kinematics solver to generate an augmented dataset of feasible compliant motions, which we use to train a reinforcement learning policy. By rewarding the policy for matching compliant responses rather than rigidly tracking the reference motion, SoftMimic learns to absorb disturbances and generalize to varied tasks from a single motion clip. I. INTRODUCTION A major goal in humanoid robotics is to build agents capable of performing a vast range of tasks humans execute in everyday environments. A promising avenue towards this goal is to leverage large-scale human motion capture data, enabling robots to learn human-like behaviors through imitation [1]. All authors are with the Improbable AI Lab, Massachusetts Institute of Technology, USA.

Language models often generate factually incorrect information unsupported by their training data, a phenomenon known as extrinsic hallucination. Existing mitigation approaches often degrade performance on open-ended generation and downstream tasks, limiting their practical utility. We propose an online reinforcement learning method using a novel binary retrieval-augmented reward (RAR) to address this tradeoff. Unlike continuous reward schemes, our approach assigns a reward of one only when the model's output is entirely factually correct, and zero otherwise. We evaluate our method on Qwen3 reasoning models across diverse tasks. For open-ended generation, binary RAR achieves a 39.3% reduction in hallucination rates, substantially outperforming both supervised training and continuous-reward RL baselines. In short-form question answering, the model learns calibrated abstention, strategically outputting "I don't know" when faced with insufficient parametric knowledge. This yields 44.4% and 21.7% fewer incorrect answers on PopQA and GPQA, respectively. Crucially, these factuality gains come without performance degradation on instruction following, math, or code, whereas continuous-reward RL, despite improving factuality, induces quality regressions.

Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.