Delays frequently occur in real-world environments, yet standard reinforcement learning (RL) algorithms often assume instantaneous perception of the environment. We study random sensor delays in POMDPs, where observations may arrive out-of-sequence, a setting that has not been previously addressed in RL. We analyze the structure of such delays and demonstrate that naive approaches, such as stacking past observations, are insufficient for reliable performance. To address this, we propose a model-based filtering process that sequentially updates the belief state based on an incoming stream of observations. We then introduce a simple delay-aware framework that incorporates this idea into model-based RL, enabling agents to effectively handle random delays. Applying this framework to Dreamer, we compare our approach to delay-aware baselines developed for MDPs. Our method consistently outperforms these baselines and demonstrates robustness to delay distribution shifts during deployment. Additionally, we present experiments on simulated robotic tasks, comparing our method to common practical heuristics and emphasizing the importance of explicitly modeling observation delays.

Abstract-- Long-horizon, high-dynamic motion tracking on humanoids remains brittle because absolute joint commands cannot compensate model-plant mismatch, leading to error accumulation. We propose RobotDancing, a simple, scalable framework that predicts residual joint targets to explicitly correct dynamics discrepancies. The pipeline is end-to-end--training, sim-to-sim validation, and zero-shot sim-to-real--and uses a single-stage reinforcement learning (RL) setup with a unified observation, reward, and hyperparameter configuration. RobotDancing can track multi-minute, high-energy behaviors (jumps, spins, cartwheels) and deploys zero-shot to hardware with high motion tracking quality. I. INTRODUCTION Humanoid robots are increasingly expected to execute long-horizon, highly dynamic behaviors such as dance, where small tracking errors compound rapidly and destabilize control. A principal source of such drift is the mismatch between idealized reference trajectories and the robot's true physics (actuation limits, friction, inertia, latency).

A deep dive into the open literature shows that there are t hree fundamental limitations to current ML approaches, namely blackbox brittleness (which renders models uninterpretable and unreliable under distribution shift [2]), causal blindness (which conflates correlation with causation [3]), and alignment failures (which produce systems optimizing objectives misaligned with human values [4]) . These deficiencies stem from a profound philosophical poverty in how ML conceptualizes knowledge, reasoning, and values. The first fundamental limitation, b lackbox brittleness, manifests when trained models fail on seemingly trivial variations of their training distribution. For example, a vision model that accurately identifies stop signs under normal conditions might misclassify them entirely when small adversarial perturbations are applied [5] . Not surprisingly, t h e same brittleness extends beyond adversarial examples to everyday distribution shifts (e.g., natural language processing models exhibit performance degradation when processing text from different cultural contexts, etc.) [6] .