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).

We study pure exploration in structured stochastic multi-armed bandits, aiming to efficiently identify the correct hypothesis from a finite set of alternatives. For a broad class of tasks, asymptotic analyses reduce to a maximin optimization that admits a two-player zero-sum game interpretation between an experimenter and a skeptic: the experimenter allocates measurements to rule out alternatives while the skeptic proposes alternatives. We reformulate the game by allowing the skeptic to adopt a mixed strategy, yielding a concave-convex saddle-point problem. This viewpoint leads to Frank-Wolfe Self-Play (FWSP): a projection-free, regularization-free, tuning-free method whose one-hot updates on both sides match the bandit sampling paradigm. However, structural constraints introduce sharp pathologies that complicate algorithm design and analysis: our linear-bandit case study exhibits nonunique optima, optimal designs with zero mass on the best arm, bilinear objectives, and nonsmoothness at the boundary. We address these challenges via a differential-inclusion argument, proving convergence of the game value for best-arm identification in linear bandits. Our analysis proceeds through a continuous-time limit: a differential inclusion with a Lyapunov function that decays exponentially, implying a vanishing duality gap and convergence to the optimal value. Although Lyapunov analysis requires differentiability of the objective, which is not guaranteed on the boundary, we show that along continuous trajectories the algorithm steers away from pathological nonsmooth points and achieves uniform global convergence to the optimal game value. We then embed the discrete-time updates into a perturbed flow and show that the discrete game value also converges. Building on FWSP, we further propose a learning algorithm based on posterior sampling. Numerical experiments demonstrate a vanishing duality gap.

Imitation Learning (IL) algorithms offer an efficient way to train an agent by mimicking an expert's behavior without requiring a reward function. IL algorithms often necessitate access to state and action information from expert demonstrations. Although expert actions can provide detailed guidance, requiring such action information may prove impractical for real-world applications where expert actions are difficult to obtain. To address this limitation, the concept of learning from observation (LfO) or state-only imitation learning (SOIL) has recently gained attention, wherein the imitator only has access to expert state visitation information. In this paper, we present a framework for LfO and use it to survey and classify existing LfO methods in terms of their trajectory construction, assumptions and algorithm's design choices. This survey also draws connections between several related fields like offline RL, model-based RL and hierarchical RL. Finally, we use our framework to identify open problems and suggest future research directions.