PianoGym: Safe post-action piano rhythm training with fatigue constraints

Bimanual piano rhythm training must maintain precise interlimb timing under limited practice time and under fatigue constraints, while feedback on performance is typically available only after an exercise. A piano practice gym environment (PianoGym) is used as a reproducible simulator for fatigue-constrained piano rhythm training under post-action feedback. The training task is formulated as a fatigue-constrained, post-action, partially observable Markov decision process (POMDP). In this POMDP, a controller observes beat asynchrony, dominance gap, synchronization fidelity, and two fatigue signals, and selects the next exercise from a finite library of structured practice actions. To handle delayed measurements and fatigue feasibility under the simulator budget, we introduce a dual-timescale safety layer. The slow Lagrangian part tracks a long-horizon average constraint using revealed true fatigue, while the fast predictive guard screens candidate actions using the online fatigue estimate. On top of this layer, a piano model predictive controller (PianoMPC) uses certainty-equivalent planning and performs finite-horizon rollouts over a calibrated surrogate environment model and searches only within guard-filtered action sets. In the main three-profile experiment, PianoMPC achieves mean time-to-mastery values of 24.4 to 28.2 steps and FeasibleRate values of 0.90 to 0.95 under the shared environment-side guard. Under the same environment-side guard, it also outperforms bandit and value-based agents. These results indicate that model-predictive planning can convert a fixed operational fatigue budget into faster progress in fatigue-aware piano practice within the PianoGym simulator and its stated surrogate fatigue and skill-dynamics assumptions.