Learning Unknown Oscillators from Bandit Feedback

We study semi-bandits driven by unknown oscillators. Each round, a learner selects two of four reward channels and observes their individual rewards. Frequency errors change future reward rankings and the resulting measurements. We show when committing to one fitted oscillator lets its greedy choices expose prediction errors. Our controller bounds reward loss (regret) over a continuous confidence set and holds the longest block within budget. An online regression policy gathers observations when the check fails. Regret grows at a square-root rate, up to logarithmic factors, across all frequencies and extends to two competing oscillators. On 96 fresh synthetic instances, checked commitment uses 49 fits instead of 1,023, with 1.5% higher mean regret than fitting every round. Matched isolated timings give a 4.69-fold speedup. The confidence sets also certify trajectory regret.