Planned Restlessness: Delayed Meta Bandits with Budgets

Sudipto Guha

We study episodic finite-horizon Bayesian bandits, or meta-bandits, with independent arms. Each episode draws fresh arm qualities from unknown recurring priors. Observations arrive after known delays, and plays obey hard per-episode caps and total budgets. A play earns reward and informs both the current quality and the recurring prior: the learner must explore, use, and generalize. We formulate a common planning optimization over learning trajectories. Its LP relaxation values experiments through current reward, resource consumption and continuation: the value of future decisions from the learning state produced. Dual prices separate the arms into local programs and certify every admissible policy, including hierarchical Thompson sampling. Execution enforces the hard constraints while preserving the promised learning transitions or accounting for their loss. The framework also represents risk-sensitive objectives and prices purchased observations and buyout options. Delayed reports create planned restlessness: an arm's information changes while it is not played, through reports of its own earlier plays arriving on a known calendar. For stationary priors, finite reward alphabets,…