Optimistic Whittle Index Policy: Online Learning for Restless Bandits
This work addresses the challenge of decision-making under uncertainty in sequential resource allocation problems, such as healthcare scheduling, by providing a novel online learning solution for RMABs, though it is incremental as it builds on the Whittle index policy.
The authors tackled the problem of planning in restless multi-armed bandits with unknown transition dynamics by proposing UCWhittle, an online learning algorithm based on the Whittle index policy, which achieves sublinear O(H √(T log T)) frequentist regret and outperforms existing baselines in empirical tests across three domains.
Restless multi-armed bandits (RMABs) extend multi-armed bandits to allow for stateful arms, where the state of each arm evolves restlessly with different transitions depending on whether that arm is pulled. Solving RMABs requires information on transition dynamics, which are often unknown upfront. To plan in RMAB settings with unknown transitions, we propose the first online learning algorithm based on the Whittle index policy, using an upper confidence bound (UCB) approach to learn transition dynamics. Specifically, we estimate confidence bounds of the transition probabilities and formulate a bilinear program to compute optimistic Whittle indices using these estimates. Our algorithm, UCWhittle, achieves sublinear $O(H \sqrt{T \log T})$ frequentist regret to solve RMABs with unknown transitions in $T$ episodes with a constant horizon $H$. Empirically, we demonstrate that UCWhittle leverages the structure of RMABs and the Whittle index policy solution to achieve better performance than existing online learning baselines across three domains, including one constructed from a real-world maternal and childcare dataset.