Threshold Structure of Optimal Policies in Restart POMDPs
We study a Restart POMDP (Partially Observable Markov Decision Process) on a general Borel state space, where the controller either lets the hidden state evolve unobserved or restarts the system and observes the new state. Exploiting a sufficient-statistic representation consisting of the last observed state and the elapsed time since restart, we reduce the problem to a fully observed MDP. Under a natural one-step cost deterioration condition, we prove that optimal policies have a threshold structure in the elapsed time for both the discounted and total undiscounted cost criteria. When the state space is partially ordered and the kernel is stochastically monotone, we further show that the...
| Authors | Konstantin Avrachenkov, Alexey Piunovskiy, Yi Zhang |
|---|---|
| Primary category | math.OC |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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