# Unpredictable Planning Under Partial Observability

arXiv: https://arxiv.org/abs/1903.07665 · HTML: https://mlsanity.com/paper/1903.07665/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs](https://mlsanity.com/paper/2108.10227/) (2021)
- [LTLf Synthesis Under Unreliable Input](https://mlsanity.com/paper/2412.14728/) (2024)

## Abstract (arXiv)

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of a decision-maker's trajectories while guaranteeing the completion of a task expressed by a reward function. First, we prove that a decision-maker with perfect observations can randomize its paths at least as well as a decision-maker with partial observations. Then, focusing on finite-state controllers, we recast the entropy maximization problem as a so-called parameter synthesis problem for a parametric Markov chain (pMC). We show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of this pMC. Finally, we present an algorithm, based on a nonlinear optimization problem, to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we demonstrate the proposed algorithm on motion planning scenarios.