# Opportunistic Qualitative Planning in Stochastic Systems with Incomplete Preferences over Reachability Objectives

arXiv: https://arxiv.org/abs/2210.01878 · HTML: https://mlsanity.com/paper/2210.01878/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Specifying User Preferences using Weighted Signal Temporal Logic](https://mlsanity.com/paper/2010.00752/) (2020)
- [What to Do When You Can't Do It All: Temporal Logic Planning with Soft Temporal Logic Constraints](https://mlsanity.com/paper/2008.01926/) (2020)
- [Minimum-Violation Planning for Autonomous Systems: Theoretical and Practical Considerations](https://mlsanity.com/paper/2009.11954/) (2020)
- [Probabilistic Planning with Preferences over Temporal Goals](https://mlsanity.com/paper/2103.14489/) (2021)
- [Probabilistic Planning with Partially Ordered Preferences over Temporal Goals](https://mlsanity.com/paper/2209.12267/) (2022)

## Built on by (most cited first, 1 of 1)

- [Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons](https://mlsanity.com/paper/2505.18030/) (2025)

## Abstract (arXiv)

Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this paper, we study how to synthesize preference satisfying plans in stochastic systems, modeled as an MDP, given a (possibly incomplete) combinative preference model over temporally extended goals. We start by introducing new semantics to interpret preferences over infinite plays of the stochastic system. Then, we introduce a new notion of improvement to enable comparison between two prefixes of an infinite play. Based on this, we define two solution concepts called safe and positively improving (SPI) and safe and almost-surely improving (SASI) that enforce improvements with a positive probability and with probability one, respectively. We construct a model called an improvement MDP, in which the synthesis of SPI and SASI strategies that guarantee at least one improvement reduces to computing positive and almost-sure winning strategies in an MDP. We present an algorithm to synthesize the SPI and SASI strategies that induce multiple sequential improvements. We demonstrate the proposed approach using a robot motion planning problem.