# Maximum Expected Hitting Cost of a Markov Decision Process and Informativeness of Rewards

arXiv: https://arxiv.org/abs/1907.02114 · HTML: https://mlsanity.com/paper/1907.02114/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Informativeness of Reward Functions in Reinforcement Learning](https://mlsanity.com/paper/2402.07019/) (2024)
- [Gazing at Rewards: Eye Movements as a Lens into Human and AI Decision-Making in Hybrid Visual Foraging](https://mlsanity.com/paper/2411.09176/) (2024)
- [On Reward Structures of Markov Decision Processes](https://mlsanity.com/paper/2308.14919/) (2023)

## Abstract (arXiv)

We propose a new complexity measure for Markov decision processes (MDPs), the maximum expected hitting cost (MEHC). This measure tightens the closely related notion of diameter [JOA10] by accounting for the reward structure. We show that this parameter replaces diameter in the upper bound on the optimal value span of an extended MDP, thus refining the associated upper bounds on the regret of several UCRL2-like algorithms. Furthermore, we show that potential-based reward shaping [NHR99] can induce equivalent reward functions with varying informativeness, as measured by MEHC. We further establish that shaping can reduce or increase MEHC by at most a factor of two in a large class of MDPs with finite MEHC and unsaturated optimal average rewards.