# Multi-objective Optimization of Long-run Average and Total Rewards

arXiv: https://arxiv.org/abs/2010.13566 · HTML: https://mlsanity.com/paper/2010.13566/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

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

- [Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective POMDPs and its Impact on Randomised Strategies](https://mlsanity.com/paper/2502.18296/) (2025)
- [MULTIGAIN 2.0: MDP controller synthesis for multiple mean-payoff, LTL and steady-state constraints](https://mlsanity.com/paper/2305.16752/) (2023)

## Abstract (arXiv)

This paper presents an efficient procedure for multi-objective model checking of long-run average reward (aka: mean pay-off) and total reward objectives as well as their combination. We consider this for Markov automata, a compositional model that captures both traditional Markov decision processes (MDPs) as well as a continuous-time variant thereof. The crux of our procedure is a generalization of Forejt et al.'s approach for total rewards on MDPs to arbitrary combinations of long-run and total reward objectives on Markov automata. Experiments with a prototypical implementation on top of the Storm model checker show encouraging results for both model types and indicate a substantial improved performance over existing multi-objective long-run MDP model checking based on linear programming.