On Satisficing in Quantitative Games
This work proposes an alternative problem formulation (satisficing) for planning and reactive synthesis problems, potentially offering algorithmic advantages for researchers and practitioners in these areas.
This paper explores replacing optimization with satisficing in two-player quantitative graph games, specifically with the discounted-sum cost model. While numerical methods for satisficing offer no significant benefit over optimization, an automata-based approach for integer discount factors is shown to be more performant both theoretically and empirically.
Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. {\em Optimization} is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the {\em satisficing problem}, where instead of searching for optimal solutions, the goal is to search for solutions that adhere to a given threshold bound. This work defines and investigates the satisficing problem on a two-player graph game with the discounted-sum cost model. We show that while the satisficing problem can be solved using numerical methods just like the optimization problem, this approach does not render compelling benefits over optimization. When the discount factor is, however, an integer, we present another approach to satisficing, which is purely based on automata methods. We show that this approach is algorithmically more performant -- both theoretically and empirically -- and demonstrates the broader applicability of satisficing overoptimization.