On Satisficing in Quantitative Games

by   Suguman Bansal, et al.

Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. Optimization is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the 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.


page 1

page 2

page 3

page 4


The Adversarial Stackelberg Value in Quantitative Games

In this paper, we study the notion of adversarial Stackelberg value for ...

Parameterized complexity of games with monotonically ordered ω-regular objectives

In recent years, two-player zero-sum games with multiple objectives have...

One-to-Two-Player Lifting for Mildly Growing Memory

We investigate so-called "one-to-two-player lifting" theorems for infini...

Hodge decomposition and the Shapley value of a cooperative game

We show that a cooperative game may be decomposed into a sum of componen...

Satisficing Paths and Independent Multi-Agent Reinforcement Learning in Stochastic Games

In multi-agent reinforcement learning (MARL), independent learners are t...

A Simple Yet Effective Approach to Robust Optimization Over Time

Robust optimization over time (ROOT) refers to an optimization problem w...