Principal-Agent Reward Shaping in MDPs

Omer Ben-Porat; Yishay Mansour; Michal Moshkovitz; Boaz Taitler

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arXiv · 2401.00298

Principal-Agent Reward Shaping in MDPs

Omer Ben-Porat·Yishay Mansour·Michal Moshkovitz·Boaz Taitler

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Abstract

Principal-agent problems arise when one party acts on behalf of another, leading to conflicts of interest. The economic literature has extensively studied principal-agent problems, and recent work has extended this to more complex scenarios such as Markov Decision Processes (MDPs). In this paper, we further explore this line of research by investigating how reward shaping under budget constraints can improve the principal's utility. We study a two-player Stackelberg game where the principal and the agent have different reward functions, and the agent chooses an MDP policy for both players. The principal offers an additional reward to the agent, and the agent picks their policy selfishly to maximize their reward, which is the sum of the original and the offered reward. Our results establish the NP-hardness of the problem and offer polynomial approximation algorithms for two classes of instances: Stochastic trees and deterministic decision processes with a finite horizon.

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Omer Ben-Porat, Yishay Mansour, Michal Moshkovitz, Boaz Taitler. 2023-12-30. Principal-Agent Reward Shaping in MDPs. https://arxiv.org/abs/2401.00298

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