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Contractual Reinforcement Learning: Pulling Arms with Invisible Hands

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Listed:
  • Jibang Wu
  • Siyu Chen
  • Mengdi Wang
  • Huazheng Wang
  • Haifeng Xu

Abstract

The agency problem emerges in today's large scale machine learning tasks, where the learners are unable to direct content creation or enforce data collection. In this work, we propose a theoretical framework for aligning economic interests of different stakeholders in the online learning problems through contract design. The problem, termed \emph{contractual reinforcement learning}, naturally arises from the classic model of Markov decision processes, where a learning principal seeks to optimally influence the agent's action policy for their common interests through a set of payment rules contingent on the realization of next state. For the planning problem, we design an efficient dynamic programming algorithm to determine the optimal contracts against the far-sighted agent. For the learning problem, we introduce a generic design of no-regret learning algorithms to untangle the challenges from robust design of contracts to the balance of exploration and exploitation, reducing the complexity analysis to the construction of efficient search algorithms. For several natural classes of problems, we design tailored search algorithms that provably achieve $\tilde{O}(\sqrt{T})$ regret. We also present an algorithm with $\tilde{O}(T^{2/3})$ for the general problem that improves the existing analysis in online contract design with mild technical assumptions.

Suggested Citation

  • Jibang Wu & Siyu Chen & Mengdi Wang & Huazheng Wang & Haifeng Xu, 2024. "Contractual Reinforcement Learning: Pulling Arms with Invisible Hands," Papers 2407.01458, arXiv.org, revised Jul 2024.
  • Handle: RePEc:arx:papers:2407.01458
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    References listed on IDEAS

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    1. Jibang Wu & Zixuan Zhang & Zhe Feng & Zhaoran Wang & Zhuoran Yang & Michael I. Jordan & Haifeng Xu, 2022. "Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning," Papers 2202.10678, arXiv.org.
    2. Hemant K. Bhargava, 2022. "The Creator Economy: Managing Ecosystem Supply, Revenue Sharing, and Platform Design," Management Science, INFORMS, vol. 68(7), pages 5233-5251, July.
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