Principal-Agent Reinforcement Learning: Orchestrating AI Agents with Contracts

We cordially thank the reviewer for these great suggestions!

We agree that exploring the sensitivity to the hyperparameter alpha (e.g., via an ablation study) and additional experiments would strengthen the paper. Regarding the latter, the other reviewers also make the case that it would be interesting to add additional experiments on more collaborative tasks (on which we should expect good/better results), in addition to focusing on very challenging settings in which the agents have very conflicting objectives (although more of these would of course be good, too).

We will work on both.

Thanks for pointing out the minor issues. We will fix these!

Thanks for the careful review and comments.

Thanks for the suggestion to try other more collaborative MARL tasks (such as division of labor tasks - e.g. clean up): We focused on tasks with conflicting objectives (such as in the coin game) as we believe these are the most challenging ones and hence most appealing ones for a contract approach (it’s not just about coordination of actions towards a joint objective, but intrinsically conflicting interest of the individual agents). It is also where we see the biggest gap in the literature. The rebuttal phase is too short to add further experiments, but we will be happy to work on adding other collaborative tasks to the list of experiments.

Regarding technical depth, we would like to emphasize Theorem 3.4, which shows that the meta-algorithm is a contraction operator. This is crucial for the practical implementation using deep Q-learning, where the algorithms will need to be stopped short of convergence. We do validate the convergence/approximation properties empirically.

Re Q1: We are not fully sure if we understand the question. Consider for a moment a single-shot contracting problem, the same rationale applies to the Markov Chain style games we consider. In the one shot game, a contract defines payments, and thus changes what the agent (or agents) consider as best responses to the contract. Intuitively, payments need to be higher if the agents’ interests are less well-aligned with each other and the principal. Conflicting interests jeopardize the stability of Q-learning, leading to instabilities or oscillations during the learning process. This has motivated us to propose and demonstrate that the meta-algorithm is a contraction, thereby enabling its practical implementation.

Re Q2: Thanks! The idea here is that at equilibrium agents will necessarily be indifferent, making solutions prone to small errors in approximation. Think of the principal having an action plan in mind, with full knowledge, in an optimal contract agent(s) will be indifferent at each step where they have to make decisions. The idea behind nudging is that the principal can just increase payments a bit to robustify this solution. (In some sense move away from the discontinuous cliffs, into the interior of the best response regions.)

Re Q3: Breach of contract. This is an interesting direction. But, of course, in many situations this would be prevented by legal provisions. We think that this could be an interesting future work to explore, but seems a bit like jumping two steps.

We thank the reviewer for the careful review and comments.

Regarding technical novelty and significance: We view our work of theory-backed practical algorithm design. We provide theoretical evidence (e.g., Theorem 3.4, showing that the meta-algorithm is iteratively applying a contraction operator) that corroborates our ultimate approach, which consists in adopting standard (scalable) ML pipelines (deep Q-learning) to solve a challenging highly combinatorial optimization problem.

It is true that prior work has considered similar approaches that modify agents’ rewards, but to the best of our knowledge the connection to contract design hasn’t been spelled out in this clarity. Contract design opens up new opportunities to design theoretically supported algorithms with the goal of minimizing the total payment. We believe that there is great value in bringing the two communities together.

It is also true that principal-agent theory can be understood more broadly, and encompasses additional directions. We will be happy to emphasize this, and include additional discussion.

Q1) Thanks for pointing this out. We will make sure to give this part another pass, and go with one of the two options that you suggest.

Q2) This is an interesting question. We believe both approaches have their pros and cons, and are worth exploring. We believe that the more centralized approach that we pursue in this work could have a lot of value, thinking of platforms that will serve to aggregate services offered by AI agents.

Thanks for the careful review and comments.

We believe that our work has some non-trivial theoretical insights, such as Theorem 3.4, which shows that the meta-algorithm is applying a contraction operator. This is crucial for the applicability of our results, because in the experimental parts we need to stop the deep Q-learning implementation short of convergence.

It is also not true that we don’t compare to existing baselines in the MARL literature (see reply to Q1 below). We do apologize that this was a bit hidden (we should have explicitly referred to the paper that inspired us to adopt this benchmark for comparison).

Re Q1: Thanks for pointing us to [2,3] (we already cite [1]), we will be happy to include additional discussion. For gifting methods as baselines, we would like to stress that these are not directly comparable with our method as agents are subtracted rewards and there is no centralized principal; we already compare with this line of work by adapting a similar method of the other contract design in MARL paper (see citation below). This is the “constant baseline” we refer to in Section 5 and Figures 2a and 2b. We found that this alternative is much less effective, achieving only around 85-90% of the welfare that our approach achieves (see the gap between the orange and gray lines in Figure 2a).

Phillip JK Christoffersen, Andreas A Haupt, and Dylan Hadfield-Menell. Get it in writing: Formal contracts mitigate social dilemmas in multi-agent RL. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems, pp. 448–456, 2023.

Re Q2: There is a profound difference between an “adaptive contract design approach” (our work) and an “adaptive mechanism design approach”. In short: These are two different branches in economics, dealing with very different incentive constraints. The emphasis on the former is on incentivizing effort, and a main obstacle is that the principal cannot directly observe how much effort the agents exert. We believe that this “incentivize effort” perspective is very adequate when thinking about creating marketplaces for AI agents, as these are quintessentially markets for services (effort).

This notwithstanding, we believe that ultimately we may want a solution that marries the two directions. Indeed, the focus of the adaptive mechanism design approach is that agents may have hidden types (think capabilities), and we would like to design mechanisms that incentivize agents to truthfully report their private types.

We would like to point to two simultaneous/subsequent works that also argue in favor of a contract design approach for AI agents. We believe that this provides additional evidence that this is a timely and important perspective.

Jibang Wu, Siyu Chen, Mengdi Wang, Huazheng Wang, Haifeng Xu. Contractual Reinforcement Learning: Pulling Arms with Invisible Hands. In ArXiv, 2024. https://arxiv.org/abs/2407.01458

Matteo Bollini, Francesco Bacchiocchi, Matteo Castiglioni, Alberto Marchesi, Nicola Gatti. Contracting with a Reinforcement Learning Agent by Playing Trick or Treat. In ArXiv, 2024. https://arxiv.org/abs/2410.13520