Periodic Reporting for period 1 - ALGOCONTRACT (Algorithmic Contract Design)
Periodo di rendicontazione: 2023-01-01 al 2025-06-30
When delegating a task – whether to human talent or to an AI agent - how do we ensure a quality outcome that aligns with our goals? By using smart, performance-based incentive models (contracts) driven by algorithms and learning, we can significantly boost efficiency and accountability. The main objective of my research project is to establish a new research field, Algorithmic Contract Design, which develops the underlying algorithmic theory needed to design such pay-for-performance contracts.
Recent years have seen a huge shift in the role of algorithms in society. Algorithm design must provide a new kind of guarantee – on the incentives the algorithm sets for exerting effort. The economic field dedicated to effort incentivization is that of contract design. This important field has amassed a vast literature in economics, culminating with the 2016 Nobel prize. Our vision is to realize the huge potential of applying the algorithmic lens to contract design.
Applications include: (1) Decision-making algorithms like classifiers – subjects exert effort to classify for loans or school admission; (2) Online platforms for services (freelancing), the essence of which is to incentivize effort algorithmically at scale; (3) Incentives for GenAI agents - we are increasingly moving towards an online world powered by markets of agents, and contracts among multiple players are needed to align interests.
Recent years have seen a huge shift in the role of algorithms in society. Algorithm design must provide a new kind of guarantee – on the incentives the algorithm sets for exerting effort. The economic field dedicated to effort incentivization is that of contract design. This important field has amassed a vast literature in economics, culminating with the 2016 Nobel prize. Our vision is to realize the huge potential of applying the algorithmic lens to contract design.
Applications include: (1) Decision-making algorithms like classifiers – subjects exert effort to classify for loans or school admission; (2) Online platforms for services (freelancing), the essence of which is to incentivize effort algorithmically at scale; (3) Incentives for GenAI agents - we are increasingly moving towards an online world powered by markets of agents, and contracts among multiple players are needed to align interests.
We briefly describe two main achievements to demonstrate our progress:
A first main achievement is understanding the computation complexity of contracts versus algorithms. In other words, how much more complex is it to design an algorithm under the extra constraint of making it incentive-compatible for rational agents to exert the effort required to realize the output? We introduce the classic knapsack problem as a testbed for the complexity of contracts. In the paper “Knapsack Contracts”, a principal incentivizes agents to perform tasks with stochastic completion times, which depend on the agent's rationally chosen effort level. We establish a deep connection between this contract design problem and the multi-choice stochastic knapsack problem with costs, a harder variant of the stochastic knapsack problem. In another paper, “An Algorithm-to-Contract Framework without Demand Queries”, we consider costly tasks that add up to the success of a project, and must be fitted into a given time-frame – a standard knapsack problem with well-known FPTAS. Now assume that the agent is performing these tasks on behalf of a principal. We show how to “lift” the FPTAS for knapsack to a multiplicative and additive FPTAS for the contract design problem. We establish our positive result through a “local to global” framework, and apply our framework to other combinatorial constraints like budgeted matroid. Taken together, these works show the extra complexity introduced by effort incentives, while identifying a class of problems for which algorithmic guarantees can be extended to hold even subject to incentive constraints.
A second major achievement is to shed new light on simple contract formats. A classic and fundamental question is: when do simple linear contracts approximate the optimal, complex one? In “Bayesian Analysis of Linear Contracts” we give the first Bayesian justification of linear contracts. We show that linear contracts are unique in that they admit approximation guarantees which improve with the degree of uncertainty in the contracting setting. In other words, linear contracts are near-optimal whenever there is enough uncertainty about the agent population tasked with exerting the required effort. This formalizes “conventional wisdom” as to the advantage of linear contracts due to their robustness.
These and other achievements are described in our new 200-page survey on Algorithmic Contract Theory, published in December 2024 with the intent of getting more computer scientists involved in the effort of establishing the new research field.
A first main achievement is understanding the computation complexity of contracts versus algorithms. In other words, how much more complex is it to design an algorithm under the extra constraint of making it incentive-compatible for rational agents to exert the effort required to realize the output? We introduce the classic knapsack problem as a testbed for the complexity of contracts. In the paper “Knapsack Contracts”, a principal incentivizes agents to perform tasks with stochastic completion times, which depend on the agent's rationally chosen effort level. We establish a deep connection between this contract design problem and the multi-choice stochastic knapsack problem with costs, a harder variant of the stochastic knapsack problem. In another paper, “An Algorithm-to-Contract Framework without Demand Queries”, we consider costly tasks that add up to the success of a project, and must be fitted into a given time-frame – a standard knapsack problem with well-known FPTAS. Now assume that the agent is performing these tasks on behalf of a principal. We show how to “lift” the FPTAS for knapsack to a multiplicative and additive FPTAS for the contract design problem. We establish our positive result through a “local to global” framework, and apply our framework to other combinatorial constraints like budgeted matroid. Taken together, these works show the extra complexity introduced by effort incentives, while identifying a class of problems for which algorithmic guarantees can be extended to hold even subject to incentive constraints.
A second major achievement is to shed new light on simple contract formats. A classic and fundamental question is: when do simple linear contracts approximate the optimal, complex one? In “Bayesian Analysis of Linear Contracts” we give the first Bayesian justification of linear contracts. We show that linear contracts are unique in that they admit approximation guarantees which improve with the degree of uncertainty in the contracting setting. In other words, linear contracts are near-optimal whenever there is enough uncertainty about the agent population tasked with exerting the required effort. This formalizes “conventional wisdom” as to the advantage of linear contracts due to their robustness.
These and other achievements are described in our new 200-page survey on Algorithmic Contract Theory, published in December 2024 with the intent of getting more computer scientists involved in the effort of establishing the new research field.
Our project connects the distinct research areas of contracts and learning theory. For example: In “Deep Contract Design via Discontinuous Networks” we initiate the study of deep learning for the automated design of optimal contracts. We provide empirical results that demonstrate success in approximating the principal's utility function with a small number of training samples and scaling to find approximately optimal contracts on problems with a large number of actions and outcomes. In our work titled “Delegated Classification”, the starting point is that when machine learning is outsourced to a rational agent, conflicts of interest might arise and severely impact predictive performance. In this work, we propose a contract-based, theoretical framework for incentive-aware delegation of machine learning tasks, and validate it empirically.
We also combine contracts with the study of information to achieve more realistic models: In “Algorithmic Cheap Talk”, we initiate the algorithmic study of natural communication among rational players, known as cheap talk. The next step is to apply this to communication among the contract designer and the agent(s). In “Information Design in the Principal-Agent Problem”, we allow the task delegator to get information about the agent's effort according to an “information structure” – a monitoring scheme designed to increase social welfare and lower losses from incomplete information.
Two works with high impact potential study (1) contracts for learning agents and (2) contracts for pricing AI services:
(1) As autonomous AI agents are increasingly used in various markets and computational systems, the classic analyses of contract theory may no longer be sufficient. The work “Contracting with a Learning Agent” initiates the study of repeated contracts with learning agents. We also provide the first analysis of optimization against learning agents with uncertainty about the time horizon. The paper has since sparked a series of follow-up works, suggesting that the model provides a useful foundation for a range of new questions at the interface of contract theory and learning.
(2) Our paper “Incentivizing Quality Text Generation via Statistical Contracts” challenges current pay-per-token pricing schemes of large language models (LLMs). From a practical perspective, the paper highlights and addresses moral hazard challenges that emerge in the deployment of large language models (LLMs), and applies contract design theory to design optimal pricing schemes which align incentives. From a theoretical perspective, the paper makes a foundational contribution by establishing a direct connection between the theory of optimal contract design and the theory of optimal hypothesis testing in statistics. “Loose” connections between moral hazard and hypothesis testing have been known for some time, but formal evidence has been limited. This work provides a rigorous direct correspondence between these two fields, which extends beyond the case of LLM pricing, and paves the way towards new results which combine ideas from statistics to solve economic problems, and vice versa.
We also combine contracts with the study of information to achieve more realistic models: In “Algorithmic Cheap Talk”, we initiate the algorithmic study of natural communication among rational players, known as cheap talk. The next step is to apply this to communication among the contract designer and the agent(s). In “Information Design in the Principal-Agent Problem”, we allow the task delegator to get information about the agent's effort according to an “information structure” – a monitoring scheme designed to increase social welfare and lower losses from incomplete information.
Two works with high impact potential study (1) contracts for learning agents and (2) contracts for pricing AI services:
(1) As autonomous AI agents are increasingly used in various markets and computational systems, the classic analyses of contract theory may no longer be sufficient. The work “Contracting with a Learning Agent” initiates the study of repeated contracts with learning agents. We also provide the first analysis of optimization against learning agents with uncertainty about the time horizon. The paper has since sparked a series of follow-up works, suggesting that the model provides a useful foundation for a range of new questions at the interface of contract theory and learning.
(2) Our paper “Incentivizing Quality Text Generation via Statistical Contracts” challenges current pay-per-token pricing schemes of large language models (LLMs). From a practical perspective, the paper highlights and addresses moral hazard challenges that emerge in the deployment of large language models (LLMs), and applies contract design theory to design optimal pricing schemes which align incentives. From a theoretical perspective, the paper makes a foundational contribution by establishing a direct connection between the theory of optimal contract design and the theory of optimal hypothesis testing in statistics. “Loose” connections between moral hazard and hypothesis testing have been known for some time, but formal evidence has been limited. This work provides a rigorous direct correspondence between these two fields, which extends beyond the case of LLM pricing, and paves the way towards new results which combine ideas from statistics to solve economic problems, and vice versa.