Personalized Reinforcement Learning with a Budget of Policies

Personalization in machine learning (ML) tailors models' decisions to the individual characteristics of users. While this approach has seen success in areas like recommender systems, its expansion into high-stakes fields such as healthcare and autonomous driving is hindered by the extensive regulatory approval processes involved. To address this challenge, we propose a novel framework termed represented Markov Decision Processes (r-MDPs) that is designed to balance the need for personalization with the regulatory constraints. In an r-MDP, we cater to a diverse user population, each with unique preferences, through interaction with a small set of representative policies. Our objective is twofold: efficiently match each user to an appropriate representative policy and simultaneously optimize these policies to maximize overall social welfare. We develop two deep reinforcement learning algorithms that efficiently solve r-MDPs. These algorithms draw inspiration from the principles of classic K-means clustering and are underpinned by robust theoretical foundations. Our empirical investigations, conducted across a variety of simulated environments, showcase the algorithms' ability to facilitate meaningful personalization even under constrained policy budgets. Furthermore, they demonstrate scalability, efficiently adapting to larger policy budgets.

Principal-Agent Reward Shaping in MDPs

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.

Learning with Exposure Constraints in Recommendation Systems

Recommendation systems are dynamic economic systems that balance the needs of multiple stakeholders. A recent line of work studies incentives from the content providers' point of view. Content providers, e.g., vloggers and bloggers, contribute fresh content and rely on user engagement to create revenue and finance their operations. In this work, we propose a contextual multi-armed bandit setting to model the dependency of content providers on exposure. In our model, the system receives a user context in every round and has to select one of the arms. Every arm is a content provider who must receive a minimum number of pulls every fixed time period (e.g., a month) to remain viable in later rounds; otherwise, the arm departs and is no longer available. The system aims to maximize the users' (content consumers) welfare. To that end, it should learn which arms are vital and ensure they remain viable by subsidizing arm pulls if needed. We develop algorithms with sub-linear regret, as well as a lower bound that demonstrates that our algorithms are optimal up to logarithmic factors.

Modeling Attrition in Recommender Systems with Departing Bandits

Traditionally, when recommender systems are formalized as multi-armed bandits, the policy of the recommender system influences the rewards accrued, but not the length of interaction. However, in real-world systems, dissatisfied users may depart (and never come back). In this work, we propose a novel multi-armed bandit setup that captures such policy-dependent horizons. Our setup consists of a finite set of user types, and multiple arms with Bernoulli payoffs. Each (user type, arm) tuple corresponds to an (unknown) reward probability. Each user's type is initially unknown and can only be inferred through their response to recommendations. Moreover, if a user is dissatisfied with their recommendation, they might depart the system. We first address the case where all users share the same type, demonstrating that a recent UCB-based algorithm is optimal. We then move forward to the more challenging case, where users are divided among two types. While naive approaches cannot handle this setting, we provide an efficient learning algorithm that achieves $\tilde{O}(\sqrt{T})$ regret, where $T$ is the number of users.

Optimizing Long-term Social Welfare in Recommender Systems: A Constrained Matching Approach

Most recommender systems (RS) research assumes that a user's utility can be maximized independently of the utility of the other agents (e.g., other users, content providers). In realistic settings, this is often not true---the dynamics of an RS ecosystem couple the long-term utility of all agents. In this work, we explore settings in which content providers cannot remain viable unless they receive a certain level of user engagement. We formulate the recommendation problem in this setting as one of equilibrium selection in the induced dynamical system, and show that it can be solved as an optimal constrained matching problem. Our model ensures the system reaches an equilibrium with maximal social welfare supported by a sufficiently diverse set of viable providers. We demonstrate that even in a simple, stylized dynamical RS model, the standard myopic approach to recommendation---always matching a user to the best provider---performs poorly. We develop several scalable techniques to solve the matching problem, and also draw connections to various notions of user regret and fairness, arguing that these outcomes are fairer in a utilitarian sense.

Learning under Invariable Bayesian Safety

A recent body of work addresses safety constraints in explore-and-exploit systems. Such constraints arise where, for example, exploration is carried out by individuals whose welfare should be balanced with overall welfare. In this paper, we adopt a model inspired by recent work on a bandit-like setting for recommendations. We contribute to this line of literature by introducing a safety constraint that should be respected in every round and determines that the expected value in each round is above a given threshold. Due to our modeling, the safe explore-and-exploit policy deserves careful planning, or otherwise, it will lead to sub-optimal welfare. We devise an asymptotically optimal algorithm for the setting and analyze its instance-dependent convergence rate.

Predicting Strategic Behavior from Free Text

The connection between messaging and action is fundamental both to web applications, such as web search and sentiment analysis, and to economics. However, while prominent online applications exploit messaging in natural (human) language in order to predict non-strategic action selection, the economics literature focuses on the connection between structured stylized messaging to strategic decisions in games and multi-agent encounters. This paper aims to connect these two strands of research, which we consider highly timely and important due to the vast online textual communication on the web. Particularly, we introduce the following question: can free text expressed in natural language serve for the prediction of action selection in an economic context, modeled as a game? In order to initiate the research on this question, we introduce the study of an individual's action prediction in a one-shot game based on free text he/she provides, while being unaware of the game to be played. We approach the problem by attributing commonsensical personality attributes via crowd-sourcing to free texts written by individuals, and employing transductive learning to predict actions taken by these individuals in one-shot games based on these attributes. Our approach allows us to train a single classifier that can make predictions with respect to actions taken in multiple games. In experiments with three well-studied games, our algorithm compares favorably with strong alternative approaches. In ablation analysis, we demonstrate the importance of our modeling choices -- the representation of the text with the commonsensical personality attributes and our classifier -- to the predictive power of our model.

Privacy, altruism, and experience: Estimating the perceived value of Internet data for medical uses

People increasingly turn to the Internet when they have a medical condition. The data they create during this process is a valuable source for medical research and for future health services. However, utilizing these data could come at a cost to user privacy. Thus, it is important to balance the perceived value that users assign to these data with the value of the services derived from them. Here we describe experiments where methods from Mechanism Design were used to elicit a truthful valuation from users for their Internet data and for services to screen people for medical conditions. In these experiments, 880 people from around the world were asked to participate in an auction to provide their data for uses differing in their contribution to the participant, to society, and in the disease they addressed. Some users were offered monetary compensation for their participation, while others were asked to pay to participate. Our findings show that 99\% of people were willing to contribute their data in exchange for monetary compensation and an analysis of their data, while 53\% were willing to pay to have their data analyzed. The average perceived value users assigned to their data was estimated at US\$49. Their value to screen them for a specific cancer was US\$22 while the value of this service offered to the general public was US\$22. Participants requested higher compensation when notified that their data would be used to analyze a more severe condition. They were willing to pay more to have their data analyzed when the condition was more severe, when they had higher education or if they had recently experienced a serious medical condition.

Protecting the Protected Group: Circumventing Harmful Fairness

Machine Learning (ML) algorithms shape our lives. Banks use them to determine if we are good borrowers; IT companies delegate them recruitment decisions; police apply ML for crime-prediction, and judges base their verdicts on ML. However, real-world examples show that such automated decisions tend to discriminate protected groups. This generated a huge hype both in media and in the research community. Quite a few formal notions of fairness were proposed, which take a form of constraints a ``fair'' algorithm must satisfy. We focus on scenarios where fairness is imposed on a self-interested party (e.g., a bank that maximizes its revenue). We find that the disadvantaged protected group can be worse off after imposing a fairness constraint. We introduce a family of Welfare-Equalizing fairness constraints that equalize per-capita welfare of protected groups, and include Demographic Parity and Equal Opportunity as particular cases. In this family, we characterize conditions under which the fairness constraint helps the disadvantaged group. We also characterize the structure of the optimal Welfare-Equalizing classifier for the self-interested party, and provide an LP-based algorithm to compute it. Overall, our Welfare-Equalizing fairness approach provides a unified framework for discussing fairness in classification in the presence of a self-interested party.

Fiduciary Bandits

Recommendation systems often face exploration-exploitation tradeoffs: the system can only learn about the desirability of new options by recommending them to some user. Such systems can thus be modeled as multi-armed bandit settings; however, users are self-interested and cannot be made to follow recommendations. We ask whether exploration can nevertheless be performed in a way that scrupulously respects agents' interests---i.e., by a system that acts as a fiduciary. More formally, we introduce a model in which a recommendation system faces an exploration-exploitation tradeoff under the constraint that it can never recommend any action that it knows yields lower reward in expectation than an agent would achieve if it acted alone. Our main contribution is a positive result: an asymptotically optimal, incentive compatible, and ex-ante individually rational recommendation algorithm.