Online Algorithms with Limited Data Retention

We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can request that it be removed from memory $m$ rounds after it arrives. To model the impact of removal, we do not allow the algorithm to store any information or calculations between rounds other than a subset of the data points (subject to the retention constraints). At the conclusion of the stream, the algorithm answers a statistical query about the full dataset. We ask: what level of performance can be guaranteed as a function of $m$? We illustrate this framework for multidimensional mean estimation and linear regression problems. We show it is possible to obtain an exponential improvement over a baseline algorithm that retains all data as long as possible. Specifically, we show that $m = \textsc{Poly}(d, \log(1/\epsilon))$ retention suffices to achieve mean squared error $\epsilon$ after observing $O(1/\epsilon)$ $d$-dimensional data points. This matches the error bound of the optimal, yet infeasible, algorithm that retains all data forever. We also show a nearly matching lower bound on the retention required to guarantee error $\epsilon$. One implication of our results is that data retention laws are insufficient to guarantee the right to be forgotten even in a non-adversarial world in which firms merely strive to (approximately) optimize the performance of their algorithms. Our approach makes use of recent developments in the multidimensional random subset sum problem to simulate the progression of stochastic gradient descent under a model of adversarial noise, which may be of independent interest.

Impact of Decentralized Learning on Player Utilities in Stackelberg Games

When deployed in the world, a learning agent such as a recommender system or a chatbot often repeatedly interacts with another learning agent (such as a user) over time. In many such two-agent systems, each agent learns separately and the rewards of the two agents are not perfectly aligned. To better understand such cases, we examine the learning dynamics of the two-agent system and the implications for each agent's objective. We model these systems as Stackelberg games with decentralized learning and show that standard regret benchmarks (such as Stackelberg equilibrium payoffs) result in worst-case linear regret for at least one player. To better capture these systems, we construct a relaxed regret benchmark that is tolerant to small learning errors by agents. We show that standard learning algorithms fail to provide sublinear regret, and we develop algorithms to achieve near-optimal $O(T^{2/3})$ regret for both players with respect to these benchmarks. We further design relaxed environments under which faster learning ($O(\sqrt{T})$) is possible. Altogether, our results take a step towards assessing how two-agent interactions in sequential and decentralized learning environments affect the utility of both agents.

Clickbait vs. Quality: How Engagement-Based Optimization Shapes the Content Landscape in Online Platforms

Online content platforms commonly use engagement-based optimization when making recommendations. This encourages content creators to invest in quality, but also rewards gaming tricks such as clickbait. To understand the total impact on the content landscape, we study a game between content creators competing on the basis of engagement metrics and analyze the equilibrium decisions about investment in quality and gaming. First, we show the content created at equilibrium exhibits a positive correlation between quality and gaming, and we empirically validate this finding on a Twitter dataset. Using the equilibrium structure of the content landscape, we then examine the downstream performance of engagement-based optimization along several axes. Perhaps counterintuitively, the average quality of content consumed by users can decrease at equilibrium as gaming tricks become more costly for content creators to employ. Moreover, engagement-based optimization can perform worse in terms of user utility than a baseline with random recommendations, and engagement-based optimization is also suboptimal in terms of realized engagement relative to quality-based optimization. Altogether, our results highlight the need to consider content creator incentives when evaluating a platform's choice of optimization metric.

Algorithmic Persuasion Through Simulation: Information Design in the Age of Generative AI

How can an informed sender persuade a receiver, having only limited information about the receiver's beliefs? Motivated by research showing generative AI can simulate economic agents, we initiate the study of information design with an oracle. We assume the sender can learn more about the receiver by querying this oracle, e.g., by simulating the receiver's behavior. Aside from AI motivations such as general-purpose Large Language Models (LLMs) and problem-specific machine learning models, alternate motivations include customer surveys and querying a small pool of live users. Specifically, we study Bayesian Persuasion where the sender has a second-order prior over the receiver's beliefs. After a fixed number of queries to an oracle to refine this prior, the sender commits to an information structure. Upon receiving the message, the receiver takes a payoff-relevant action maximizing her expected utility given her posterior beliefs. We design polynomial-time querying algorithms that optimize the sender's expected utility in this Bayesian Persuasion game. As a technical contribution, we show that queries form partitions of the space of receiver beliefs that can be used to quantify the sender's knowledge.

Maximizing Welfare with Incentive-Aware Evaluation Mechanisms

Motivated by applications such as college admission and insurance rate determination, we propose an evaluation problem where the inputs are controlled by strategic individuals who can modify their features at a cost. A learner can only partially observe the features, and aims to classify individuals with respect to a quality score. The goal is to design an evaluation mechanism that maximizes the overall quality score, i.e., welfare, in the population, taking any strategic updating into account. We further study the algorithmic aspect of finding the welfare maximizing evaluation mechanism under two specific settings in our model. When scores are linear and mechanisms use linear scoring rules on the observable features, we show that the optimal evaluation mechanism is an appropriate projection of the quality score. When mechanisms must use linear thresholds, we design a polynomial time algorithm with a (1/4)-approximation guarantee when the underlying feature distribution is sufficiently smooth and admits an oracle for finding dense regions. We extend our results to settings where the prior distribution is unknown and must be learned from samples.

Bayesian Exploration with Heterogeneous Agents

It is common in recommendation systems that users both consume and produce information as they make strategic choices under uncertainty. While a social planner would balance "exploration" and "exploitation" using a multi-armed bandit algorithm, users' incentives may tilt this balance in favor of exploitation. We consider Bayesian Exploration: a simple model in which the recommendation system (the "principal") controls the information flow to the users (the "agents") and strives to incentivize exploration via information asymmetry. A single round of this model is a version of a well-known "Bayesian Persuasion game" from [Kamenica and Gentzkow]. We allow heterogeneous users, relaxing a major assumption from prior work that users have the same preferences from one time step to another. The goal is now to learn the best personalized recommendations. One particular challenge is that it may be impossible to incentivize some of the user types to take some of the actions, no matter what the principal does or how much time she has. We consider several versions of the model, depending on whether and when the user types are reported to the principal, and design a near-optimal "recommendation policy" for each version. We also investigate how the model choice and the diversity of user types impact the set of actions that can possibly be "explored" by each type.

Adversarial Bandits with Knapsacks

We consider Bandits with Knapsacks (henceforth, BwK), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known knapsack problem: find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the "classic" adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the competitive ratio: the ratio of the benchmark reward to the algorithm's reward. We design an algorithm with competitive ratio O(log T) relative to the best fixed distribution over actions, where T is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version and use it as a subroutine to solve the latter.

Incentivizing Exploration with Unbiased Histories

In a social learning setting, there is a set of actions, each of which has a payoff that depends on a hidden state of the world. A sequence of agents each chooses an action with the goal of maximizing payoff given estimates of the state of the world. A disclosure policy tries to coordinate the choices of the agents by sending messages about the history of past actions. The goal of the algorithm is to minimize the regret of the action sequence. In this paper, we study a particular class of disclosure policies that use messages, called unbiased subhistories, consisting of the actions and rewards from by a subsequence of past agents, where the subsequence is chosen ahead of time. One trivial message of this form contains the full history; a disclosure policy that chooses to use such messages risks inducing herding behavior among the agents and thus has regret linear in the number of rounds. Our main result is a disclosure policy using unbiased subhistories that obtains regret $\tilde{O}(\sqrt{T})$. We also exhibit simpler policies with higher, but still sublinear, regret. These policies can be interpreted as dividing a sublinear number of agents into constant-sized focus groups, whose histories are then fed to future agents.

The Disparate Effects of Strategic Manipulation

When consequential decisions are informed by algorithmic input, individuals may feel compelled to alter their behavior in order to gain a system's approval. Previous models of agent responsiveness, termed "strategic manipulation," have analyzed the interaction between a learner and agents in a world where all agents are equally able to manipulate their features in an attempt to "trick" a published classifier. In cases of real world classification, however, an agent's ability to adapt to an algorithm, is not simply a function of her personal interest in receiving a positive classification, but is bound up in a complex web of social factors that affect her ability to pursue certain action responses. In this paper, we adapt models of strategic manipulation to better capture dynamics that may arise in a setting of social inequality wherein candidate groups face different costs to manipulation. We find that whenever one group's costs are higher than the other's, the learner's equilibrium strategy exhibits an inequality-reinforcing phenomenon wherein the learner erroneously admits some members of the advantaged group, while erroneously excluding some members of the disadvantaged group. We also consider the effects of potential interventions in which a learner can subsidize members of the disadvantaged group, lowering their costs in order to improve her own classification performance. Here we encounter a paradoxical result: there exist cases in which providing a subsidy improves only the learner's utility while actually making both candidate groups worse-off--even the group receiving the subsidy. Our results reveal the potentially adverse social ramifications of deploying tools that attempt to evaluate an individual's "quality" when agents' capacities to adaptively respond differ.

Unleashing Linear Optimizers for Group-Fair Learning and Optimization

Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for example, when balancing performance or loss with fairness across people. We prove that, from a computational perspective, optimizing arbitrary objectives that take into account performance over a small number of groups is not significantly harder to optimize than average performance. Our main result is a polynomial-time reduction that uses a linear optimizer to optimize an arbitrary (Lipschitz continuous) function of performance over a (constant) number of possibly-overlapping groups. This includes fairness objectives over small numbers of groups, and we further point out that other existing notions of fairness such as individual fairness can be cast as convex optimization and hence more standard convex techniques can be used. Beyond learning, our approach applies to multi-objective optimization, more generally.