Meena Jagadeesan

Xinyan Hu, Meena Jagadeesan, Michael I. Jordan et al.

In content recommender systems such as TikTok and YouTube, the platform's recommendation algorithm shapes content producer incentives. Many platforms employ online learning, which generates intertemporal incentives, since content produced today affects recommendations of future content. We study the game between producers and analyze the content created at equilibrium. We show that standard online learning algorithms, such as Hedge and EXP3, unfortunately incentivize producers to create low-quality content, where producers' effort approaches zero in the long run for typical learning rate schedules. Motivated by this negative result, we design learning algorithms that incentivize producers to invest high effort and achieve high user welfare. At a conceptual level, our work illustrates the unintended impact that a platform's learning algorithm can have on content quality and introduces algorithmic approaches to mitigating these effects.

Meena Jagadeesan, Nikhil Garg, Jacob Steinhardt

Algorithmic recommender systems such as Spotify and Netflix affect not only consumer behavior but also producer incentives. Producers seek to create content that will be shown by the recommendation algorithm, which can impact both the diversity and quality of their content. In this work, we investigate the resulting supply-side equilibria in personalized content recommender systems. We model users and content as $D$-dimensional vectors, the recommendation algorithm as showing each user the content with highest dot product, and producers as maximizing the number of users who are recommended their content minus the cost of production. Two key features of our model are that the producer decision space is multi-dimensional and the user base is heterogeneous, which contrasts with classical low-dimensional models. Multi-dimensionality and heterogeneity create the potential for specialization, where different producers create different types of content at equilibrium. Using a duality argument, we derive necessary and sufficient conditions for whether specialization occurs: these conditions depend on the extent to which users are heterogeneous and to which producers can perform well on all dimensions at once without incurring a high cost. Then, we characterize the distribution of content at equilibrium in concrete settings with two populations of users. Lastly, we show that specialization can enable producers to achieve positive profit at equilibrium, which means that specialization can reduce the competitiveness of the marketplace. At a conceptual level, our analysis of supply-side competition takes a step towards elucidating how personalized recommendations shape the marketplace of digital goods, and towards understanding what new phenomena arise in multi-dimensional competitive settings.

Meena Jagadeesan, Michael I. Jordan, Jacob Steinhardt et al.

As the scale of machine learning models increases, trends such as scaling laws anticipate consistent downstream improvements in predictive accuracy. However, these trends take the perspective of a single model-provider in isolation, while in reality providers often compete with each other for users. In this work, we demonstrate that competition can fundamentally alter the behavior of these scaling trends, even causing overall predictive accuracy across users to be non-monotonic or decreasing with scale. We define a model of competition for classification tasks, and use data representations as a lens for studying the impact of increases in scale. We find many settings where improving data representation quality (as measured by Bayes risk) decreases the overall predictive accuracy across users (i.e., social welfare) for a marketplace of competing model-providers. Our examples range from closed-form formulas in simple settings to simulations with pretrained representations on CIFAR-10. At a conceptual level, our work suggests that favorable scaling trends for individual model-providers need not translate to downstream improvements in social welfare in marketplaces with multiple model providers.

Meena Jagadeesan, Michael I. Jordan, Nika Haghtalab

Competition between traditional platforms is known to improve user utility by aligning the platform's actions with user preferences. But to what extent is alignment exhibited in data-driven marketplaces? To study this question from a theoretical perspective, we introduce a duopoly market where platform actions are bandit algorithms and the two platforms compete for user participation. A salient feature of this market is that the quality of recommendations depends on both the bandit algorithm and the amount of data provided by interactions from users. This interdependency between the algorithm performance and the actions of users complicates the structure of market equilibria and their quality in terms of user utility. Our main finding is that competition in this market does not perfectly align market outcomes with user utility. Interestingly, market outcomes exhibit misalignment not only when the platforms have separate data repositories, but also when the platforms have a shared data repository. Nonetheless, the data sharing assumptions impact what mechanism drives misalignment and also affect the specific form of misalignment (e.g. the quality of the best-case and worst-case market outcomes). More broadly, our work illustrates that competition in digital marketplaces has subtle consequences for user utility that merit further investigation.

Meena Jagadeesan, Michael I. Jordan, Jacob Steinhardt

Emerging marketplaces for large language models and other large-scale machine learning (ML) models appear to exhibit market concentration, which has raised concerns about whether there are insurmountable barriers to entry in such markets. In this work, we study this issue from both an economic and an algorithmic point of view, focusing on a phenomenon that reduces barriers to entry. Specifically, an incumbent company risks reputational damage unless its model is sufficiently aligned with safety objectives, whereas a new company can more easily avoid reputational damage. To study this issue formally, we define a multi-objective high-dimensional regression framework that captures reputational damage, and we characterize the number of data points that a new company needs to enter the market. Our results demonstrate how multi-objective considerations can fundamentally reduce barriers to entry -- the required number of data points can be significantly smaller than the incumbent company's dataset size. En route to proving these results, we develop scaling laws for high-dimensional linear regression in multi-objective environments, showing that the scaling rate becomes slower when the dataset size is large, which could be of independent interest.

Nivasini Ananthakrishnan, Meena Jagadeesan

When designing compound AI systems, a common approach is to query multiple copies of the same model and aggregate the responses to produce a synthesized output. Given the homogeneity of these models, this raises the question of whether aggregation unlocks access to a greater set of outputs than querying a single model. In this work, we investigate the power and limitations of aggregation within a stylized principal-agent framework. This framework models how the system designer can partially steer each agent's output through its reward function specification, but still faces limitations due to prompt engineering ability and model capabilities. Our analysis uncovers three natural mechanisms -- feasibility expansion, support expansion, and binding set contraction -- through which aggregation expands the set of outputs that are elicitable by the system designer. We prove that any aggregation operation must implement one of these mechanisms in order to be elicitability-expanding, and that strengthened versions of these mechanisms provide necessary and sufficient conditions that fully characterize elicitability-expansion. Finally, we provide an empirical illustration of our findings for LLMs deployed in a toy reference-generation task. Altogether, our results take a step towards characterizing when compound AI systems can overcome limitations in model capabilities and in prompt engineering.

Alexander Pan, Erik Jones, Meena Jagadeesan et al.

Language models influence the external world: they query APIs that read and write to web pages, generate content that shapes human behavior, and run system commands as autonomous agents. These interactions form feedback loops: LLM outputs affect the world, which in turn affect subsequent LLM outputs. In this work, we show that feedback loops can cause in-context reward hacking (ICRH), where the LLM at test-time optimizes a (potentially implicit) objective but creates negative side effects in the process. For example, consider an LLM agent deployed to increase Twitter engagement; the LLM may retrieve its previous tweets into the context window and make them more controversial, increasing engagement but also toxicity. We identify and study two processes that lead to ICRH: output-refinement and policy-refinement. For these processes, evaluations on static datasets are insufficient -- they miss the feedback effects and thus cannot capture the most harmful behavior. In response, we provide three recommendations for evaluation to capture more instances of ICRH. As AI development accelerates, the effects of feedback loops will proliferate, increasing the need to understand their role in shaping LLM behavior.

Sarah Dean, Evan Dong, Meena Jagadeesan et al.

As AI systems enter into a growing number of societal domains, these systems increasingly shape and are shaped by user preferences, opinions, and behaviors. However, the design of AI systems rarely accounts for how AI and users shape one another. In this position paper, we argue for the development of formal interaction models which mathematically specify how AI and users shape one another. Formal interaction models can be leveraged to (1) specify interactions for implementation, (2) monitor interactions through empirical analysis, (3) anticipate societal impacts via counterfactual analysis, and (4) control societal impacts via interventions. The design space of formal interaction models is vast, and model design requires careful consideration of factors such as style, granularity, mathematical complexity, and measurability. Using content recommender systems as a case study, we critically examine the nascent literature of formal interaction models with respect to these use-cases and design axes. More broadly, we call for the community to leverage formal interaction models when designing, evaluating, or auditing any AI system which interacts with users.

Kate Donahue, Nicole Immorlica, Meena Jagadeesan et al.

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.

Jessica Dai, Bailey Flanigan, Nika Haghtalab et al. · harvard

A common explanation for negative user impacts of content recommender systems is misalignment between the platform's objective and user welfare. In this work, we show that misalignment in the platform's objective is not the only potential cause of unintended impacts on users: even when the platform's objective is fully aligned with user welfare, the platform's learning algorithm can induce negative downstream impacts on users. The source of these user impacts is that different pieces of content may generate observable user reactions (feedback information) at different rates; these feedback rates may correlate with content properties, such as controversiality or demographic similarity of the creator, that affect the user experience. Since differences in feedback rates can impact how often the learning algorithm engages with different content, the learning algorithm may inadvertently promote content with certain such properties. Using the multi-armed bandit framework with probabilistic feedback, we examine the relationship between feedback rates and a learning algorithm's engagement with individual arms for different no-regret algorithms. We prove that no-regret algorithms can exhibit a wide range of dependencies: if the feedback rate of an arm increases, some no-regret algorithms engage with the arm more, some no-regret algorithms engage with the arm less, and other no-regret algorithms engage with the arm approximately the same number of times. From a platform design perspective, our results highlight the importance of looking beyond regret when measuring an algorithm's performance, and assessing the nature of a learning algorithm's engagement with different types of content as well as their resulting downstream impacts.

S. Nageeb Ali, Nicole Immorlica, Meena Jagadeesan et al.

In the digital economy, technological innovations make it cheaper to produce high-quality content. For example, generative AI tools reduce costs for creators who develop content to be distributed online, but can also reduce production costs for the users who consume that content. These innovations can thus lead to disintermediation, since consumers may choose to use these technologies directly, bypassing intermediaries. To investigate when technological improvements lead to disintermediation, we study a game with an intermediary, suppliers of a production technology, and consumers. First, we show disintermediation occurs whenever production costs are too high or too low. We then investigate the consequences of disintermediation for welfare and content quality at equilibrium. While the intermediary is welfare-improving, the intermediary extracts all gains to social welfare and its presence can raise or lower content quality. We further analyze how disintermediation is affected by the level of competition between suppliers and the intermediary's fee structure. More broadly, our results take a step towards assessing how production technology innovations affect the survival of intermediaries and impact the digital economy.

Natalie Collina, Eshwar Ram Arunachaleswaran, Meena Jagadeesan

AI agents are increasingly deployed in ecosystems where they repeatedly interact not only with each other but also with humans. In this work, we study these human-AI ecosystems from a theoretical perspective, focusing on the classical framework of repeated pricing games. In our stylized model, the AI agents play equilibrium strategies, and one or more humans manually perform the pricing task instead of adopting an AI agent, thereby defecting to a no-regret strategy. Motivated by how populations of AI agents can sustain supracompetitive prices, we investigate whether high prices persist under such defections. Our main finding is that even a single human defection can destabilize collusion and drive down prices, and multiple defections push prices even closer to competitive levels. We further show how the nature of collusion changes under defection-aware AI agents. Taken together, our results characterize when algorithmic collusion is fragile--and when it persists--in mixed ecosystems of AI agents and humans.

Nicole Immorlica, Meena Jagadeesan, Brendan Lucier

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.

Moritz Hardt, Meena Jagadeesan, Celestine Mendler-Dünner

We introduce the notion of performative power, which measures the ability of a firm operating an algorithmic system, such as a digital content recommendation platform, to cause change in a population of participants. We relate performative power to the economic study of competition in digital economies. Traditional economic concepts struggle with identifying anti-competitive patterns in digital platforms not least due to the complexity of market definition. In contrast, performative power is a causal notion that is identifiable with minimal knowledge of the market, its internals, participants, products, or prices. Low performative power implies that a firm can do no better than to optimize their objective on current data. In contrast, firms of high performative power stand to benefit from steering the population towards more profitable behavior. We confirm in a simple theoretical model that monopolies maximize performative power. A firm's ability to personalize increases performative power, while competition and outside options decrease performative power. On the empirical side, we propose an observational causal design to identify performative power from discontinuities in how digital platforms display content. This allows to repurpose causal effects from various studies about digital platforms as lower bounds on performative power. Finally, we speculate about the role that performative power might play in competition policy and antitrust enforcement in digital marketplaces.

Meena Jagadeesan, Tijana Zrnic, Celestine Mendler-Dünner

In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it induces. We study the problem of finding near-optimal models under performativity while maintaining low regret. On the surface, this problem might seem equivalent to a bandit problem. However, it exhibits a fundamentally richer feedback structure that we refer to as performative feedback: after every deployment, the learner receives samples from the shifted distribution rather than only bandit feedback about the reward. Our main contribution is an algorithm that achieves regret bounds scaling only with the complexity of the distribution shifts and not that of the reward function. The algorithm only relies on smoothness of the shifts and does not assume convexity. Moreover, its final iterate is guaranteed to be near-optimal. The key algorithmic idea is careful exploration of the distribution shifts that informs a novel construction of confidence bounds on the risk of unexplored models. More broadly, our work establishes a conceptual approach for leveraging tools from the bandits literature for the purpose of regret minimization with performative feedback.

Meena Jagadeesan, Alexander Wei, Yixin Wang et al.

Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) are unfortunately of limited value in the learning setting, given that preferences are inherently uncertain and destabilizing while they are being learned. To bridge this gap, we develop a framework and algorithms for learning stable market outcomes under uncertainty. Our primary setting is matching with transferable utilities, where the platform both matches agents and sets monetary transfers between them. We design an incentive-aware learning objective that captures the distance of a market outcome from equilibrium. Using this objective, we analyze the complexity of learning as a function of preference structure, casting learning as a stochastic multi-armed bandit problem. Algorithmically, we show that "optimism in the face of uncertainty," the principle underlying many bandit algorithms, applies to a primal-dual formulation of matching with transfers and leads to near-optimal regret bounds. Our work takes a first step toward elucidating when and how stable matchings arise in large, data-driven marketplaces.

Meena Jagadeesan, Celestine Mendler-Dünner, Moritz Hardt

When reasoning about strategic behavior in a machine learning context it is tempting to combine standard microfoundations of rational agents with the statistical decision theory underlying classification. In this work, we argue that a direct combination of these standard ingredients leads to brittle solution concepts of limited descriptive and prescriptive value. First, we show that rational agents with perfect information produce discontinuities in the aggregate response to a decision rule that we often do not observe empirically. Second, when any positive fraction of agents is not perfectly strategic, desirable stable points -- where the classifier is optimal for the data it entails -- cease to exist. Third, optimal decision rules under standard microfoundations maximize a measure of negative externality known as social burden within a broad class of possible assumptions about agent behavior. Recognizing these limitations we explore alternatives to standard microfoundations for binary classification. We start by describing a set of desiderata that help navigate the space of possible assumptions about how agents respond to a decision rule. In particular, we analyze a natural constraint on feature manipulations, and discuss properties that are sufficient to guarantee the robust existence of stable points. Building on these insights, we then propose the noisy response model. Inspired by smoothed analysis and empirical observations, noisy response incorporates imperfection in the agent responses, which we show mitigates the limitations of standard microfoundations. Our model retains analytical tractability, leads to more robust insights about stable points, and imposes a lower social burden at optimality.

Meena Jagadeesan, Ilya Razenshteyn, Suriya Gunasekar

We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting hypothesis on ReLU networks trained using gradient descent. We define an induced regularizer in the function space as the minimum $\ell_2$ norm of weights of a network required to realize a function. For two layer linear convolutional networks with $C$ output channels and kernel size $K$, we show the following: (a) If the inputs to the network are single channeled, the induced regularizer for any $K$ is independent of the number of output channels $C$. Furthermore, we derive the regularizer is a norm given by a semidefinite program (SDP). (b) In contrast, for multi-channel inputs, multiple output channels can be necessary to merely realize all matrix-valued linear functions and thus the inductive bias does depend on $C$. However, for sufficiently large $C$, the induced regularizer is again given by an SDP that is independent of $C$. In particular, the induced regularizer for $K=1$ and $K=D$ (input dimension) is given in closed form as the nuclear norm and the $\ell_{2,1}$ group-sparse norm, respectively, of the Fourier coefficients of the linear predictor. We investigate the broader applicability of our theoretical results to implicit regularization from gradient descent on linear and ReLU networks through experiments on MNIST and CIFAR-10 datasets.

Cynthia Dwork, Christina Ilvento, Meena Jagadeesan

It is well understood that a system built from individually fair components may not itself be individually fair. In this work, we investigate individual fairness under pipeline composition. Pipelines differ from ordinary sequential or repeated composition in that individuals may drop out at any stage, and classification in subsequent stages may depend on the remaining "cohort" of individuals. As an example, a company might hire a team for a new project and at a later point promote the highest performer on the team. Unlike other repeated classification settings, where the degree of unfairness degrades gracefully over multiple fair steps, the degree of unfairness in pipelines can be arbitrary, even in a pipeline with just two stages. Guided by a panoply of real-world examples, we provide a rigorous framework for evaluating different types of fairness guarantees for pipelines. We show that naïve auditing is unable to uncover systematic unfairness and that, in order to ensure fairness, some form of dependence must exist between the design of algorithms at different stages in the pipeline. Finally, we provide constructions that permit flexibility at later stages, meaning that there is no need to lock in the entire pipeline at the time that the early stage is constructed.

Shuchi Chawla, Meena Jagadeesan

Recent empirical work demonstrates that online advertisement can exhibit bias in the delivery of ads across users even when all advertisers bid in a non-discriminatory manner. We study the design of ad auctions that, given fair bids, are guaranteed to produce fair outcomes. Following the works of Dwork and Ilvento (2019) and Chawla et al. (2020), our goal is to design a truthful auction that satisfies ``individual fairness'' in its outcomes: informally speaking, users that are similar to each other should obtain similar allocations of ads. Within this framework we quantify the tradeoff between social welfare maximization and fairness. This work makes two conceptual contributions. First, we express the fairness constraint as a kind of stability condition: any two users that are assigned multiplicatively similar values by all the advertisers must receive additively similar allocations for each advertiser. This value stability constraint is expressed as a function that maps the multiplicative distance between value vectors to the maximum allowable $\ell_{\infty}$ distance between the corresponding allocations. Standard auctions do not satisfy this kind of value stability. Second, we introduce a new class of allocation algorithms called Inverse Proportional Allocation that achieve a near optimal tradeoff between fairness and social welfare for a broad and expressive class of value stability conditions. These allocation algorithms are truthful and prior-free, and achieve a constant factor approximation to the optimal (unconstrained) social welfare. In particular, the approximation ratio is independent of the number of advertisers in the system. In this respect, these allocation algorithms greatly surpass the guarantees achieved in previous work. We also extend our results to broader notions of fairness that we call subset fairness.

Shuchi Chawla, Christina Ilvento, Meena Jagadeesan

Fairness in advertising is a topic of particular concern motivated by theoretical and empirical observations in both the computer science and economics literature. We examine the problem of fairness in advertising for general purpose platforms that service advertisers from many different categories. First, we propose inter-category and intra-category fairness desiderata that take inspiration from individual fairness and envy-freeness. Second, we investigate the "platform utility" (a proxy for the quality of the allocation) achievable by mechanisms satisfying these desiderata. More specifically, we compare the utility of fair mechanisms against the unfair optimal, and we show by construction that our fairness desiderata are compatible with utility. That is, we construct a family of fair mechanisms with high utility that perform close to optimally within a class of fair mechanisms. Our mechanisms also enjoy nice implementation properties including metric-obliviousness, which allows the platform to produce fair allocations without needing to know the specifics of the fairness requirements.

Meena Jagadeesan

Feature hashing and other random projection schemes are commonly used to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in $\mathbb{R}^n$ into a much lower-dimensional space $\mathbb{R}^m$, while approximately preserving Euclidean norm. These schemes can be constructed using sparse random projections, for example using a sparse Johnson-Lindenstrauss (JL) transform. A line of work introduced by Weinberger et. al (ICML '09) analyzes the accuracy of sparse JL with sparsity 1 on feature vectors with small $\ell_\infty$-to-$\ell_2$ norm ratio. Recently, Freksen, Kamma, and Larsen (NeurIPS '18) closed this line of work by proving a tight tradeoff between $\ell_\infty$-to-$\ell_2$ norm ratio and accuracy for sparse JL with sparsity $1$. In this paper, we demonstrate the benefits of using sparsity $s$ greater than $1$ in sparse JL on feature vectors. Our main result is a tight tradeoff between $\ell_\infty$-to-$\ell_2$ norm ratio and accuracy for a general sparsity $s$, that significantly generalizes the result of Freksen et. al. Our result theoretically demonstrates that sparse JL with $s > 1$ can have significantly better norm-preservation properties on feature vectors than sparse JL with $s = 1$; we also empirically demonstrate this finding.