When algorithmic predictors inform resource allocation in high-stakes domains such as healthcare, these predictors must account for strategic manipulation of input features. The typical solution is to redesign the predictor itself to explicitly account for strategic interactions. In practice, however, decision makers are often constrained to adjusting coarser levers within existing prediction pipelines. For example, healthcare organizations often select which features to exclude based on perceived manipulability, while using standard regularization procedures to shrink the coefficients of retained features. In this work, we initiate a formal study of strategic classification through feature selection and its interaction with ridge regularization. Our main finding is that excluding individual features based on their manipulability alone is generally suboptimal. We provide a fine-grained characterization of the performance of a feature subset under optimal regularization, yielding new insights for policy design. Motivated by this characterization, we develop a practical algorithm for jointly choosing the feature set and the level of ridge regularization. Through a real-world case study on a healthcare payments benchmark, we illustrate how our algorithm can guide the design of coarse policy levers in practice. Our results provide a principled, practical framework for mitigating the effects of strategic behavior in algorithmic decision-making systems.

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.

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.

Emerging marketplaces for large language models and other large-scale machine learning 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

We present a self-designing key-value storage engine, Cosine, which can always take the shape of the close to "perfect" engine architecture given an input workload, a cloud budget, a target performance, and required cloud SLAs. By identifying and formalizing the first principles of storage engine layouts and core key-value algorithms, Cosine constructs a massive design space comprising of sextillion (1036) possible storage engine designs over a diverse space of hardware and cloud pricing policies for three cloud providers AWS, GCP, and Azure. Cosine spans across diverse designs such as Log-Structured Merge-trees, B-trees, Log-Structured Hash-tables, in-memory accelerators for filters and indexes as well as trillions of hybrid designs that do not appear in the literature or industry but emerge as valid combinations of the above. Cosine includes a unified distribution-aware I/O model and a learned concurrency-aware CPU model that with high accuracy can calculate the performance and cloud cost of any possible design on any workload and virtual machines. Cosine can then search through that space in a matter of seconds to find the best design and materializes the actual code of the resulting storage engine design using a templated Rust implementation. We demonstrate that on average Cosine outperforms state-of-the-art storage engines such as write-optimized RocksDB, read-optimized WiredTiger, and very write-optimized FASTER by 53x, 25x, and 20x, respectively, for diverse workloads, data sizes, and cloud budgets across all YCSB core workloads and many variants.

We present a self-designing key-value storage engine, Cosine, which can always take the shape of the close to "perfect" engine architecture given an input workload, a cloud budget, a target performance, and required cloud SLAs. By identifying and formalizing the first principles of storage engine layouts and core key-value algorithms, Cosine constructs a massive design space comprising of sextillion (10 36 ) possible storage engine designs over a diverse space of hardware and cloud pricing policies for three cloud providers - AWS, GCP, and Azure. Cosine spans across diverse designs such as Log-Structured Merge-trees, B-trees, Log-Structured Hash-tables, in-memory accelerators for filters and indexes as well as trillions of hybrid designs that do not appear in the literature or industry but emerge as valid combinations of the above. Cosine includes a unified distribution-aware I/O model and a learned concurrency-aware CPU model that with high accuracy can calculate the performance and cloud cost of any possible design on any workload and virtual machines. Cosine can then search through that space in a matter of seconds to find the best design and materializes the actual code of the resulting storage engine design using a templated Rust implementation. We demonstrate that on average Cosine outperforms state-of-the-art storage engines such as write-optimized RocksDB, read-optimized WiredTiger, and very write-optimized FASTER by 53x, 25x, and 20x, respectively, for diverse workloads, data sizes, and cloud budgets across all YCSB core workloads and many variants.

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.