Juan C. Perdomo

Juan C. Perdomo, Tolani Britton, Moritz Hardt et al.

Early warning systems (EWS) are predictive tools at the center of recent efforts to improve graduation rates in public schools across the United States. These systems assist in targeting interventions to individual students by predicting which students are at risk of dropping out. Despite significant investments in their widespread adoption, there remain large gaps in our understanding of the efficacy of EWS, and the role of statistical risk scores in education. In this work, we draw on nearly a decade's worth of data from a system used throughout Wisconsin to provide the first large-scale evaluation of the long-term impact of EWS on graduation outcomes. We present empirical evidence that the prediction system accurately sorts students by their dropout risk. We also find that it may have caused a single-digit percentage increase in graduation rates, though our empirical analyses cannot reliably rule out that there has been no positive treatment effect. Going beyond a retrospective evaluation of DEWS, we draw attention to a central question at the heart of the use of EWS: Are individual risk scores necessary for effectively targeting interventions? We propose a simple mechanism that only uses information about students' environments -- such as their schools, and districts -- and argue that this mechanism can target interventions just as efficiently as the individual risk score-based mechanism. Our argument holds even if individual predictions are highly accurate and effective interventions exist. In addition to motivating this simple targeting mechanism, our work provides a novel empirical backbone for the robust qualitative understanding among education researchers that dropout is structurally determined. Combined, our insights call into question the marginal value of individual predictions in settings where outcomes are driven by high levels of inequality.

Juan C. Perdomo, Akshay Krishnamurthy, Peter Bartlett et al.

Offline policy evaluation is a fundamental statistical problem in reinforcement learning that involves estimating the value function of some decision-making policy given data collected by a potentially different policy. In order to tackle problems with complex, high-dimensional observations, there has been significant interest from theoreticians and practitioners alike in understanding the possibility of function approximation in reinforcement learning. Despite significant study, a sharp characterization of when we might expect offline policy evaluation to be tractable, even in the simplest setting of linear function approximation, has so far remained elusive, with a surprising number of strong negative results recently appearing in the literature. In this work, we identify simple control-theoretic and linear-algebraic conditions that are necessary and sufficient for classical methods, in particular Fitted Q-iteration (FQI) and least squares temporal difference learning (LSTD), to succeed at offline policy evaluation. Using this characterization, we establish a precise hierarchy of regimes under which these estimators succeed. We prove that LSTD works under strictly weaker conditions than FQI. Furthermore, we establish that if a problem is not solvable via LSTD, then it cannot be solved by a broad class of linear estimators, even in the limit of infinite data. Taken together, our results provide a complete picture of the behavior of linear estimators for offline policy evaluation, unify previously disparate analyses of canonical algorithms, and provide significantly sharper notions of the underlying statistical complexity of offline policy evaluation.

Michael P. Kim, Juan C. Perdomo

Decision-makers often act in response to data-driven predictions, with the goal of achieving favorable outcomes. In such settings, predictions don't passively forecast the future; instead, predictions actively shape the distribution of outcomes they are meant to predict. This performative prediction setting raises new challenges for learning "optimal" decision rules. In particular, existing solution concepts do not address the apparent tension between the goals of forecasting outcomes accurately and steering individuals to achieve desirable outcomes. To contend with this concern, we introduce a new optimality concept -- performative omniprediction -- adapted from the supervised (non-performative) learning setting. A performative omnipredictor is a single predictor that simultaneously encodes the optimal decision rule with respect to many possibly-competing objectives. Our main result demonstrates that efficient performative omnipredictors exist, under a natural restriction of performative prediction, which we call outcome performativity. On a technical level, our results follow by carefully generalizing the notion of outcome indistinguishability to the outcome performative setting. From an appropriate notion of Performative OI, we recover many consequences known to hold in the supervised setting, such as omniprediction and universal adaptability.

Gabriele Farina, Juan Carlos Perdomo

We study the problem of efficiently producing, in an online fashion, generative models of scalar, multiclass, and vector-valued outcomes that cannot be falsified on the basis of the observed data and a pre-specified collection of computational tests. Our contributions are twofold. First, we expand on connections between online high-dimensional multicalibration with respect to an RKHS and recent advances in expected variational inequality problems, enabling efficient algorithms for the former. We then apply this algorithmic machinery to the problem of outcome indistinguishability. Our procedure, Defensive Generation, is the first to efficiently produce online outcome indistinguishable generative models of non-Bernoulli outcomes that are unfalsifiable with respect to infinite classes of tests, including those that examine higher-order moments of the generated distributions. Furthermore, our method runs in near-linear time in the number of samples and achieves the optimal, vanishing T^{-1/2} rate for generation error.

Gabriele Farina, Juan Carlos Perdomo

We give a Gordon-Greenwald-Marks (GGM) style black-box reduction from online learning to online multicalibration. Concretely, we show that to achieve high-dimensional multicalibration with respect to a class of functions H, it suffices to combine any no-regret learner over H with an expected variational inequality (EVI) solver. We also prove a converse statement showing that efficient multicalibration implies efficient EVI solving, highlighting how EVIs in multicalibration mirror the role of fixed points in the GGM result for $Φ$-regret. This first set of results resolves the main open question in Garg, Jung, Reingold, and Roth (SODA '24), showing that oracle-efficient online multicalibration with $\sqrt{T}$-type guarantees is possible in full generality. Furthermore, our GGM-style reduction unifies the analyses of existing online multicalibration algorithms, enables new algorithms for challenging environments with delayed observations or censored outcomes, and yields the first efficient black-box reduction between online learning and multiclass omniprediction. Our second main result is a fine-grained reduction from high-dimensional online multicalibration to (contextual) $Φ$-regret minimization. Together with our first result, this establishes a new route from external regret to Phi-regret that bypasses sophisticated fixed-point or semi-separation machinery, dramatically simplifies a result of Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25) while improving rates, and yields new algorithms that are robust to richer deviation classes, such as those belonging to any reproducing kernel Hilbert space.

Unai Fischer-Abaigar, Emily Aiken, Christoph Kern et al.

Institutions increasingly use prediction to allocate scarce resources. From a design perspective, better predictions compete with other investments, such as expanding capacity or improving treatment quality. Here, the big question is not how to solve a specific allocation problem, but rather which problem to solve. In this work, we develop an empirical toolkit to help planners form principled answers to this question and quantify the bottom-line welfare impact of investments in prediction versus other policy levers such as expanding capacity and improving treatment quality. Applying our framework in two real-world case studies on German employment services and poverty targeting in Ethiopia, we illustrate how decision-makers can reliably derive context-specific conclusions about the relative value of prediction in their allocation problem. We make our software toolkit, rvp, and parts of our data available in order to enable future empirical work in this area.

Juan Carlos Perdomo

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-à-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.

Cynthia Dwork, Chris Hays, Nicole Immorlica et al. · harvard

Professional networks provide invaluable entree to opportunity through referrals and introductions. A rich literature shows they also serve to entrench and even exacerbate a status quo of privilege and disadvantage. Hiring platforms, equipped with the ability to nudge link formation, provide a tantalizing opening for beneficial structural change. We anticipate that key to this prospect will be the ability to estimate the likelihood of edge formation in an evolving graph. Outcome-indistinguishable prediction algorithms ensure that the modeled world is indistinguishable from the real world by a family of statistical tests. Omnipredictors ensure that predictions can be post-processed to yield loss minimization competitive with respect to a benchmark class of predictors for many losses simultaneously, with appropriate post-processing. We begin by observing that, by combining a slightly modified form of the online K29 star algorithm of Vovk (2007) with basic facts from the theory of reproducing kernel Hilbert spaces, one can derive simple and efficient online algorithms satisfying outcome indistinguishability and omniprediction, with guarantees that improve upon, or are complementary to, those currently known. This is of independent interest. We apply these techniques to evolving graphs, obtaining online outcome-indistinguishable omnipredictors for rich -- possibly infinite -- sets of distinguishers that capture properties of pairs of nodes, and their neighborhoods. This yields, inter alia, multicalibrated predictions of edge formation with respect to pairs of demographic groups, and the ability to simultaneously optimize loss as measured by a variety of social welfare functions.

Gavin Brown, Jonathan Hayase, Samuel Hopkins et al.

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix. All prior private algorithms for this task require either $d^{3/2}$ examples, error growing polynomially with the condition number, or exponential time. Our near-optimal accuracy guarantee holds for any dataset with bounded statistical leverage and bounded residuals. Technically, we build on the approach of Brown et al. (2023) for private mean estimation, adding scaled noise to a carefully designed stable nonprivate estimator of the empirical regression vector.

Gabriele Farina, Juan Carlos Perdomo

The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in their work on performative prediction. Our main result is an unconditional reduction showing that any no-regret algorithm deployed in performative settings converges to a (mixed) performatively stable equilibrium: a solution in which models actively shape data distributions in ways that their own predictions look optimal in hindsight. Prior to our work, all positive results in this area made strong restrictions on how models influenced distributions. By using a martingale argument and allowing randomization, we avoid any such assumption and sidestep recent hardness results for finding stable models. Lastly, on a more conceptual note, our connection sheds light on why common algorithms, like gradient descent, are naturally stabilizing and prevent runaway feedback loops. We hope our work enables future technical transfer of ideas between online optimization and performativity.

Unai Fischer-Abaigar, Christoph Kern, Juan Carlos Perdomo

Machine learning is increasingly used in government programs to identify and support the most vulnerable individuals, prioritizing assistance for those at greatest risk over optimizing aggregate outcomes. This paper examines the welfare impacts of prediction in equity-driven contexts, and how they compare to other policy levers, such as expanding bureaucratic capacity. Through mathematical models and a real-world case study on long-term unemployment amongst German residents, we develop a comprehensive understanding of the relative effectiveness of prediction in surfacing the worst-off. Our findings provide clear analytical frameworks and practical, data-driven tools that empower policymakers to make principled decisions when designing these systems.

Josh Gardner, Juan C. Perdomo, Ludwig Schmidt

Tabular data -- structured, heterogeneous, spreadsheet-style data with rows and columns -- is widely used in practice across many domains. However, while recent foundation models have reduced the need for developing task-specific datasets and predictors in domains such as language modeling and computer vision, this transfer learning paradigm has not had similar impact in the tabular domain. In this work, we seek to narrow this gap and present TabuLa-8B, a language model for tabular prediction. We define a process for extracting a large, high-quality training dataset from the TabLib corpus, proposing methods for tabular data filtering and quality control. Using the resulting dataset, which comprises over 2.1B rows from over 4M unique tables, we fine-tune a Llama 3-8B large language model (LLM) for tabular data prediction (classification and binned regression) using a novel packing and attention scheme for tabular prediction. Through evaluation across a test suite of 329 datasets, we find that TabuLa-8B has zero-shot accuracy on unseen tables that is over 15 percentage points (pp) higher than random guessing, a feat that is not possible with existing state-of-the-art tabular prediction models (e.g. XGBoost, TabPFN). In the few-shot setting (1-32 shots), without any fine-tuning on the target datasets, TabuLa-8B is 5-15 pp more accurate than XGBoost and TabPFN models that are explicitly trained on equal, or even up to 16x more data. We release our model, code, and data along with the publication of this paper.

Jack Umenberger, Max Simchowitz, Juan C. Perdomo et al.

We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of $\textit{informativity}$, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a $\textit{regularizer}$ which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a ``reconditioning step'' - converges to the globally optimal cost a $\mathcal{O}(1/T)$ rate. Our analysis relies on several new results which may be of independent interest, including a new framework for analyzing non-convex gradient descent via convex reformulation, and novel bounds on the solution to linear Lyapunov equations in terms of (our quantitative measure of) informativity.

Juan C. Perdomo, Jack Umenberger, Max Simchowitz

Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free methods have become increasingly popular in practice due to their simplicity and flexibility, stabilization via direct policy search has received surprisingly little attention. Our algorithm proceeds by solving a series of discounted LQR problems, where the discount factor is gradually increased. We prove that this method efficiently recovers a stabilizing controller for linear systems, and for smooth, nonlinear systems within a neighborhood of their equilibria. Our approach overcomes a significant limitation of prior work, namely the need for a pre-given stabilizing control policy. We empirically evaluate the effectiveness of our approach on common control benchmarks.

Juan C. Perdomo, Max Simchowitz, Alekh Agarwal et al.

We study the problem of adaptive control of the linear quadratic regulator for systems in very high, or even infinite dimension. We demonstrate that while sublinear regret requires finite dimensional inputs, the ambient state dimension of the system need not be bounded in order to perform online control. We provide the first regret bounds for LQR which hold for infinite dimensional systems, replacing dependence on ambient dimension with more natural notions of problem complexity. Our guarantees arise from a novel perturbation bound for certainty equivalence which scales with the prediction error in estimating the system parameters, without requiring consistent parameter recovery in more stringent measures like the operator norm. When specialized to finite dimensional settings, our bounds recover near optimal dimension and time horizon dependence.

John Miller, Juan C. Perdomo, Tijana Zrnic

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points of repeated retraining. However, stable solutions can be far from optimal when evaluated in terms of the performative risk, the loss experienced by the decision maker when deploying a model. In this paper, we shift attention beyond performative stability and focus on optimizing the performative risk directly. We identify a natural set of properties of the loss function and model-induced distribution shift under which the performative risk is convex, a property which does not follow from convexity of the loss alone. Furthermore, we develop algorithms that leverage our structural assumptions to optimize the performative risk with better sample efficiency than generic methods for derivative-free convex optimization.

Celestine Mendler-Dünner, Juan C. Perdomo, Tijana Zrnic et al.

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction. What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model. The latter triggers a shift in the distribution that affects future data, while the former keeps the distribution as is. Assuming smoothness and strong convexity, we prove rates of convergence for both greedily deploying models after each stochastic update (greedy deploy) as well as for taking several updates before redeploying (lazy deploy). In both cases, our bounds smoothly recover the optimal $O(1/k)$ rate as the strength of performativity decreases. Furthermore, they illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other. We experimentally explore the trade-off on both synthetic data and a strategic classification simulator.

Juan C. Perdomo, Tijana Zrnic, Celestine Mendler-Dünner et al.

When predictions support decisions they may influence the outcome they aim to predict. We call such predictions performative; the prediction influences the target. Performativity is a well-studied phenomenon in policy-making that has so far been neglected in supervised learning. When ignored, performativity surfaces as undesirable distribution shift, routinely addressed with retraining. We develop a risk minimization framework for performative prediction bringing together concepts from statistics, game theory, and causality. A conceptual novelty is an equilibrium notion we call performative stability. Performative stability implies that the predictions are calibrated not against past outcomes, but against the future outcomes that manifest from acting on the prediction. Our main results are necessary and sufficient conditions for the convergence of retraining to a performatively stable point of nearly minimal loss. In full generality, performative prediction strictly subsumes the setting known as strategic classification. We thus also give the first sufficient conditions for retraining to overcome strategic feedback effects.

Juan C. Perdomo, Yaron Singer

We address the challenge of designing optimal adversarial noise algorithms for settings where a learner has access to multiple classifiers. We demonstrate how this problem can be framed as finding strategies at equilibrium in a two-player, zero-sum game between a learner and an adversary. In doing so, we illustrate the need for randomization in adversarial attacks. In order to compute Nash equilibrium, our main technical focus is on the design of best response oracles that can then be implemented within a Multiplicative Weights Update framework to boost deterministic perturbations against a set of models into optimal mixed strategies. We demonstrate the practical effectiveness of our approach on a series of image classification tasks using both linear classifiers and deep neural networks.