Omnipredictors are simple prediction functions that encode loss-minimizing predictions with respect to a hypothesis class ℋ, simultaneously for every loss function within a class of losses ℒ. In this work, we give near-optimal learning algorithms for omniprediction, in both the online and offline settings. To begin, we give an oracle-efficient online learning algorithm that achieves (ℒ, ℋ)-omniprediction with $\tilde O\left( {\sqrt {T\log |\mathcal{H}|} } \right)$ regret for any class of Lipschitz loss functions ℒ ⊆ ℒLip. Quite surprisingly, this regret bound matches the optimal regret for minimization of a single loss function (up to a $\sqrt {\log (T)} $ factor). Given this online algorithm, we develop an online-to-offline conversion that achieves near-optimal complexity across a number of measures. In particular, for all bounded loss functions within the class of Bounded Variation losses ℒBV(which include all convex, all Lipschitz, and all proper losses) and any (possibly-infinite) ℋ, we obtain an offline learning algorithm that, leveraging an (offline) ERM oracle and m samples from $\mathcal{D}$, returns an efficient (ℒBV, ℋ, ε(m))-omnipredictor for ε(m) scaling near-linearly in the Rademacher complexity of Th◦ℋ, the class of all binary threshold functions on ℋ.

We present a new perspective on loss minimization and the recent notion of Omniprediction through the lens of Outcome Indistingusihability. For a collection of losses and hypothesis class, omniprediction requires that a predictor provide a loss-minimization guarantee simultaneously for every loss in the collection compared to the best (loss-specific) hypothesis in the class. We present a generic template to learn predictors satisfying a guarantee we call Loss Outcome Indistinguishability. For a set of statistical tests--based on a collection of losses and hypothesis class--a predictor is Loss OI if it is indistinguishable (according to the tests) from Nature's true probabilities over outcomes. By design, Loss OI implies omniprediction in a direct and intuitive manner. We simplify Loss OI further, decomposing it into a calibration condition plus multiaccuracy for a class of functions derived from the loss and hypothesis classes. By careful analysis of this class, we give efficient constructions of omnipredictors for interesting classes of loss functions, including non-convex losses. This decomposition highlights the utility of a new multi-group fairness notion that we call calibrated multiaccuracy, which lies in between multiaccuracy and multicalibration. We show that calibrated multiaccuracy implies Loss OI for the important set of convex losses arising from Generalized Linear Models, without requiring full multicalibration. For such losses, we show an equivalence between our computational notion of Loss OI and a geometric notion of indistinguishability, formulated as Pythagorean theorems in the associated Bregman divergence. We give an efficient algorithm for calibrated multiaccuracy with computational complexity comparable to that of multiaccuracy. In all, calibrated multiaccuracy offers an interesting tradeoff point between efficiency and generality in the omniprediction landscape.

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.

We introduce and study the notion of Swap Agnostic Learning. The problem can be phrased as a game between a *predictor* and an *adversary*: first, the predictor selects a hypothesis $h$; then, the adversary plays in response, and for each level set of the predictor, selects a loss-minimizing hypothesis $c_v \in \mathcal{C}$; the predictor wins if $h$ competes with the adaptive adversary's loss. Despite the strength of the adversary, our main result demonstrates the feasibility Swap Agnostic Learning for any convex loss. Somewhat surprisingly, the result follows by proving an *equivalence* between Swap Agnostic Learning and swap variants of the recent notions Omniprediction (ITCS'22) and Multicalibration (ICML'18). Beyond this equivalence, we establish further connections to the literature on Outcome Indistinguishability (STOC'20, ITCS'23), revealing a unified notion of OI that captures all existing notions of omniprediction and multicalibration.

Recently, Dwork et al. (STOC 2021) introduced Outcome Indistinguishability as a new desideratum for binary prediction tasks. Outcome Indistinguishability (OI) articulates the goals of prediction in the language of computational indistinguishability: a predictor is Outcome Indistinguishable if no computationally-bounded observer can distinguish Nature’s outcomes from outcomes that are generated based on the predictions. In this sense, OI suggests a generative model for binary outcomes that cannot be refuted given the empirical evidence and computational resources at hand. In this work, we extend Outcome Indistinguishability beyond Bernoulli, to outcomes that live in a large discrete or continuous domain. While the idea of OI for non-binary outcomes is natural for many applications, defining OI in generality is not simply a syntactic exercise. We introduce and study multiple definitions of OI—each with its own semantics—for predictors that completely specify each individuals’ outcome distributions, as well as predictors that only partially specify the outcome distributions through statistics, such as moments. With the definitions in place, we provide learning algorithms for producing OI generative outcome models for general random outcomes. Finally, we study the relation of Outcome Indistinguishability and Multicalibration of statistics (beyond the mean) and relate our findings to the recent work of Jung et al. (COLT 2021) on Moment Multicalibration. We find an equivalence between Outcome Indistinguishability and Multicalibration that is more subtle than in the binary case and sheds light on the techniques employed by Jung et al. to obtain Moment Multicalibration.

Introduced as a notion of algorithmic fairness, multicalibration has proved to be a powerful and versatile concept with implications far beyond its original intent. This stringent notion—that predictions be well-calibrated across a rich class of intersecting subpopulations—provides its strong guarantees at a cost: the computational and sample complexity of learning multicalibrated predictors are high, and grow exponentially with the number of class labels. In contrast, the relaxed notion of multiaccuracy can be achieved more efficiently, yet many of the most desirable properties of multicalibration cannot be guaranteed assuming multiaccuracy alone. This tension raises a key question: \emph{Can we learn predictors with multicalibration-style guarantees at a cost commensurate with multiaccuracy?} In this work, we define and initiate the study of \emph{Low-Degree Multicalibration}. Low-Degree Multicalibration defines a hierarchy of increasingly-powerful multi-group fairness notions that spans multiaccuracy and the original formulation of multicalibration at the extremes. Our main technical contribution demonstrates that key properties of multicalibration, related to fairness and accuracy, actually manifest as low-degree properties. Importantly, we show that low-degree multicalibration can be significantly more efficient than full multicalibration. In the multi-class setting, the sample complexity to achieve low-degree multicalibration improves exponentially (in the number of classes) over full multicalibration. Our work presents compelling evidence that low-degree multicalibration represents a sweet spot, pairing computational and sample efficiency with strong fairness and accuracy guarantees.

Given the computational cost and technical expertise required to train machine learning models, users may delegate the task of learning to a service provider. Delegation of learning has clear benefits, and at the same time raises serious concerns of trust. This work studies possible abuses of power by untrusted learners.We show how a malicious learner can plant an undetectable backdoor into a classifier. On the surface, such a backdoored classifier behaves normally, but in reality, the learner maintains a mechanism for changing the classification of any input, with only a slight perturbation. Importantly, without the appropriate “backdoor key,” the mechanism is hidden and cannot be detected by any computationally-bounded observer. We demonstrate two frameworks for planting undetectable backdoors, with incomparable guarantees.•First, we show how to plant a backdoor in any model, using digital signature schemes. The construction guarantees that given query access to the original model and the backdoored version, it is computationally infeasible to find even a single input where they differ. This property implies that the backdoored model has generalization error comparable with the original model. Moreover, even if the distinguisher can request backdoored inputs of its choice, they cannot backdoor a new input—a property we call non-replicability.•Second, we demonstrate how to insert undetectable backdoors in models trained using the Random Fourier Features (RFF) learning paradigm (Rahimi, Recht; NeurIPS 2007). In this construction, undetectability holds against powerful white-box distinguishers: given a complete description of the network and the training data, no efficient distinguisher can guess whether the model is “clean” or contains a backdoor. The backdooring algorithm executes the RFF algorithm faithfully on the given training data, tampering only with its random coins. We prove this strong guarantee under the hardness of the Continuous Learning With Errors problem (Bruna, Regev, Song, Tang; STOC 2021). We show a similar white-box undetectable backdoor for random ReLU networks based on the hardness of Sparse PCA (Berthet, Rigollet; COLT 2013).Our construction of undetectable backdoors also sheds light on the related issue of robustness to adversarial examples. In particular, by constructing undetectable backdoor for an “adversarially-robust” learning algorithm, we can produce a classifier that is indistinguishable from a robust classifier, but where every input has an adversarial example! In this way, the existence of undetectable backdoors represent a significant theoretical roadblock to certifying adversarial robustness.

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated--- amongst the inputs that receive a predicted vector of class probabilities q, the actual distribution over classes is given by q. For multi-class prediction problems, however, directly optimizing predictions under distribution calibration tends to be infeasible, requiring sample complexity that grows exponentially in the number of classes C. In this work, we introduce a new notion---decision calibration---that requires the predicted distribution and true distribution over classes to be ``indistinguishable'' to downstream decision-makers. This perspective gives a new characterization of distribution calibration: a predictor is distribution calibrated if and only if it is decision calibrated with respect to all decision-makers. Our main result shows that under a mild restriction, unlike distribution calibration, decision calibration is actually feasible. We design a recalibration algorithm that provably achieves decision calibration efficiently, provided that the decision-makers have a bounded number of actions (e.g., polynomial in C). We validate our recalibration algorithm empirically: compared to existing methods, decision calibration improves decision-making on skin lesion and ImageNet classification with modern neural network predictors.

Prediction algorithms assign numbers to individuals that are popularly understood as individual “probabilities”—what is the probability of 5-year survival after cancer diagnosis?—and which increasingly form the basis for life-altering decisions. Drawing on an understanding of computational indistinguishability developed in complexity theory and cryptography, we introduce Outcome Indistinguishability. Predictors that are Outcome Indistinguishable (OI) yield a generative model for outcomes that cannot be efficiently refuted on the basis of the real-life observations produced by .

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework – distributional Shapley– where the value of a point is defined in the context of an underlying data distribution. We prove that distributional Shapley has several desirable statistical properties; for example, the values are stable under perturbations to the data points themselves and to the underlying data distribution. We leverage these properties to develop a new algorithm for estimating values from data, which comes with formal guarantees and runs two orders of magnitude faster than state-of-the-art algorithms for computing the (non distributional) data Shapley values. We apply distributional Shapley to diverse data sets and demonstrate its utility in a data market setting.

In this work, we study notions of fairness in decision-making systems when individuals have diverse preferences over the possible outcomes of the decisions. Our starting point is the seminal work of Dwork et al. [ITCS 2012] which introduced a notion of individual fairness (IF): given a task-specific similarity metric, every pair of individuals who are similarly qualified according to the metric should receive similar outcomes. We show that when individuals have diverse preferences over outcomes, requiring IF may unintentionally lead to less-preferred outcomes for the very individuals that IF aims to protect (e.g. a protected minority group). A natural alternative to IF is the classic notion of fair division, envy-freeness (EF): no individual should prefer another individual’s outcome over their own. Although EF allows for solutions where all individuals receive a highly-preferred outcome, EF may also be overly-restrictive for the decision-maker. For instance, if many individuals agree on the best outcome, then if any individual receives this outcome, they all must receive it, regardless of each individual’s underlying qualifications for the outcome. We introduce and study a new notion of preference-informed individual fairness (PIIF) that is a relaxation of both individual fairness and envy-freeness. At a high-level, PIIF requires that outcomes satisfy IF-style constraints, but allows for deviations provided they are in line with individuals' preferences. We show that PIIF can permit outcomes that are more favorable to individuals than any IF solution, while providing considerably more flexibility to the decision-maker than EF. In addition, we show how to efficiently optimize any convex objective over the outcomes subject to PIIF for a rich class of individual preferences. Finally, we demonstrate the broad applicability of the PIIF framework by extending our definitions and algorithms to the multiple-task targeted advertising setting introduced by Dwork and Ilvento [ITCS 2019].

Prediction systems are successfully deployed in applications ranging from disease diagnosis, to predicting credit worthiness, to image recognition. Even when the overall accuracy is high, these systems may exhibit systematic biases that harm specific subpopulations; such biases may arise inadvertently due to underrepresentation in the data used to train a machine-learning model, or as the result of intentional malicious discrimination. We develop a rigorous framework of *multiaccuracy* auditing and post-processing to ensure accurate predictions across *identifiable subgroups*. Our algorithm, MULTIACCURACY-BOOST, works in any setting where we have black-box access to a predictor and a relatively small set of labeled data for auditing; importantly, this black-box framework allows for improved fairness and accountability of predictions, even when the predictor is minimally transparent. We prove that MULTIACCURACY-BOOST converges efficiently and show that if the initial model is accurate on an identifiable subgroup, then the post-processed model will be also. We experimentally demonstrate the effectiveness of the approach to improve the accuracy among minority subgroups in diverse applications (image classification, finance, population health). Interestingly, MULTIACCURACY-BOOST can improve subpopulation accuracy (e.g. for "black women") even when the sensitive features (e.g. "race", "gender") are not given to the algorithm explicitly.

Many selection procedures involve ordering candidates according to their qualifications. For example, a university might order applicants according to a perceived probability of graduation within four years, and then select the top 1000 applicants. In this work, we address the problem of ranking members of a population according to their "probability" of success, based on a training set of historical binary outcome data (e.g., graduated in four years or not). We show how to obtain rankings that satisfy a number of desirable accuracy and fairness criteria, despite the coarseness of the training data. As the task of ranking is global (the rank of every individual depends not only on their own qualifications, but also on every other individuals' qualifications) ranking is more subtle and vulnerable to manipulation than standard prediction tasks. Towards mitigating unfair discrimination caused by inaccuracies in rankings, we develop two parallel definitions of evidence-based rankings. The first definition relies on a semantic notion of domination-compatibility: if the training data suggest that members of a set S are more qualified (on average) than the members of T, then a ranking that favors T over S (i.e. where T dominates S) is blatantly inconsistent with the evidence, and likely to be discriminatory. The definition asks for domination-compatibility, not just for a pair of sets, but rather for every pair of sets from a rich collection C of subpopulations. The second definition aims at precluding even more general forms of discrimination; this notion of evidence-consistency requires that the ranking must be justified on the basis of consistency with the expectations for every set in the collection C. Somewhat surprisingly, while evidence-consistency is a strictly stronger notion than domination-compatibility when the collection C is predefined, the two notions are equivalent when the collection C may depend on the ranking in question.

Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually producing an alignment (i.e., the sequence of edits) has received far less attention. Somewhat surprisingly, we show that any algorithm to estimate edit distance can be used in a black-box fashion to produce an approximate alignment of strings, with modest loss in approximation factor and small loss in run time. Plugging in the result of Andoni, Krauthgamer, and Onak, we obtain an alignment that is a $(\log n)^{O(1/\varepsilon^2)}$ approximation in time $\tilde{O}(n^{1 + \varepsilon})$. Closely related to the study of approximation algorithms is the study of metric embeddings for edit distance. We show that min-hash techniques can be useful in designing edit distance embeddings through three results: (1) An embedding from Ulam distance (edit distance over permutations) to Hamming space that matches the best known distortion of $O(\log n)$ and also implicitly encodes a sequence of edits between the strings; (2) In the case where the edit distance between the input strings is known to have an upper bound $K$, we show that embeddings of edit distance into Hamming space with distortion $f(n)$ can be modified in a black-box fashion to give distortion $O(f(\operatorname{poly}(K)))$ for a class of periodic-free strings; (3) A randomized dimension-reduction map with contraction $c$ and asymptotically optimal expected distortion $O(c)$, improving on the previous $\tilde{O}(c^{1 + 2 / \log \log \log n})$ distortion result of Batu, Ergun, and Sahinalp.

We develop and study multicalibration as a new measure of fairness in machine learning that aims to mitigate inadvertent or malicious discrimination that is introduced at training time (even from ground truth data). Multicalibration guarantees meaningful (calibrated) predictions for every subpopulation that can be identified within a specified class of computations. The specified class can be quite rich; in particular, it can contain many overlapping subgroups of a protected group. We demonstrate that in many settings this strong notion of protection from discrimination is provably attainable and aligned with the goal of obtaining accurate predictions. Along the way, we present algorithms for learning a multicalibrated predictor, study the computational complexity of this task, and illustrate tight connections to the agnostic learning model.

We study the problem of fair classification within the versatile framework of Dwork et al. [ITCS '12], which assumes the existence of a metric that measures similarity between pairs of individuals. Unlike earlier work, we do not assume that the entire metric is known to the learning algorithm; instead, the learner can query this arbitrary metric a bounded number of times. We propose a new notion of fairness called metric multifairness and show how to achieve this notion in our setting. Metric multifairness is parameterized by a similarity metric d on pairs of individuals to classify and a rich collection C of (possibly overlapping) "comparison sets" over pairs of individuals. At a high level, metric multifairness guarantees that similar subpopulations are treated similarly, as long as these subpopulations are identified within the class C.

A single-elimination (SE) tournament is a popular way to select a winner both in sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that the organizer's favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so-called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that every player in an $n$ player tournament generated by the Condorcet random model will be an SE winner even when the noise is as small as possible, $p=\Theta(\ln n/n)$; prior work only had such results for $p\geq \Omega(\sqrt{\ln n/n})$. We also establish new results for significantly more general generative models.

A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that every player in an n player tournament generated by the Condorcet Random Model will be an SE winner even when the noise is as small as possible, p = Θ(ln n/n); prior work only had such results for p ≥ Ω( ln n/n). We also establish new results for significantly more general generative models.