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Existing algorithms for online conformal prediction -- guaranteeing marginal coverage in adversarial settings -- are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between threshold calibrated coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the follow the perturbed leader family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs & Candes [2021] 

In traditional reinforcement learning (RL), the learner aims to solve a single objective optimization problem: find the policy that maximizes expected reward. However, in many real-world settings, it is important to optimize over multiple objectives simultaneously. For example, when we are interested in fairness, states might have feature annotations corresponding to multiple (intersecting) demographic groups to whom reward accrues, and our goal might be to maximize the reward of the group receiving the minimal reward. In this work, we consider a multi-objective optimization problem in which each objective is defined by a state-based reweighting of a single scalar reward function. This generalizes the problem of maximizing the reward of the minimum reward group. We provide oracle-efficient algorithms to solve these multi-objective RL problems even when the number of objectives is exponentially large-for tabular MDPs, as well as for large MDPs when the group functions have additional structure. Finally, we experimentally validate our theoretical results and demonstrate applications on a preferential attachment graph MDP. 

We give an efficient reduction through which any machine learning algorithm can be converted into an interactive protocol that can interact with another party (such as a human) to reach agreement on predictions and improve accuracy. The requirements on each party are calibration conditions which are computationally and statistically tractable relaxations of Bayesian rationality --- that are sensible even in prior free settings --- and hence are a substantial generalization of Aumann's classic ``agreement theorem''. In the interactive protocol, the machine learning model first produces a prediction. Then, the human responds to the model's prediction by either conveying agreement, or else providing feedback of some sort. The model then updates its state and provides a new prediction, and the human in turn may update their beliefs. The process continues until the model and the human reach agreement. The first setting we study generalizes past work on Aumann's Agreement Theorem, in which the parties aim to agree on a one-dimensional expectation. At each round, each party simply communicates an estimate of their current prediction for the expectation. In this setting we recover the quantitative convergence theorem of [Aaronson, 2005] (but under our much weaker assumptions). We then move on to the case in which the parties maintain beliefs about a distribution over d outcomes and consider two feedback mechanisms. The first simply corresponds to a vector-valued estimate of the agents' current prediction. The second takes a decision theoretic perspective: if the human needs to take some downstream action from a finite set, and has an arbitrary utility function of their action and the outcome, then we show that the parties can communicate and reach agreement about the correct downstream action to take by simply communicating at each round the action that they believe to be utility maximizing. The number of rounds until agreement remains independent of $$d$$ in this case. We can also generalize our protocols to more than 2 parties, with computational complexity that degrades only linearly with the number of parties. Our protocols are based on simple, efficiently maintainable conditions and result in predictions that are more accurate than any single party's alone. 

Blasiok et al. [2023] proposed distance to calibration as a natural measure of calibration error that unlike expected calibration error (ECE) is continuous. Recently, Qiao and Zheng [2024] gave a non-constructive argument establishing the existence of an online predictor that can obtain O(√T ) distance to calibration in the adversarial setting, which is known to be impossible for ECE. They leave as an open problem finding an explicit, efficient algorithm. We resolve this problem and give an extremely simple, efficient, deterministic algorithm that obtains distance to calibration error at most 2√T . 

There has been substantial recent concern that pricing algorithms might learn to ``collude.'' Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors who refuse to support high prices, and these strategies can be automatically learned. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to optimize their payoff. Is this intuition correct? Would preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can emerge even when both players are using algorithms which do not encode threats, and which optimize for their own revenue. We study sequential pricing games in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would -- and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of ``algorithmic collusion'' may need to be expanded, to include strategies without explicitly encoded threats. 

We study the problem of online prediction, in which at each time step t, an individual xt arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees. 

We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar distributional property G if and only if G is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable G, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a G-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property G1 is not elicitable by itself, but is elicitable conditionally on another elicitable property G0, then there is a canonical algorithm that jointly multicalibrates G1 and G0; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment. 

Individual probabilities refer to the probabilities of outcomes that are realized only once: the probability that it will rain tomorrow, the probability that Alice will die within the next 12 months, the probability that Bob will be arrested for a violent crime in the next 18 months, etc. Individual probabilities are fundamentally unknowable. Nevertheless, we show that two parties who agree on the data—or on how to sample from a data distribution—cannot agree to disagree on how to model individual probabilities. This is because any two models of individual probabilities that substantially disagree can together be used to empirically falsify and improve at least one of the two models. This can be efficiently iterated in a process of “reconciliation” that results in models that both parties agree are superior to the models they started with, and which themselves (almost) agree on the forecasts of individual probabilities (almost) everywhere. We conclude that although individual probabilities are unknowable, they are contestable via a computationally and data efficient process that must lead to agreement. Thus we cannot find ourselves in a situation in which we have two equally accurate and unimprovable models that disagree substantially in their predictions—providing an answer to what is sometimes called the predictive or model multiplicity problem. 

A reconstruction attack on a private dataset D takes as input some publicly accessible information about the dataset and produces a list of candidate elements of D . We introduce a class of data reconstruction attacks based on randomized methods for nonconvex optimization. We empirically demonstrate that our attacks can not only reconstruct full rows of D from aggregate query statistics Q ( D )∈ℝ m but can do so in a way that reliably ranks reconstructed rows by their odds of appearing in the private data, providing a signature that could be used for prioritizing reconstructed rows for further actions such as identity theft or hate crime. We also design a sequence of baselines for evaluating reconstruction attacks. Our attacks significantly outperform those that are based only on access to a public distribution or population from which the private dataset D was sampled, demonstrating that they are exploiting information in the aggregate statistics Q ( D ) and not simply the overall structure of the distribution. In other words, the queries Q ( D ) are permitting reconstruction of elements of this dataset, not the distribution from which D was drawn. These findings are established both on 2010 US decennial Census data and queries and Census-derived American Community Survey datasets. Taken together, our methods and experiments illustrate the risks in releasing numerically precise aggregate statistics of a large dataset and provide further motivation for the careful application of provably private techniques such as differential privacy. 

We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random variable that is dependent on the population one is born into. Individuals then apply to a downstream agent, which we treat as a university throughout the paper (but could also represent an employer) who makes a decision about whether to admit them or not. The university does not directly observe talent or wealth, but rather a signal (representing e.g. a standardized test) that is a convex combination of both. The university knows the distributions from which an individual's type and wealth are drawn, and makes its decisions based on the posterior distribution of the applicant's characteristics conditional on their population and signal. Each population's wealth distribution at the next round then depends on the fraction of that population that was admitted by the university at the previous round. We study wealth dynamics in this model, and give conditions under which the dynamics have a single attracting fixed point (which implies population wealth inequality is transitory), and conditions under which it can have multiple attracting fixed points (which implies that population wealth inequality can be persistent). In the case in which there are multiple attracting fixed points, we study interventions aimed at eliminating or mitigating inequality, including increasing the capacity of the university to admit more people, aligning the signal generated by individuals with the preferences of the university, and making direct monetary transfers to the less wealthy population.