High-Dimensional Prediction for Sequential Decision Making

We study the problem of making predictions of an adversarially chosen high-dimensional state that are unbiased subject to an arbitrary collection of conditioning events, with the goal of tailoring these events to downstream decision makers. We give efficient algorithms for solving this problem, as well as a number of applications that stem from choosing an appropriate set of conditioning events. For example, we can efficiently make predictions targeted at polynomially many decision makers, giving each of them optimal swap regret if they best-respond to our predictions. We generalize this to online combinatorial optimization, where the decision makers have a very large action space, to give the first algorithms offering polynomially many decision makers no regret on polynomially many subsequences that may depend on their actions and the context. We apply these results to get efficient no-subsequence-regret algorithms in extensive-form games (EFGs), yielding a new family of regret guarantees for EFGs that generalizes some existing EFG regret notions, e.g. regret to informed causal deviations, and is generally incomparable to other known such notions. Next, we develop a novel transparent alternative to conformal prediction for building valid online adversarial multiclass prediction sets. We produce class scores that downstream algorithms can use for producing valid-coverage prediction sets, as if these scores were the true conditional class probabilities. We show this implies strong conditional validity guarantees including set-size-conditional and multigroup-fair coverage for polynomially many downstream prediction sets. Moreover, our class scores can be guaranteed to have improved $L_2$ loss, cross-entropy loss, and generally any Bregman loss, compared to any collection of benchmark models, yielding a high-dimensional real-valued version of omniprediction.

Oracle Efficient Algorithms for Groupwise Regret

We study the problem of online prediction, in which at each time step $t$, an individual $x_t$ 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.

Gait Design of a Novel Arboreal Concertina Locomotion for Snake-like Robots

In this paper, we propose a novel strategy for a snake robot to move straight up a cylindrical surface. Prior works on pole-climbing for a snake robot mainly utilized a rolling helix gait, and although proven to be efficient, it does not reassemble movements made by a natural snake. We take inspiration from nature and seek to imitate the Arboreal Concertina Locomotion (ACL) from real-life serpents. In order to represent the 3D curves that make up the key motion patterns of ACL, we establish a set of parametric equations that identify periodic functions, which produce a sequence of backbone curves. We then build up the gait equation using the curvature integration method, and finally, we propose a simple motion estimation strategy using virtual chassis and non-slip model assumptions. We present experimental results using a 20-DOF snake robot traversing outside of a straight pipe.

Oracle Efficient Online Multicalibration and Omniprediction

A recent line of work has shown a surprising connection between multicalibration, a multi-group fairness notion, and omniprediction, a learning paradigm that provides simultaneous loss minimization guarantees for a large family of loss functions. Prior work studies omniprediction in the batch setting. We initiate the study of omniprediction in the online adversarial setting. Although there exist algorithms for obtaining notions of multicalibration in the online adversarial setting, unlike batch algorithms, they work only for small finite classes of benchmark functions $F$, because they require enumerating every function $f \in F$ at every round. In contrast, omniprediction is most interesting for learning theoretic hypothesis classes $F$, which are generally continuously large. We develop a new online multicalibration algorithm that is well defined for infinite benchmark classes $F$, and is oracle efficient (i.e. for any class $F$, the algorithm has the form of an efficient reduction to a no-regret learning algorithm for $F$). The result is the first efficient online omnipredictor -- an oracle efficient prediction algorithm that can be used to simultaneously obtain no regret guarantees to all Lipschitz convex loss functions. For the class $F$ of linear functions, we show how to make our algorithm efficient in the worst case. Also, we show upper and lower bounds on the extent to which our rates can be improved: our oracle efficient algorithm actually promises a stronger guarantee called swap-omniprediction, and we prove a lower bound showing that obtaining $O(\sqrt{T})$ bounds for swap-omniprediction is impossible in the online setting. On the other hand, we give a (non-oracle efficient) algorithm which can obtain the optimal $O(\sqrt{T})$ omniprediction bounds without going through multicalibration, giving an information theoretic separation between these two solution concepts.

Scalable Membership Inference Attacks via Quantile Regression

Membership inference attacks are designed to determine, using black box access to trained models, whether a particular example was used in training or not. Membership inference can be formalized as a hypothesis testing problem. The most effective existing attacks estimate the distribution of some test statistic (usually the model's confidence on the true label) on points that were (and were not) used in training by training many \emph{shadow models} -- i.e. models of the same architecture as the model being attacked, trained on a random subsample of data. While effective, these attacks are extremely computationally expensive, especially when the model under attack is large. We introduce a new class of attacks based on performing quantile regression on the distribution of confidence scores induced by the model under attack on points that are not used in training. We show that our method is competitive with state-of-the-art shadow model attacks, while requiring substantially less compute because our attack requires training only a single model. Moreover, unlike shadow model attacks, our proposed attack does not require any knowledge of the architecture of the model under attack and is therefore truly ``black-box". We show the efficacy of this approach in an extensive series of experiments on various datasets and model architectures.

Balanced Filtering via Non-Disclosive Proxies

We study the problem of non-disclosively collecting a sample of data that is balanced with respect to sensitive groups when group membership is unavailable or prohibited from use at collection time. Specifically, our collection mechanism does not reveal significantly more about group membership of any individual sample than can be ascertained from base rates alone. To do this, we adopt a fairness pipeline perspective, in which a learner can use a small set of labeled data to train a proxy function that can later be used for this filtering task. We then associate the range of the proxy function with sampling probabilities; given a new candidate, we classify it using our proxy function, and then select it for our sample with probability proportional to the sampling probability corresponding to its proxy classification. Importantly, we require that the proxy classification itself not reveal significant information about the sensitive group membership of any individual sample (i.e., it should be sufficiently non-disclosive). We show that under modest algorithmic assumptions, we find such a proxy in a sample- and oracle-efficient manner. Finally, we experimentally evaluate our algorithm and analyze generalization properties.

Improved Differentially Private Regression via Gradient Boosting

We revisit the problem of differentially private squared error linear regression. We observe that existing state-of-the-art methods are sensitive to the choice of hyper-parameters -- including the ``clipping threshold'' that cannot be set optimally in a data-independent way. We give a new algorithm for private linear regression based on gradient boosting. We show that our method consistently improves over the previous state of the art when the clipping threshold is taken to be fixed without knowledge of the data, rather than optimized in a non-private way -- and that even when we optimize the clipping threshold non-privately, our algorithm is no worse. In addition to a comprehensive set of experiments, we give theoretical insights to explain this behavior.

The Scope of Multicalibration: Characterizing Multicalibration via Property Elicitation

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 $\Gamma$ if and only if $\Gamma$ 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 $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-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 $\Gamma^1$ is not elicitable by itself, but is elicitable conditionally on another elicitable property $\Gamma^0$, then there is a canonical algorithm that jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; 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.

Multicalibration as Boosting for Regression

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.