Online Agnostic Boosting via Regret Minimization

Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules. While in statistical learning numerous boosting methods exist both in the realizable and agnostic settings, in online learning they exist only in the realizable case. In this work we provide the first agnostic online boosting algorithm; that is, given a weak learner with only marginally-better-than-trivial regret guarantees, our algorithm boosts it to a strong learner with sublinear regret. Our algorithm is based on an abstract (and simple) reduction to online convex optimization, which efficiently converts an arbitrary online convex optimizer to an online booster. Moreover, this reduction extends to the statistical as well as the online realizable settings, thus unifying the 4 cases of statistical/online and agnostic/realizable boosting

Characterizing notions of omniprediction via multicalibration

A recent line of work shows that notions of multigroup fairness imply surprisingly strong notions of omniprediction: loss minimization guarantees that apply not just for a specific loss function, but for any loss belonging to a large family of losses. While prior work has derived various notions of omniprediction from multigroup fairness guarantees of varying strength, it was unknown whether the connection goes in both directions. In this work, we answer this question in the affirmative, establishing equivalences between notions of multicalibration and omniprediction. The new definitions that hold the key to this equivalence are new notions of swap omniprediction, which are inspired by swap regret in online learning. We show that these can be characterized exactly by a strengthening of multicalibration that we refer to as swap multicalibration. One can go from standard to swap multicalibration by a simple discretization; moreover all known algorithms for standard multicalibration in fact give swap multicalibration. In the context of omniprediction though, introducing the notion of swapping results in provably stronger notions, which require a predictor to minimize expected loss at least as well as an adaptive adversary who can choose both the loss function and hypothesis based on the value predicted by the predictor. Building on these characterizations, we paint a complete picture of the relationship between the various omniprediction notions in the literature by establishing implications and separations between them. Our work deepens our understanding of the connections between multigroup fairness, loss minimization and outcome indistinguishability and establishes new connections to classic notions in online learning

A Unified View of Large-scale Zero-sum Equilibrium Computation

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio

Comparative Learning: A Sample Complexity Theory for Two Hypothesis Classes

In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the learned model by comparing it with the best hypothesis in the class (the agnostic setting). Taking a step beyond these classic setups that involve only a single hypothesis class, we study a variety of problems that involve two hypothesis classes simultaneously. We introduce comparative learning as a combination of the realizable and agnostic settings in PAC learning: given two binary hypothesis classes S and B, we assume that the data is labeled according to a hypothesis in the source class S and require the learned model to achieve an accuracy comparable to the best hypothesis in the benchmark class B. Even when both S and B have infinite VC dimensions, comparative learning can still have a small sample complexity. We show that the sample complexity of comparative learning is characterized by the mutual VC dimension VC(S,B) which we define to be the maximum size of a subset shattered by both S and B. We also show a similar result in the online setting, where we give a regret characterization in terms of the analogous mutual Littlestone dimension Ldim(S,B). These results also hold for partial hypotheses. We additionally show that the insights necessary to characterize the sample complexity of comparative learning can be applied to other tasks involving two hypothesis classes. In particular, we characterize the sample complexity of realizable multiaccuracy and multicalibration using the mutual fat-shattering dimension, an analogue of the mutual VC dimension for real-valued hypotheses. This not only solves an open problem proposed by Hu, Peale, Reingold (2022), but also leads to independently interesting results extending classic ones about regression, boosting, and covering number to our two-hypothesis-class setting