This paper considers the implicit update algorithm for online learning (a.k.a. It is shown that the algorithm achieves a regret bound that is adapted to the variability of the sequence of loss functions. This holds even without the smoothness of the loss. I believe this is a firm contribution to the fields of online learning and stochastic optimization. Firstly, Implicit updates are known to have practical advantages, but their theoretical understanding has been limited to the fact that they enjoy the same worst-case regret guarantees as their explicit counterparts. This is one of a very few works (if not the first one) which shows a nontrivial advantages of the implicit methods and thus makes a significant progress in better understanding of their behavior.

The paper concerns a new online learning problem subject to the constraint of individual fairness. It provides a framework that reduces online classification in the considered model to standard online classification, obtaining an algorithm with sublinear regret both in terms of accuracy and fairness, as well as strong generalization bounds in the i.i.d. All the reviewers liked the paper and the proposed metric-free approach. The appreciated an interesting problem formulation and a clean reduction technique to a known online learning problem. The paper received very high uniform scores of 8 from each reviewer. The reviewers found some issues with the presentation, and I hope the authors will address them in the final version of the manuscript.

A theory paper showing that a reduction from online learning to differentially private PAC learning, e.g., a differentially private PAC learner for concept class H can be used in a black-box fashion to obtain a low regret bound for online learning with 0/1 loss for concept class H. The key contribution here is that this is a computationally efficient reduction, which resolves an open problem of Neel/Roth/Wu and improves on the information theoretic result of Feldman/Xiao. In addition to the strong result, the reviewers point out that the paper contains many interesting observations along the way (e.g., an innovative use of online boosting).

Learning Objects represent a widespread approach to structuring instructional materials in a large variety of educational contexts. The main aim of this work consists of analyzing from a qualitative point of view the process of generating reusable learning objects (RLOs) followed by Clavy, a tool that can be used to retrieve data from multiple medical knowledge sources and reconfigure such sources in diverse multimedia-based structures and organizations. From these organizations, Clavy is able to generate learning objects which can be adapted to various instructional healthcare scenarios with several types of user profiles and distinct learning requirements. Moreover, Clavy provides the capability of exporting these learning objects through educational standard specifications, which improves their reusability features. The analysis insights highlight the importance of having a tool able to transfer knowledge from the available digital medical collections to learning objects that can be easily accessed by medical students and healthcare practitioners through the most popular e-learning platforms.

This paper proposes an online stochastic optimization algorithm (similar to SGD) that has optimal convergence rate of the last iterate in two settings (O(1/sqrt(T)) for Lipschitz convex functions and O(1/T) strongly convex functions), and additionally it allows an arbitrary non-smooth regularizer (e.g. Many subsets of the properties are achieved by prior works. Namely, it was known how to achieve these results up to O(log T) factors. It was known how to achieve the optimal rates with averaging, which, however, destroys sparsity. However, this paper has the first algorithm that has all the properties simultaneously and removes the log factors. The paper has rigorous proofs of the convergence rates and extensive numerical experiments.

Consider mentioning what sort of complexity you are after.

The rebuttal answered all my technical questions, in particular the one about probability and expectations in Theorems 1(ii) and 3. My scores (which were given assuming the technicalities can be fixed) remain the same. The theoretical results do not feel that exciting. The regret bounds seem more or less what one might expect, and there is no comparison to bounds for other algorithms. I understand that there are no directly comparable bounds since you have both budget size and dimensionality of random projections as significant parameters, but still some discussion would be nice. The dependence on budget B in your bounds could perhaps be pointed out more explicitly.

The present work takes a significant step in addressing this. The primary contribution of the paper are variations of Online Newton Step that remove this drawback using a sketching approximation to the scaling matrix and a clever implementation of sparse updates. The primary theoretical contributions are the analysis of the RP and FD versions of the algorithm. For RP they show a regret bound which holds when the matrix G_T (the matrix of observed gradients) is actually low-rank. Given the structure of the loss functions assumed, f_t(w) \ell( w, x_t), gradients will always be in the direction of the examples x_t, and so I think this theorem only holds when the data is actually low-rank.

Online convex minimization is a fundamental problem in learning theory with various applications. Here, we are given a sequence of convex functions f1,...,fT in an online fashion and we seek to predict the minimizer of the sum so as to minimize the regret. This is a very well studied question with various guarantees known even when only given gradient information about the functions fi. For general functions this leads to a regret of sqrt(T) and for some special cases, we know better guarantees: O(log T) for strongly convex functions, O(d log T) for exp-convex functions etc. However, the algorithms that achieve the latter better guarantees are quite different and in some cases need to know bounds on the specific parameters of the functions (e.g., strong-convexity of the fi's, although this can now be avoided).

In many applications, learning systems are required to process continuous non-stationary data streams.We study this problem in an online learning framework and propose an algorithm that can deal with adversarial time-varying and nonlinear constraints.As we show in our work, the algorithm called Constraint Violation Velocity Projection (CVV-Pro) achieves \sqrt{T} regret and converges to the feasible set at a rate of 1/\sqrt{T}, despite the fact that the feasible set is slowly time-varying and a priori unknown to the learner. CVV-Pro only relies on local sparse linear approximations of the feasible set and therefore avoids optimizing over the entire set at each iteration, which is in sharp contrast to projected gradients or Frank-Wolfe methods. We also empirically evaluate our algorithm on two-player games, where the players are subjected to a shared constraint.