Summary In the submission, authors explore a new "community exploration problem", both in an offline and online setting: An agent choose at each round t \in [K] one community among C_1,…,C_m. Then, a member is uniformly sampled (with replacement) from the chosen community. The goal for the agent is to maximize the overall number of distinct members sampled. In the offline setting, the agent knows each community size. If the allocation strategy k_1 ... k_m K has to be given before the beginning of the game (scenario 1), then a greedy non-adaptive strategy is shown to be optimal.

One of the main current challenges in Educational Data Mining and Learning Analytics is the portability or transferability of predictive models obtained for a particular course so that they can be applied to other different courses. To handle this challenge, one of the foremost problems is the models excessive dependence on the low-level attributes used to train them, which reduces the models portability. To solve this issue, the use of high level attributes with more semantic meaning, such as ontologies, may be very useful. Along this line, we propose the utilization of an ontology that uses a taxonomy of actions that summarises students interactions with the Moodle learning management system. We compare the results of this proposed approach against our previous results when we used low-level raw attributes obtained directly from Moodle logs. The results indicate that the use of the proposed ontology improves the portability of the models in terms of predictive accuracy. The main contribution of this paper is to show that the ontological models obtained in one source course can be applied to other different target courses with similar usage levels without losing prediction accuracy.

SUMMARY While I am not heavily familiar with the literature on adaptive online learning, this paper seems to be a breakthrough, offering in the form of Theorem 1 a very strong result that can be leveraged to obtain adaptive (in the model complexity sense) online learning bounds in a number of settings. The efficiency, at least in the polytime sense, of the algorithms for the various settings makes these results all the more interesting. I was very surprised by the aside'' on the 1-mixability of logistic loss and the argument for circumventing the lower bound of Hazan, Koren, and Levy in the supervised learning setting. I wish that the authors could give more detail to this observation and the consequences, as the implications are so interesting that I would be (almost) sold on acceptance from this fact alone. I found the results of this paper to be very interesting, technically strong, and important, so I would strongly recommend acceptance.

This paper describes an algorithm for optizimization of Hawkes process parameters in on-line settings, where non-parametric form of a kernel is learnt. The paper reports a gradient approach to optimization, with theoretical analysis thereof. In particular, the authors provide: a regret bound, justification for simplification steps (discretization of time and truncation of time over which previous posts influence a new post), an approach to a tractable projection of the solution (a step in the algorithm), time complexity analysis. The paper is very well written, which is very helpful given it is mathematically involved. I found it tackling an important problem (on-line learning is important for large scale datasets, and non-parametricity is a very reasonable setting when it is hard to specify a reasonable kernel form a priori).

This paper proposes a novel data-driven control strategy for maintaining connectivity in networked multi-robot systems. Existing approaches often rely on a pre-determined communication model specifying whether pairwise robots can communicate given their relative distance to guide the connectivity-aware control design, which may not capture real-world communication conditions. To relax that assumption, we present the concept of Data-driven Connectivity Barrier Certificates, which utilize Control Barrier Functions (CBF) and Gaussian Processes (GP) to characterize the admissible control space for pairwise robots based on communication performance observed online. This allows robots to maintain a satisfying level of pairwise communication quality (measured by the received signal strength) while in motion. Then we propose a Data-driven Connectivity Maintenance (DCM) algorithm that combines (1) online learning of the communication signal strength and (2) a bi-level optimization-based control framework for the robot team to enforce global connectivity of the realistic multi-robot communication graph and minimally deviate from their task-related motions. We provide theoretical proofs to justify the properties of our algorithm and demonstrate its effectiveness through simulations with up to 20 robots.

This paper studies the online learning (stochastic and full-information) problem of bidding in multi commodity first price auctions. The paper introduces a polynomial time algorithm that achieves a regret of \sqrt{T log(T)} that has a near optimal dependence on T. The main challenge that the paper has to deal with is to find a computationally efficient algorithm for computing the best biding strategy given a known distribution.The authors first demonstrate that natural approaches for solving this problem exactly are not computationally efficient (this is not a formal np-hardness proof). Then, they provide a FPTAS for solving the problem using dynamic programming. Once they have a FPTAS for the offline problem, their results hold for the stochastic online setting using existing reductions. I haven't carefully looked in to the details of their analysis of the dynamic programming, but I think the effectiveness of it here is interesting and surprising -- specially given that the variation of this problem for the second price auctions is hard to approximate.

The paper concerns online linear optimization where at each trial, the player, prior to prediction, receives a hint about the loss function. The hint has a form of a unit vector which is weakly correlated with the loss vector (its angle's cosine with loss vector is at least alpha). The paper shows that: - When the set of feasible actions is strongly convex, there exists an algorithm which gets logarithmic regret (in T). The algorithm is obtained by a reduction to the online learning problem with exp-concave losses. The bound is unimprovable in general, as shown in the Lower Bounds section.

A) My main concern with this paper is with respect to the main results (Theorems 2 and 3). It seems the authors have not put sufficient care to the fact that \partial \hat{Q} in Algorithm 2 is a biased estimator of the true gradient \partial Q. Also, \hat{Q} defined in Line 189 depends on \hat{\pi} which is an estimate of \pi. Thus, a probabilistic proof would require to look at a conditional probability of the estimation of Q depending on the estimation of \pi. B) Regardless of the above, the final high probability statement in Theorems 2 and 3, seem to be missing the union bound of the error probability in Assumption 1.

This can be done in a batch or in an online fashion from the data. The authors provide an online approach for doing this and prove that it can achieve a regret O(1/sqrt(T)) as a function of data size T. 1. I believe the paper is not written very well. For example, the underlying idea of inverse optimization is not clearly explained as in main references such as [1]. Moreover, the problem has been posed in a quite general setup but at the end the authors have focused on the convex and strongly convex setup where they have used the result already in the literature with some minor modifications.

This paper studies online convex optimization in dynamic environments, where one wishes to control the regret with respect to sequences of comparators, as opposed to a static comparator. The complexity of a comparator sequence is measured by its path length P_T, and the goal is to obtain an optimal regret bound simultaneously for all path lengths. A first bound in this setting was established in the pioneering paper [1], which showed that online gradient descent (OGD, projected on the convex compact domain) with step-size 1/sqrt(T) achieves an at most T {1/2} (1 P_T) regret for all comparator sequences. However, there is a gap between this upper bound and the (T (1 P_T)) {1/2} lower bound on worst-case regret established in Theorem 2 of the present paper, which is the first lower bound for this problem. On the other hand, if the path length P_T one wishes to compare against is known in advance, optimally tuning the step-size of OGD with respect to P_T in the OGD regret bound yields optimal (T (1 P_T)) {1/2} regret for this path length.