R1, R2, R3, R4: We thank the reviewers for the numerous positive comments. R4: ''The proposed tool can have a1 good impact on the community and help standardize several experiments with synthetic data. I was impressed2 by the versatility of the framework". R3: "The task of constructing harder and non-fixed datasets for training3 and evaluation is of great practical important.". R1: "There is a paradigm shift happening from datasets to4 dataset generators (e.g.

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We thank the reviewers for their encouraging and constructive comments. We are pleased that they find the paper well1 written and acknowledge the novelty and originality of the proposed task, which "has a potential to spark interest"2 (R1) and "may lead to future papers studying it" (R2). Regarding the proposed framework, R1 and R2 not only find it3 "sound" and "novel" but also stress the "re-implementation ease" from which "practitioners may benefit" (R1). Still,4 the reviewers raise points of improvement (R1, R3) and suggest a discussion about a related task (R2). We carefully5 address these comments below.

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Let f be a non-negative submodular function on [n] that is bounded above by 1. First, suppose that Xi are monotone increasing. Construct a sequence X0i as follows. If i / I then set X0i = X0i 1. If i I then set X0i = X0i 1 (Xi \Xi 1). For the monotone decreasing case, consider the submodular function g(X) = f([n] X) and set Yi = [n] Xi.

We consider the problem of nonnegative submodular maximization in the online setting. At time step t, an algorithm selects a set St C 2V where C is a feasible family of sets. An adversary then reveals a submodular function ft. The goal is to design an efficient algorithm for minimizing the expected approximate regret. In this work, we give a general approach for improving regret bounds in online submodular maximization by exploiting "first-order" regret bounds for online linear optimization. For monotone submodular maximization subject to a matroid, we give an efficient algorithm which achieves a (1 c/e ε)-regret of O( p kTln(n/k)) where n is the size of the ground set, k is the rank of the matroid, ε > 0 is a constant, and cis the average curvature. Even without assuming any curvature (i.e., taking c = 1), this regret bound improves on previous results of Streeter et al. (2009) and Golovin et al. (2014). For nonmonotone, unconstrained submodular functions, we give an algorithm with 1/2-regret O( nT), improving on the results of Roughgarden and Wang (2018). Our approach is based on Blackwell approachability; in particular, we give a novel first-order regret bound for the Blackwell instances that arise in this setting.