The paper proposes a new inference task for graphical models. It consists in finding a MAP assignment w.r.t. It contains as special cases several interesting graphical model problems like m-best assigments. The method uses a transformation to multiple choice knapsack for cmputationally solving the problem. Authors agree that the new problem is interesting and the transformation to multiple choice knapsack is interesting. The main criticism pertains to the small experiments that are not necessarily indicative of real-world problems.

The paper formulates the problem of optimizing a strategy for crawling remote contents to track their changes as an optimization problem called the freshness crawl scheduling problem. This problem is an obviously important problem in applications like Internet search engine, and the presented formulation seems to give a practical solution to those applications. The paper presents an algorithm for solving the freshness crawl scheduling problem to optimality, assuming that the contents change rates are known. The idea behind the algorithm is based on the deep understanding of statistics and continuous optimization, and it seems to me that the contribution is solid (although I could not very all the technical details). For the case where the contents change rates are not known, a reinforcement learning algorithm is presented.

Summary: This paper proposes a method for multi-objective Bayesian optimization when a user has given "preference order constraints", i.e. preferences about the importance of different objectives. For example, a user might specify that he or she wants to determine where, along the pareto front, a given objective varies significantly with respect to other objectives (which the authors term "diversity") or when the objective is static with respect to other objectives (which they term "stability"). The authors give algorithms for this setting and show empirical results on synthetic functions and on a model search task. Comments: My main criticism of this paper is that I am not convinced about the motivation for, and uses cases of, the described task of finding regions of the pareto front where an objective is "diverse" or "stable" as they are defined in the paper. There are two potential examples given in the introduction, but these are brief and unconvincing (another comment on these below). A real experiment is shown on a neural network model search task, but it is unclear how the method, when applied here, provides real benefits over other multi-objective optimization methods.

Summary and Contributions: Update after reading the author rebuttal: I'd like to thank the authors for their detailed rebuttal. I appreciate that they aim to expand the experimental section and related work, and simplify the notation and descriptions where possible. I certainly think these changes can make the paper even more accessible and hope that the authors will also incorporate the other suggestions made to improve the manuscript. With regards to the runtime shown in Figure 7, I am still not convinced this is "almost linear": connecting the mean of the boxplots does not seem to give a linear relationship, but more likely a quadratic one. I'd recommend the authors fit a polynomial to this data and work out whether it is linear or quadratic in the number of samples.

This paper describes a method for estimating the p-values associated with the change points detected through optimal partitioning. The reviewers were unanimous in their vote to accept. Someone stated that it was a "great read and a great method" and wants to use their code.

We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate data-dependent constraints so that they are calibrated: enforcing the reformulated constraints guarantees that their expected value counterparts are satisfied with a user-prescribed probability. The resulting optimization problem is amendable to standard stochastic optimization algorithms, and we demonstrate the efficacy of our method on a fairness-sensitive classification task where we wish to guarantee the classifier's fairness (at test time).

Summary and Contributions: In this paper, the authors study the stochastic optimization algorithm for variational inference. In particular, the authors argue that existing methods stochastic optimization techniques for variational inference are fragile with respect to the hyperparameters of the optimization algorithm. Mainly, authors argue that the standard stopping rule for a stochastic optimization for variational inference is insufficient. The authors view the SGD algorithm with ELBO objective as a Markov chain with a stationary distribution centered around the true variational posterior. The main contribution of this paper are: a) to use iterate averaging to determine the parameter of the variational posterior.

I have read the rebuttal and I believe the authors have satisfactorily addressed my comments on prior work, so I have increased my rating. The SDE approximation method is well-established. Moreover, Minibatch SGD's continuous approximation has been considered by several prior works, e.g. Summary and review comments: The paper is well-written and one of its strengths in generally good comparison with prior work. The main theoretical results are: * SDE approximation for minibatch SGD and SVRG * Well-posedness of the SDEs * Matching convergence bounds using Lyapunov functions * Interpreting time-dependent adjustments as time-change and landscape-stretching.

Scientific optimization problems are usually concerned with balancing multiple competing objectives, which come as preferences over both the outcomes of an experiment (e.g. maximize the reaction yield) and the corresponding input parameters (e.g. minimize the use of an expensive reagent). Typically, practical and economic considerations define a hierarchy over these objectives, which must be reflected in algorithms for sample-efficient experiment planning. Herein, we introduce BoTier, a composite objective that can flexibly represent a hierarchy of preferences over both experiment outcomes and input parameters. We provide systematic benchmarks on synthetic and real-life surfaces, demonstrating the robust applicability of BoTier across a number of use cases. Importantly, BoTier is implemented in an auto-differentiable fashion, enabling seamless integration with the BoTorch library, thereby facilitating adoption by the scientific community.

Inverse Constraint Learning (ICL) is the problem of inferring constraints from safe (i.e., constraint-satisfying) demonstrations. The hope is that these inferred constraints can then be used downstream to search for safe policies for new tasks and, potentially, under different dynamics. Our paper explores the question of what mathematical entity ICL recovers. Somewhat surprisingly, we show that both in theory and in practice, ICL recovers the set of states where failure is inevitable, rather than the set of states where failure has already happened. In the language of safe control, this means we recover a backwards reachable tube (BRT) rather than a failure set . In contrast to the failure set, the BRT depends on the dynamics of the data collection system. We discuss the implications of the dynamics-conditionedness of the recovered constraint on both the sample-efficiency of policy search and the transferability of learned constraints.