First-price auctions have recently gained significant traction in digital advertising markets, exemplified by Google's transition from second-price to first-price auctions. Unlike in second-price auctions, where bidding one's private valuation is a dominant strategy, determining an optimal bidding strategy in first-price auctions is more complex. From a learning perspective, the learner (a specific bidder) can interact with the environment (other bidders) sequentially to infer their behaviors. Existing research often assumes specific environmental conditions and benchmarks performance against the best fixed policy (static benchmark). While this approach ensures strong learning guarantees, the static benchmark can deviate significantly from the optimal strategy in environments with even mild non-stationarity. To address such scenarios, a dynamic benchmark, which represents the sum of the best possible rewards at each time step, offers a more suitable objective. However, achieving no-regret learning with respect to the dynamic benchmark requires additional constraints. By inspecting reward functions in online first-price auctions, we introduce two metrics to quantify the regularity of the bidding sequence, which serve as measures of non-stationarity. We provide a minimax-optimal characterization of the dynamic regret when either of these metrics is sub-linear in the time horizon.

The problem is relevant and the method is based on an interesting attention based idea to look at different regions in the image for the task of ZSL The losses used focus on (i) making each attention map peaky, while making different maps diverse, (ii) embedding based softmax for better prediction and (iii) class center triplet loss which makes the features closer to their respective class centers relative to the other class centers. Line 190 mentions that the image and parts are sent to "separate backbone networks", which implies that the network parameters are not shared. If that is the case then the method will have 3x parameters cf competing methods ie. a significantly higher capacity network overall. What happens when the CNN params are shared? And what happens when the image only baseline has a higher capacity network backbone (which is also then end-to-end finetuned)?

This paper derives a novel algorithm for solving the dual DRLR problem when \kappa \infty (i.e. the labels may change during transport). The algorithm performs a golden section search for \lambda, within which the sub-problem for optimal \beta, fixing \lambda, is solved by an ADMM algorithm. The ADMM algorithm differs from typical ADMM approaches in two ways: (1) the \beta-update is ill-conditioned, requiring a careful choice of iterative method, while (2) the auxiliary \mu update is locally strongly convex, enabling the use of a first-order (not quadratic) approximation with a fixed step size. I see three theoretical contributions: 1. An upper bound on optimal \lambda, stated in Proposition 1, which enables the golden section search.

The paper proposes to solve the Wasserstein distributionally robust logistic regression problem by using an ADMM-style algorithm. All reviewers and myself find it interesting and can have practical and theoretical impacts.

Strengths: Preface I understand that reviews that claim that a method is not sufficiently novel or significant are often subjective and are difficult for authors to rebut. To make my review easier to engage with, I'm offering the following criteria along which I assess "significance" of a paper: (*i*) Does the paper offer a novel, non-obvious theoretical insight in the form of a proof or derivation? I will touch on these three criteria in my comments below and mark my comment accordingly. Relevance Bayesian inference applied to a variety of problems is an active area of research and the paper under review proposes a novel algorithm for fast convergence to a posterior distribution in Bayesian inference problems. While the proposed method is still limited in the parameter dimension, it improves on related methods and makes stein variational gradient descent more practically relevant.

Leveraging low-dimensional structure in approximate inference algorithms is an interesting area of study, and this adaptation of SVGD is a promising approach. There were concerns about lack of clarity and presentation of the algorithm, as well as theoretical justification and motivation of this procedure.

Response to rebuttal: I think the author responses were done well. I think they have satisfactorily answered the questions that I had raised. The reason I am torn between a strong accept and an accept is: most of the techniques used in this paper have already appeared before in various quantum algorithms and are well-known in the quantum community. Having said that, I think putting together known techniques in a rigorous fashion and also practically implementing their algorithm on a quantum simulator is interesting, especially to a problem which is practically important. I think the final aspect might be of interest to a classical ML community; to see how quantum can provide polynomial speedups to relevant ML problems using a toolbag of interesting techniques.

This paper is about employing advances in computational efficiency of mixed integer programming methods towards decision tree construction problems. While locally optimal methods can achieve an upper bound on the minimization problem efficiently, closing the optimality gap requires tight lower bounds. The authors use an interval relaxation and a support-vector machine procedure to tighten the lower bound. To scale the algorithm, the authors use a LP-based data selection procedure, and perform all experiments using this procedure. It is not clear whether the global optimality properties of the MIP formulation carry through with the data-selection procedure.

Response to authors' feedback: I thank the authors for the rebuttal. My score remains the same. With this initialization, the networks are shown to converge linearly to zero loss, under conditions (for discrete-time GD) that are different from and perhaps conceptually simpler than previous works. For instance, compared to reference [2] (Arora et al "A convergence analysis of gradient descent for deep linear neural networks", ICLR 2019), this work removes completely the delta-balanced condition in [2] by showing that this condition actually holds, for most layers, on the GD trajectory (Lemma 4.2 and Eq. While certain elements have already been seen in previous works (e.g. the property in Lemma 4.2 is similar to the delta-balanced condition in [2], or the requirement of zero initialization for the last layer's weight has been seen in "fixup initialization" of reference [21] in the context of residual networks), I think the proposed initialization as well as the convergence analysis here deserve credits for novelty.

The reviewers appreciated the work on the initialization even if they deemed it incremental. The experiments on the nonlinear network in the rebuttal was useful and I encourage the authors to expand the experimental section using more realistic setups to show how the theory matters in practice.