All reviewers agreed that this paper makes an interesting contribution to NeurIPS. Please make sure to take the reviewers' comments in consideration for the camera-ready version, in particular improving the clarity of the presentation and making the overall statements more precise.

Summary and Contributions: Contribution: The paper gives a new deterministic algorithm for maximizing a non-monotone submodular function subject to a matroid constraint. The algorithm achieves a 1/4 approximation and it has a running time of O(n r), where n is the size of the ground set and r is the rank of the matroid. Using known techniques, one can speed up the algorithm to nearly-linear at a small loss in the approximation. Comparison to previous work: Previously, there were two main approaches for obtaining deterministic algorithms for the problem. The first approach, due to Lee et al., uses local search and it obtains a 1/4 - eps approximation but the running time is a much larger polynomial (at least n 4).

Supervised classification techniques use training samples to find classification rules with small expected 0-1 loss. Conventional methods achieve efficient learning and out-of-sample generalization by minimizing surrogate losses over specific families of rules. This paper presents minimax risk classifiers (MRCs) that do not rely on a choice of surrogate loss and family of rules. MRCs achieve efficient learning and out-of-sample generalization by minimizing worst-case expected 0-1 loss w.r.t. In addition, MRCs' learning stage provides performance guarantees as lower and upper tight bounds for expected 0-1 loss.

The proliferation of web agents necessitates advanced navigation and interaction strategies within complex web environments. Current models often struggle with efficient navigation and action execution due to limited visibility and understanding of web structures. Our proposed R2D2 framework addresses these challenges by integrating two paradigms: Remember and Reflect. The Remember paradigm utilizes a replay buffer that aids agents in reconstructing the web environment dynamically, thus enabling the formulation of a detailed ``map'' of previously visited pages. This helps in reducing navigational errors and optimizing the decision-making process during web interactions. Conversely, the Reflect paradigm allows agents to learn from past mistakes by providing a mechanism for error analysis and strategy refinement, enhancing overall task performance. We evaluate R2D2 using the WEBARENA benchmark, demonstrating significant improvements over existing methods, including a 50% reduction in navigation errors and a threefold increase in task completion rates. Our findings suggest that a combination of memory-enhanced navigation and reflective learning promisingly advances the capabilities of web agents, potentially benefiting various applications such as automated customer service and personal digital assistants.

Testing and evaluation is an important step before the large-scale application of the autonomous driving systems (ADSs). Based on the three level of scenario abstraction theory, a testing can be performed within a logical scenario, followed by an evaluation stage which is inputted with the testing results of each concrete scenario generated from the logical parameter space. During the above process, abundant testing information is produced which is beneficial for comprehensive and accurate evaluations. To make full use of testing information, this paper proposes an Integrated accelerated Testing and Evaluation Method (ITEM). Based on a Monte Carlo Tree Search (MCTS) paradigm and a dual surrogates testing framework proposed in our previous work, this paper applies the intermediate information (i.e., the tree structure, including the affiliation of each historical sampled point with the subspaces and the parent-child relationship between subspaces) generated during the testing stage into the evaluation stage to achieve accurate hazardous domain identification. Moreover, to better serve this purpose, the UCB calculation method is improved to allow the search algorithm to focus more on the hazardous domain boundaries. Further, a stopping condition is constructed based on the convergence of the search algorithm. Ablation and comparative experiments are then conducted to verify the effectiveness of the improvements and the superiority of the proposed method. The experimental results show that ITEM could well identify the hazardous domains in both low- and high-dimensional cases, regardless of the shape of the hazardous domains, indicating its generality and potential for the safety evaluation of ADSs.

Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally tackled by humans through visual representations that harness our innate ability for spatial reasoning. In this study, we propose transforming graphs into images to preserve their higher-order structural features accurately, revolutionizing the representation used in solving graph-structured combinatorial tasks. This approach allows machines to emulate human-like processing in addressing complex combinatorial challenges. By combining the innovative paradigm powered by multimodal large language models (MLLMs) with simple search techniques, we aim to develop a novel and effective framework for tackling such problems. Our investigation into MLLMs spanned a variety of graph-based tasks, from combinatorial problems like influence maximization to sequential decision-making in network dismantling, as well as addressing six fundamental graph-related issues. Our findings demonstrate that MLLMs exhibit exceptional spatial intelligence and a distinctive capability for handling these problems, significantly advancing the potential for machines to comprehend and analyze graph-structured data with a depth and intuition akin to human cognition. These results also imply that integrating MLLMs with simple optimization strategies could form a novel and efficient approach for navigating graph-structured combinatorial challenges without complex derivations, computationally demanding training and fine-tuning.

Existing approaches to enforcing design constraints in Reinforcement Learning (RL) applications often rely on training-time penalties in the reward function or training/inference-time invalid action masking, but these methods either cannot be modified after training, or are limited in the types of constraints that can be implemented. To address this limitation, we propose Reinforcement Learning Constrained Beam Search (RLCBS) for inference-time refinement in combinatorial optimization problems. This method respects flexible, inference-time constraints that support exclusion of invalid actions and forced inclusion of desired actions, and employs beam search to maximize sequence probability for more sensible constraint incorporation. RLCBS is extensible to RL-based planning and optimization problems that do not require real-time solution, and we apply the method to optimize process parameters for a novel modular testbed for paper drying. An RL agent is trained to minimize energy consumption across varying machine speed levels by generating optimal dryer module and air supply temperature configurations. Our results demonstrate that RLCBS outperforms NSGA-II under complex design constraints on drying module configurations at inference-time, while providing a 2.58-fold or higher speed improvement.

While I would certainly agree with the claim that developing local minimax bounds is of interest, I feel that the interest of considering risks for 2-point subproblems is unclear. Note that many (probably, a majority of) known bounds in convex stochastic optimization are obtained on 2-point subproblems (see, e.g. In other words, the minimax risks (up to an absolute factor) for general classes of convex problems are attained already on the hardest 2-point subproblems (1-parametric families), so that, in the paper notation, R_T(\cal F)\sim \sup_{f\in \cal F} R_T(f, \cal F) On the other hand, it is unclear for me if the notion of R_T(f, \cal F) is of interest for its own sake (not as just a technical tool to construct a more general lower bound). For instance, it is not clear why and when the "2-point risk" R_T(f, \cal F) is an adequate measure of local complexity. Note that this is generally not the case in nonparametric estimation (except for few situations such as the case of linear functional estimation in [4-6]).

This is a nice result. I am going to list a few nits I had about the paper as I read along. I think addressing some of these points would improve the presentation of the paper. There are a few cases which are not covered by the results. For instance, strict-saddle in noisy case local min are close to global in high rank, noisy case. A discussion about why these cases are not covered would be nice; I am assuming that it is not just straightforward modification of the current proof? 2. In practice, I believe that random init gradient descent without noise is sufficient.

The technical results appear to be correct and the experimental results (which I think are quite preliminary) suggest the minimax SVM might be a good idea. I think the idea of robust Bayes decision rules makes sense and the authors show how under squared loss a connection to the Huber loss emerges. My main comment is that the paper itself is a somewhat difficult read due to terseness at key places, which might limit the impact of the paper. So, the rest of my comments are just geared towards improving the clarity of the paper. Technically, in every instance where the authors apply Danskin's theorem, it was not really clear what form of Danskin's theorem was being used, and therefore it was difficult to follow the derivation.