The analysis of the algorithm is conducted under two models: stochastic inputs (columns of LP drawn i.i.d.) and random permutation model (columns of LP revealed in a random order). The authors develop a simple and fast online algorithm performing stochastic subgradient descent on a dual problem with provable guarantees on the regret and constraint violation. The paper received borderline reviews with a slight lean towards acceptance. The main strengths of the paper are: - New techniques for deriving the regret bounds in the random permutation model (permutational Rademacher complexity). The main weaknesses were: - Insufficient comparison with the existing online LP literature, in particular with the competitive ratio bounds of previous work.

Applying ALM to the Burer-Monterio problem and to nonlinear programs in general is natural and well summarized in the monograph Ref [8]. Allowing first-order and second-order approximate solvers for the primal subproblems is also classic, and can be found in, e.g., Ch 8 & 9 of Ref [8]. I think the main novelties here lie at the nonsmooth, convex term g(x) and the convergence rate results. Sec 5 of the paper has provided a comprehensive review of pertinent results under different assumptions. I have several concerns that I hope the authors can address: * The BM example does not quite justify the inclusion of the possibly nonsmooth term g in (1). The authors may want to balance out and briefly discuss other examples as appearing in the experiments.

This paper uses the Augmented Lagrangian method to solve optimization problems for a sum of functions f and g, where f is nonconvex and g is convex but'proximal-friendly' subject to quite general nonlinear constraints. The proposed method solves the primal problem within some error epsilon_k that is gradually decreased as a penalty schedule beta_k is increasing across iterations. The approximate intermediate problems are solved using first order and second order solvers. The proposed analysis is technically non-trivial and interesting. The presentation of the paper was poor and at times confusing which made this a borderline paper.

Weaknesses: From the results, it seems that separate models are trained for each of the systems, but within each system, there is not that much procedural generation in the structure/relative distances of the system particles, just on the initial positions/velocities. Do you expect this to work in cases where there is more procedural variation in the relative positioning of the points (e.g. if sometimes the rigid it is a square, sometimes an arbitrary trapezoid). I guess this could work if you added another input to C with the previous state, or with some reference distances, but it does not seem it would work on the current form of the model, since it would be impossible for the C function to tell whether the constraints are being satisfied or not, just by looking at the position of the points, since it does not know if the constraints to be satisfied should be that of a square or that of a specific trapezoid. Similarly, I wonder how much of the context of the other particles the model is relying on to infer how systems should collide against a wall. For example, if we were making predictions for a system with a single particle that in a single timestep would bounce elastically of a wall, I wonder if the system would always put the particle right at the wall (the linear prediction would move it past the wall, and the constraint satisfaction would put it back right at the wall, where the constraint is satisfied with minimal displacement, but would not make it bounce back off the wall. Then in the next step the linear extrapolation, would essentially do the same thing once more, and then beyond that the particle would become permanently stuck at the wall once two consecutive positions place it at the wall).

This paper formalizes the problem of inverse reinforcement learning in which the learner's goal is not only to imitate the teacher's demonstration, but also to satisfy her own preferences and constraints. It analyzes the suboptimality of learner-agnostic teaching, where the teacher gives demonstrations without considering the learner's preferences. It then proposes a learner-aware teaching algorithm, where the teacher selects demonstrations while accounting for the learner's preferences. It considers different types of learner models with hard or soft preference constraints. It also develops learner-aware teaching methods for both cases where the teacher has full knowledge of the learner's constraints or does not know it.

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary Attracted Re-solve Method for full information, an online learning algorithm for scenarios with no prior information, and an estimate-then-select re-solve algorithm that leverages machine-learned informed prices with known upper bound of estimation errors. The Boundary Attracted Re-solve Method achieves logarithmic regret without requiring the non-degeneracy condition, while the online learning algorithm attains an optimal $O(\sqrt{T})$ regret. Our estimate-then-select approach bridges the gap between these settings, providing improved regret bounds when reliable offline data is available. Numerical experiments validate the effectiveness and robustness of our algorithms across various scenarios. This work advances the understanding of online resource allocation and dynamic pricing, offering practical solutions adaptable to different informational structures.

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster inference through parallelism, they typically deliver solutions of inferior quality compared to autoregressive ones. To enhance the solution quality while maintaining fast inference, we propose DEITSP, a diffusion model with efficient iterations tailored for TSP that operates in a NAR manner. Firstly, we introduce a one-step diffusion model that integrates the controlled discrete noise addition process with self-consistency enhancement, enabling optimal solution prediction through simultaneous denoising of multiple solutions. Secondly, we design a dual-modality graph transformer to bolster the extraction and fusion of features from node and edge modalities, while further accelerating the inference with fewer layers. Thirdly, we develop an efficient iterative strategy that alternates between adding and removing noise to improve exploration compared to previous diffusion methods. Additionally, we devise a scheduling framework to progressively refine the solution space by adjusting noise levels, facilitating a smooth search for optimal solutions. Extensive experiments on real-world and large-scale TSP instances demonstrate that DEITSP performs favorably against existing neural approaches in terms of solution quality, inference latency, and generalization ability. Our code is available at $\href{https://github.com/DEITSP/DEITSP}{https://github.com/DEITSP/DEITSP}$.

Distributed Constraint Optimization Problems (DCOPs) offer a powerful framework for multi-agent coordination but often rely on labor-intensive, manual problem construction. To address this, we introduce VL-DCOPs, a framework that takes advantage of large multimodal foundation models (LFMs) to automatically generate constraints from both visual and linguistic instructions. We then introduce a spectrum of agent archetypes for solving VL-DCOPs: from a neuro-symbolic agent that delegates some of the algorithmic decisions to an LFM, to a fully neural agent that depends entirely on an LFM for coordination. We evaluate these agent archetypes using state-of-the-art LLMs (large language models) and VLMs (vision language models) on three novel VL-DCOP tasks and compare their respective advantages and drawbacks. Lastly, we discuss how this work extends to broader frontier challenges in the DCOP literature.

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a significant challenge arises when applying GNNs to ILPs with symmetry: classic GNN architectures struggle to differentiate between symmetric variables, which limits their predictive accuracy. In this work, we investigate the properties of permutation equivariance and invariance in GNNs, particularly in relation to the inherent symmetry of ILP formulations. We reveal that the interaction between these two factors contributes to the difficulty of distinguishing between symmetric variables. To address this challenge, we explore the potential of feature augmentation and propose several guiding principles for constructing augmented features. Building on these principles, we develop an orbit-based augmentation scheme that first groups symmetric variables and then samples augmented features for each group from a discrete uniform distribution. Empirical results demonstrate that our proposed approach significantly enhances both training efficiency and predictive performance. Integer Linear Programs (ILPs) are fundamental optimization problems characterized by a linear objective function and linear constraints, where the decision variables are restricted to integer values. These problems play a critical role in various fields, including operations research, computer science, and engineering (Pochet & Wolsey, 2006; Liu & Fan, 2018; Watson & Woodruff, 2011; Luathep et al., 2011; Schöbel, 2001).

Additional Feedback: Do you have any comments on how your hard shape constraint formulation affects overlapping quantiles versus the soft constraint (PDCD)? It would be more informative to display Figure 1 alongside plots from alternative methods. Is it reasonable to attribute the comments on l304 regarding non-crossing to the additional regularizing properties of the concavity constraint? Regarding Table 1, it seems SOC performs _worse_ than PDCD on 5/9 datasets. This opens the question of when and where are hard constraints more beneficial over soft constraints.