This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex optimization-based solvers often struggle to efficiently handle these problems in their most general form. While neural network (NN)-based approaches offer a promising alternative, ensuring the feasibility of NN-generated solutions and effectively training the NN remain key hurdles, largely because finite-capacity networks can produce infeasible outputs. To overcome these issues, we propose a projection-based method that projects any infeasible NN output onto the feasible domain, thus guaranteeing strict adherence to the constraints without compromising the NN's optimization capability. Furthermore, we derive the objective function values for both the raw NN outputs and their projected counterparts, along with the gradients of these values with respect to the NN parameters. This derivation enables label-free (unsupervised) training, reducing reliance on labeled data and improving scalability. Experimental results demonstrate that the proposed projection-based method consistently ensures feasibility.

We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints. In this problem, after selecting a feasible action from the convex decision set $X,$ a convex constraint function is revealed alongside the cost function in each round. Our goal is to design a computationally efficient learning policy that achieves a small regret with respect to the cost functions and a small cumulative constraint violation (CCV) with respect to the constraint functions over a horizon of length $T$. It is well-known that the projection step constitutes the major computational bottleneck of the standard OCO algorithms. However, for many structured decision sets, linear functions can be efficiently optimized over the decision set. We propose a *projection-free* online policy which makes a single call to a Linear Program (LP) solver per round. Our method outperforms state-of-the-art projection-free online algorithms with adversarial constraints, achieving improved bounds of $\tilde{O}(T^{\frac{3}{4}})$ for both regret and CCV. The proposed algorithm is conceptually simple - it first constructs a surrogate cost function as a non-negative linear combination of the cost and constraint functions. Then, it passes the surrogate costs to a new, adaptive version of the online conditional gradient subroutine, which we propose in this paper.

Summary ------- The authors address a major drawback of constraint-based causal structure learning algorithms (PC algorithm and derivatives), namely, that for finite sample sizes the outputted graphs may be inconsistent regarding separating sets: The final graph may imply different separating sets than those identified in the algorithm. This implies in particular that outputted graphs are not guarenteed to belong to their presumed class of graphical models, for example CPDAGs or PAGs. The main reason is that PC-based methods remove too many true links in the skeleton phase. The authors' solution is based on an iterative application of a modified version of PC until the final graph is consistent with the separating sets. They prove that their solution fixes the problem and demonstrate these improvements with numerical experiments.

Summary and Contributions: The paper considers the problem of maximizing a general monotone DR-submodular function subject to a general convex constraint (general up to some natural assumptions) in the online regret-minimization setting. The paper presents two algorithms for this problem, and proves bounds on their regret (with respect to the 1-1/e offline approximation) as well as the extent to which they violate the constraint on average. In that respect, the paper considers three kinds of regrets: - The traditional adversarial static regret in which the input is selected by an adversary and the algorithm competes with the best single solution in hindsight. For some of these benchmarks there are previous results for the special case in which the constraints are linear. The current paper improves over them both in terms of the generality of the constraint, and in terms of the quality of the guarantees.

The paper converts the constrained optimization problem to min-max optimization using Lagrangian function. To show the efficacy of the model, three experiments are conducted in 5.1 SRL, 5.2 NER and 5.3 Fine grained entity typing. The paper brings in a structured way of training with output constraints. However, I am not sure how much gain this model has on top of fixed weight on constraints (Metha et al 2018 & Diligenti et al 2017) with the provided experiments. Also while the experiments seem convincing as itself, it is hard to see how much significance this work brings in as the baselines significantly differ with related work. Also, it would give a better picture of this method if the paper could provide more analysis: an analysis on convergence, an analysis on experiment results on why more labeled data sometimes hurt, etc. [originality ] 1. The full Lagrangian expression and linking the output constraint to the model parameter and optimizing them with subgradient seems novel. However, how exactly the authors formulate f(w) is unclear to me. Is it just following the way Diligenti 2017 does it?

Municipal inspections are an important part of maintaining the quality of goods and services. In this paper, we approach the problem of intelligently scheduling service inspections to maximize their impact, using the case of food establishment inspections in Chicago as a case study. The Chicago Department of Public Health (CDPH) inspects thousands of establishments each year, with a substantial fail rate (over 3,000 failed inspection reports in 2023). To balance the objectives of ensuring adherence to guidelines, minimizing disruption to establishments, and minimizing inspection costs, CDPH assigns each establishment an inspection window every year and guarantees that they will be inspected exactly once during that window. These constraints create a challenge for a restless multi-armed bandit (RMAB) approach, for which there are no existing methods. We develop an extension to Whittle index-based systems for RMABs that can guarantee action window constraints and frequencies, and furthermore can be leveraged to optimize action window assignments themselves. Briefly, we combine MDP reformulation and integer programming-based lookahead to maximize the impact of inspections subject to constraints. A neural network-based supervised learning model is developed to model state transitions of real Chicago establishments using public CDPH inspection records, which demonstrates 10\% AUC improvements compared with directly predicting establishments' failures. Our experiments not only show up to 24\% (in simulation) or 33\% (on real data) reward improvements resulting from our approach but also give insight into the impact of scheduling constraints.

This work investigates data-driven prediction and control of Hammerstein-Wiener systems using physics-informed Gaussian process models. Data-driven prediction algorithms have been developed for structured nonlinear systems based on Willems' fundamental lemma. However, existing frameworks cannot treat output nonlinearities and require a dictionary of basis functions for Hammerstein systems. In this work, an implicit predictor structure is considered, leveraging the multi-step-ahead ARX structure for the linear part of the model. This implicit function is learned by Gaussian process regression with kernel functions designed from Gaussian process priors for the nonlinearities. The linear model parameters are estimated as hyperparameters by assuming a stable spline hyperprior. The implicit Gaussian process model provides explicit output prediction by optimizing selected optimality criteria. The model is also applied to receding horizon control with the expected control cost and chance constraint satisfaction guarantee. Numerical results demonstrate that the proposed prediction and control algorithms are superior to black-box Gaussian process models.

We investigate constrained online convex optimization, in which decisions must belong to a fixed and typically complicated domain, and are required to approximately satisfy additional time-varying constraints over the long term. In this setting, the commonly used projection operations are often computationally expensive or even intractable. To avoid the time-consuming operation, several projection-free methods have been proposed with an $\mathcal{O}(T^{3/4} \sqrt{\log T})$ regret bound and an $\mathcal{O}(T^{7/8})$ cumulative constraint violation (CCV) bound for general convex losses. In this paper, we improve this result and further establish \textit{novel} regret and CCV bounds when loss functions are strongly convex. The primary idea is to first construct a composite surrogate loss, involving the original loss and constraint functions, by utilizing the Lyapunov-based technique. Then, we propose a parameter-free variant of the classical projection-free method, namely online Frank-Wolfe (OFW), and run this new extension over the online-generated surrogate loss. Theoretically, for general convex losses, we achieve an $\mathcal{O}(T^{3/4})$ regret bound and an $\mathcal{O}(T^{3/4} \log T)$ CCV bound, both of which are order-wise tighter than existing results. For strongly convex losses, we establish new guarantees of an $\mathcal{O}(T^{2/3})$ regret bound and an $\mathcal{O}(T^{5/6})$ CCV bound. Moreover, we also extend our methods to a more challenging setting with bandit feedback, obtaining similar theoretical findings. Empirically, experiments on real-world datasets have demonstrated the effectiveness of our methods.

Virtually all verification techniques using formal methods rely on the availability of a formal specification, which describes the design requirements precisely. However, formulating specifications remains a manual task that is notoriously challenging and error-prone. To address this bottleneck in formal verification, recent research has thus focussed on automatically generating specifications for formal verification from examples of (desired and undesired) system behavior. In this survey, we list and compare recent advances in mining specifications in Linear Temporal Logic (LTL), the de facto standard specification language for reactive systems. Several approaches have been designed for learning LTL formulas, which address different aspects and settings of specification design. Moreover, the approaches rely on a diverse range of techniques such as constraint solving, neural network training, enumerative search, etc. We survey the current state-of-the-art techniques and compare them for the convenience of the formal methods practitioners.

Additional Feedback: Post-response update: The author response adressed my concerns very well, and the paper is good enough to be accepted, despite the lacking novelty. I am increasing my score to 7. ---- The paper proposes a new more general formalism to handle output constraints in BNNs. The space of constrained neural networks is already crowded, and while section 2 does make a good overview of the differences, it would greatly improve the paper to also define mathematically the differences in competing constraining methods and their scopes. Overall I had hard time understanding the contraint definitions (see below for minor comments). The constraint formalism needs to be explicated better. I could not follow the math anymore.