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.

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.