An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear and/or nonconvex, and when constraint values and derivatives are tractable to compute, but objective function values and derivatives can only be estimated. The algorithm is intended primarily for a setting that is similar for stochastic-gradient methods for unconstrained optimization, namely, the setting when stochastic-gradient estimates are available and employed in place of gradients of the objective, and when no objective function values (nor estimates of them) are employed. This is achieved by the interior-point framework having a single-loop structure rather than the nested-loop structure that is typical of contemporary interior-point methods. For completeness, convergence guarantees for the framework are provided both for deterministic and stochastic settings. Numerical experiments show that the algorithm yields good performance on a large set of test problems.

Tree ensembles, including boosting methods, are highly effective and widely used for tabular data. However, large ensembles lack interpretability and require longer inference times. We introduce a method to prune a tree ensemble into a reduced version that is "functionally identical" to the original model. In other words, our method guarantees that the prediction function stays unchanged for any possible input. As a consequence, this pruning algorithm is lossless for any aggregated metric. We formalize the problem of functionally identical pruning on ensembles, introduce an exact optimization model, and provide a fast yet highly effective method to prune large ensembles. Our algorithm iteratively prunes considering a finite set of points, which is incrementally augmented using an adversarial model. In multiple computational experiments, we show that our approach is a "free lunch", significantly reducing the ensemble size without altering the model's behavior. Thus, we can preserve state-of-the-art performance at a fraction of the original model's size.

Humans can exploit contacts anywhere on their body surface to manipulate large and heavy items, objects normally out of reach or multiple objects at once. However, such manipulation through contacts using the whole surface of the body remains extremely challenging to achieve on robots. This can be labelled as Whole-Body Contact-Rich Manipulation (WBCRM) problem. In addition to the high-dimensionality of the Contact-Rich Manipulation problem due to the combinatorics of contact modes, admitting contact creation anywhere on the body surface adds complexity, which hinders planning of manipulation within a reasonable time. We address this computational problem by formulating the contact and motion planning of planar WBCRM as hierarchical continuous optimization problems. To enable this formulation, we propose a novel continuous explicit representation of the robot surface, that we believe to be foundational for future research using continuous optimization for WBCRM. Our results demonstrate a significant improvement of convergence, planning time and feasibility - with, on the average, 99% less iterations and 96% reduction in time to find a solution over considered scenarios, without recourse to prone-to-failure trajectory refinement steps.

More refined resource management and Quality of Service (QoS) provisioning is a critical goal of wireless communication technologies. In this paper, we propose a novel Business-Centric Network (BCN) aimed at enabling scalable QoS provisioning, based on a cross-layer framework that captures the relationship between application, transport parameters, and channels. We investigate both continuous flow and event-driven flow models, presenting key QoS metrics such as throughput, delay, and reliability. By jointly considering power and bandwidth allocation, transmission parameters, and AP network topology across layers, we optimize weighted resource efficiency with statistical QoS provisioning. To address the coupling among parameters, we propose a novel deep reinforcement learning (DRL) framework, which is Collaborative Optimization among Heterogeneous Actors with Experience Sharing (COHA-ES). Power and sub-channel (SC) Actors representing multiple APs are jointly optimized under the unified guidance of a common critic. Additionally, we introduce a novel multithreaded experience-sharing mechanism to accelerate training and enhance rewards. Extensive comparative experiments validate the effectiveness of our DRL framework in terms of convergence and efficiency. Moreover, comparative analyses demonstrate the comprehensive advantages of the BCN structure in enhancing both spectral and energy efficiency.

Stochastic Network Optimization (SNO) concerns scheduling in stochastic queueing systems. It has been widely studied in network theory. Classical SNO algorithms require network conditions to be stationary with time, which fails to capture the non-stationary components in many real-world scenarios. Many existing algorithms also assume knowledge of network conditions before decision, which rules out applications where unpredictability presents. Motivated by these issues, we consider Adversarial Network Optimization (ANO) under bandit feedback. Specifically, we consider the task of *i)* maximizing some unknown and time-varying utility function associated to scheduler's actions, where *ii)* the underlying network is a non-stationary multi-hop one whose conditions change arbitrarily with time, and *iii)* only bandit feedback (effect of actually deployed actions) is revealed after decisions. Our proposed `UMO2` algorithm ensures network stability and also matches the utility maximization performance of any "mildly varying" reference policy up to a polynomially decaying gap. To our knowledge, no previous ANO algorithm handled multi-hop networks or achieved utility guarantees under bandit feedback, whereas ours can do both. Technically, our method builds upon a novel integration of online learning into Lyapunov analyses: To handle complex inter-dependencies among queues in multi-hop networks, we propose meticulous techniques to balance online learning and Lyapunov arguments. To tackle the learning obstacles due to potentially unbounded queue sizes, we design a new online linear optimization algorithm that automatically adapts to loss magnitudes. To maximize utility, we propose a bandit convex optimization algorithm with novel queue-dependent learning rate scheduling that suites drastically varying queue lengths. Our new insights in online learning can be of independent interest.

We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed dynamics are based on the proximal augmented Lagrangian and they provide a viable alternative to ADMM which faces significant challenges from both analysis and implementation viewpoints in large-scale multi-block scenarios. In contrast to customized algorithms with individualized convergence guarantees, we provide a systematic approach for solving a broad class of challenging composite optimization problems. We leverage various structural properties to establish global (exponential) convergence guarantees for the proposed dynamics. Our assumptions are much weaker than those required to prove (exponential) stability of various primal-dual dynamics as well as (linear) convergence of discrete-time methods, e.g., standard two-block and multi-block ADMM and EXTRA algorithms. Finally, we show necessity of some of our structural assumptions for exponential stability and provide computational experiments to demonstrate the convenience of the proposed dynamics for parallel and distributed computing applications.

Using a portfolio of multiple search operators with different characteristics has been shown to improve the exploration and exploitation ability and, consequently, to enhance the overall performance of the meta-heuristics in solving different combinatorial optimization problems (COPs) [1, 2, 3, 4, 5]. From a theoretical perspective, the search space of a COP represents a non-stationary environment, meaning that the performance of different search operators varies depending on the region of the search space being explored. An operator working well in one region might be less effective in another region. Accordingly, incorporating a portfolio of diverse operators into a meta-heuristic is expected to enhance its overall performance [6]. For every COP, numerous search operators are available in the literature (either variations of the same operator with different configurations or entirely distinct operators), with the possibility of proposing new ones. Since the operators' performance is not pre-determined but rather dependent on the algorithm's performance on specific problems/instances, predicting the operators' performance proves challenging. Even if the most efficient operators could be determined, the order in which these efficient operators should be involved during the search process remains undetermined. Hence, optimizing the performance of a metaheuristic with multiple operators for solving different problem instances is always challenging [6, 7, 8, 9]. We label this problem as operator management problem in meta-heuristics, wherein the user should address two questions: What operators should I include in the portfolio?, and How (in which order) should I involve the in-portfolio operators during the search process?

The paper deals with the interpretability of Graph Neural Networks in the context of Boolean Satisfiability. The goal is to demystify the internal workings of these models and provide insightful perspectives into their decision-making processes. This is done by uncovering connections to two approximation algorithms studied in the domain of Boolean Satisfiability: Belief Propagation and Semidefinite Programming Relaxations. Revealing these connections has empowered us to introduce a suite of impactful enhancements. The first significant enhancement is a curriculum training procedure, which incrementally increases the problem complexity in the training set, together with increasing the number of message passing iterations of the Graph Neural Network. We show that the curriculum, together with several other optimizations, reduces the training time by more than an order of magnitude compared to the baseline without the curriculum. Furthermore, we apply decimation and sampling of initial embeddings, which significantly increase the percentage of solved problems.

This paper proposes a metric to measure the dissimilarity between graphs that may have a different number of nodes. The proposed metric extends the generalised optimal subpattern assignment (GOSPA) metric, which is a metric for sets, to graphs. The proposed graph GOSPA metric includes costs associated with node attribute errors for properly assigned nodes, missed and false nodes and edge mismatches between graphs. The computation of this metric is based on finding the optimal assignments between nodes in the two graphs, with the possibility of leaving some of the nodes unassigned. We also propose a lower bound for the metric, which is also a metric for graphs and is computable in polynomial time using linear programming. The metric is first derived for undirected unweighted graphs and it is then extended to directed and weighted graphs. The properties of the metric are demonstrated via simulated and empirical datasets.

Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes are prone to generating biased data based on the training dataset. To address this issue, we develop constrained diffusion models by imposing diffusion constraints based on desired distributions that are informed by requirements. Specifically, we cast the training of diffusion models under requirements as a constrained distribution optimization problem that aims to reduce the distribution difference between original and generated data while obeying constraints on the distribution of generated data. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints. To train constrained diffusion models, we develop a dual training algorithm and characterize the optimality of the trained constrained diffusion model. We empirically demonstrate the effectiveness of our constrained models in two constrained generation tasks: (i) we consider a dataset with one or more underrepresented classes where we train the model with constraints to ensure fairly sampling from all classes during inference; (ii) we fine-tune a pre-trained diffusion model to sample from a new dataset while avoiding overfitting.