This work investigates the performance limits of projected stochastic first-order methods for minimizing functions under the $(\alpha,\tau,\mathcal{X})$-projected-gradient-dominance property, that asserts the sub-optimality gap $F(\mathbf{x})-\min_{\mathbf{x}'\in \mathcal{X}}F(\mathbf{x}')$ is upper-bounded by $\tau\cdot\|\mathcal{G}_{\eta,\mathcal{X}}(\mathbf{x})\|^{\alpha}$ for some $\alpha\in[1,2)$ and $\tau>0$ and $\mathcal{G}_{\eta,\mathcal{X}}(\mathbf{x})$ is the projected-gradient mapping with $\eta>0$ as a parameter. For non-convex functions, we show that the complexity lower bound of querying a batch smooth first-order stochastic oracle to obtain an $\epsilon$-global-optimum point is $\Omega(\epsilon^{-{2}/{\alpha}})$. Furthermore, we show that a projected variance-reduced first-order algorithm can obtain the upper complexity bound of $\mathcal{O}(\epsilon^{-{2}/{\alpha}})$, matching the lower bound. For convex functions, we establish a complexity lower bound of $\Omega(\log(1/\epsilon)\cdot\epsilon^{-{2}/{\alpha}})$ for minimizing functions under a local version of gradient-dominance property, which also matches the upper complexity bound of accelerated stochastic subgradient methods.

Painting classification plays a vital role in organizing, finding, and suggesting artwork for digital and classic art galleries. Existing methods struggle with adapting knowledge from the real world to artistic images during training, leading to poor performance when dealing with different datasets. Our innovation lies in addressing these challenges through a two-step process. First, we generate more data using Style Transfer with Adaptive Instance Normalization (AdaIN), bridging the gap between diverse styles. Then, our classifier gains a boost with feature-map adaptive spatial attention modules, improving its understanding of artistic details. Moreover, we tackle the problem of imbalanced class representation by dynamically adjusting augmented samples. Through a dual-stage process involving careful hyperparameter search and model fine-tuning, we achieve an impressive 87.24\% accuracy using the ResNet-50 backbone over 40 training epochs. Our study explores quantitative analyses that compare different pretrained backbones, investigates model optimization through ablation studies, and examines how varying augmentation levels affect model performance. Complementing this, our qualitative experiments offer valuable insights into the model's decision-making process using spatial attention and its ability to differentiate between easy and challenging samples based on confidence ranking.

--We introduce a real-time identification method for discrete-time state-dependent switching systems in both the input-output and state-space domains. In particular, we design a system of adaptive algorithms running in two timescales; a stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale and estimates the mode-switching signal, and an recursive identification algorithm runs at a faster timescale and updates the parameters of the local models based on the estimate of the switching signal. We first focus on piece-wise affine systems and discuss identifiability conditions and convergence properties based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for switched systems, the proposed approach gradually estimates the number of modes and is appropriate for real-time system identification using sequential data acquisition. The progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off. Finally, we address specific challenges that arise in the application of the proposed methodology in identification of more general switching systems. Simulation results validate the efficacy of the proposed methodology. Hybrid systems, described by interacting continuous and discrete dynamics, are a powerful modeling tool in the analysis of systems where logic and continuous processes are interlaced, as in most complex cyber-physical systems. In addition to being able to describe switching dynamics, hybrid systems can be used as a tool to approximate highly non-linear dynamics by a collection of simpler models, and boost model explainability and robustness, by decomposing the behavior of a complex system into sub-systems where first principles and domain knowledge can be used for precise model tuning [1], [2]. As a result, hybrid systems have attracted significant attention in the control community. However, first principles modelling is often too complicated and sub-optimal, and a hybrid model needs to be identified on the basis of observations. The majority of the work in this area is based on piece-wise affine (PW A) systems, a class of state-dependent switched systems with important applications in identification, verification, and control synthesis of hybrid and nonlinear systems [2]-[5]. The input-output representation of PW A systems is the class of piece-wise affine auto-regressive exogenous (PW ARX) systems with the switching signal depending on a partitioning of the domain of a vector containing the recent history of input-output pairs.

Planning for a wide range of real-world robotic tasks necessitates to know and write all constraints. However, instances exist where these constraints are either unknown or challenging to specify accurately. A possible solution is to infer the unknown constraints from expert demonstration. This paper presents a novel Positive-Unlabeled Constraint Learning (PUCL) algorithm to infer a continuous arbitrary constraint function from demonstration, without requiring prior knowledge of the true constraint parameterization or environmental model as existing works. Within our framework, we treat all data in demonstrations as positive (feasible) data, and learn a control policy to generate potentially infeasible trajectories, which serve as unlabeled data. In each iteration, we first update the policy and then a two-step positive-unlabeled learning procedure is applied, where it first identifies reliable infeasible data using a distance metric, and secondly learns a binary feasibility classifier (i.e., constraint function) from the feasible demonstrations and reliable infeasible data. The proposed framework is flexible to learn complex-shaped constraint boundary and will not mistakenly classify demonstrations as infeasible as previous methods. The effectiveness of the proposed method is verified in three robotic tasks, using a networked policy or a dynamical system policy. It successfully infers and transfers the continuous nonlinear constraints and outperforms other baseline methods in terms of constraint accuracy and policy safety.

Machine learning has witnessed remarkable breakthroughs in recent years. As machine learning permeates various aspects of daily life, individuals and organizations increasingly interact with these systems, exhibiting a wide range of social and adversarial behaviors. These behaviors may have a notable impact on the behavior and performance of machine learning systems. Specifically, during these interactions, data may be generated by strategic individuals, collected by self-interested data collectors, possibly poisoned by adversarial attackers, and used to create predictors, models, and policies satisfying multiple objectives. As a result, the machine learning systems' outputs might degrade, such as the susceptibility of deep neural networks to adversarial examples (Shafahi et al., 2018; Szegedy et al., 2013) and the diminished performance of classic algorithms in the presence of strategic individuals (Ahmadi et al., 2021). Addressing these challenges is imperative for the success of machine learning in societal settings.

Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have exactly two children and where datapoints are assessed on a set of discrete features and (ii) leaf vertices at which datapoints are given a prediction, and can be obtained by solving a biobjective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. Branching vertices are linear combinations of training features and therefore can be thought of as hyperplanes. In this paper, we propose two cut-based mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees (leaf vertices assign discrete classes). Our models leverage on-the-fly identification of minimal infeasible subsystems (MISs) from which we derive cutting planes that hold the form of packing constraints. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available datasets to show our models' ability to scale, strength against traditional branch and bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub.

Layered control architectures (Matni et al., 2024; Chiang et al., 2007) are ubiquitous in complex cyber-physical systems, such as power networks, communication networks, and autonomous robots. For example, a typical autonomous robot has an autonomy stack consisting of decision-making, trajectory optimization, and low-level control. However, despite the widespread presence of such layered control architectures, there has been a lack of a principled framework for their design, especially in the data-driven regime. In this work, we propose an algorithm for jointly learning a trajectory planner and a tracking controller. We start from an optimal control problem and show that a suitable relaxation of the problem naturally decomposes into reference generation and trajectory tracking layers. We then propose an algorithm to train a layered policy parameterized in a way that parallels this decomposition using actor-critic methods. Different from previous methods, we show how a dual network can be trained to coordinate the trajectory optimizer and the tracking controller. Our theoretical analysis and numerical experiments demonstrate that the proposed algorithm can achieve good performance in various settings while enjoying inherent interpretability and modularity.

Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management and advertising. Existing OLP algorithms fall into two categories: LP-based algorithms and LP-free algorithms. The former one typically guarantees better performance, even offering a constant regret, but requires solving a large number of LPs, which could be computationally expensive. In contrast, LP-free algorithm only requires first-order computations but induces a worse performance, lacking a constant regret bound. In this work, we bridge the gap between these two extremes by proposing an algorithm that achieves a constant regret while solving LPs only $O(\log\log T)$ times over the time horizon $T$. Moreover, when we are allowed to solve LPs only $M$ times, we propose an algorithm that can guarantee an $O\left(T^{(1/2+\epsilon)^{M-1}}\right)$ regret. Furthermore, when the arrival probabilities are known at the beginning, our algorithm can guarantee a constant regret by solving LPs $O(\log\log T)$ times, and an $O\left(T^{(1/2+\epsilon)^{M}}\right)$ regret by solving LPs only $M$ times. Numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms.

Multiple-input multiple-output (MIMO) systems play a key role in wireless communication technologies. A widely considered approach to realize scalable MIMO systems involves architectures comprised of multiple separate modules, each with its own beamforming capability. Such models accommodate cell-free massive MIMO and partially connected hybrid MIMO architectures. A core issue with the implementation of modular MIMO arises from the need to rapidly set the beampatterns of the modules, while maintaining their power efficiency. This leads to challenging constrained optimization that should be repeatedly solved on each coherence duration. In this work, we propose a power-oriented optimization algorithm for beamforming in uplink modular hybrid MIMO systems, which learns from data to operate rapidly. We derive our learned optimizer by tackling the rate maximization objective using projected gradient ascent steps with momentum. We then leverage data to tune the hyperparameters of the optimizer, allowing it to operate reliably in a fixed and small number of iterations while completely preserving its interpretable operation. We show how power efficient beamforming can be encouraged by the learned optimizer, via boosting architectures with low-resolution phase shifts and with deactivated analog components. Numerical results show that our learn-to-optimize method notably reduces the number of iterations and computation latency required to reliably tune modular MIMO receivers, and that it allows obtaining desirable balances between power efficient designs and throughput.

Gaussian process (GP) models have received increasingly attentions in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed learning for GPs are often adopted. Current aggregation models for distributed GPs are not time-efficient when incorporating correlations between GP experts. In this work, we propose a novel approach for aggregated prediction in distributed GPs. The technique is suitable for both the exact and sparse variational GPs. The proposed method incorporates correlations among experts, leading to better prediction accuracy with manageable computational requirements. As demonstrated by empirical studies, the proposed approach results in more stable predictions in less time than state-of-the-art consistent aggregation models.