Domain adaptation has shown appealing performance by leveraging knowledge from a source domain with rich annotations. However, for a specific target task, it is cumbersome to collect related and high-quality source domains. In real-world scenarios, large-scale datasets corrupted with noisy labels are easy to collect, stimulating a great demand for automatic recognition in a generalized setting, i.e., weakly-supervised partial domain adaptation (WS-PDA), which transfers a classifier from a large source domain with noises in labels to a small unlabeled target domain. As such, the key issues of WS-PDA are: 1) how to sufficiently discover the knowledge from the noisy labeled source domain and the unlabeled target domain, and 2) how to successfully adapt the knowledge across domains. In this paper, we propose a simple yet effective domain adaptation approach, termed as self-paced transfer classifier learning (SP-TCL), to address the above issues, which could be regarded as a well-performing baseline for several generalized domain adaptation tasks. The proposed model is established upon the self-paced learning scheme, seeking a preferable classifier for the target domain. Specifically, SP-TCL learns to discover faithful knowledge via a carefully designed prudent loss function and simultaneously adapts the learned knowledge to the target domain by iteratively excluding source examples from training under the self-paced fashion. Extensive evaluations on several benchmark datasets demonstrate that SP-TCL significantly outperforms state-of-the-art approaches on several generalized domain adaptation tasks.

Photonic surfaces designed with specific optical characteristics are becoming increasingly important for use in in various energy harvesting and storage systems. , In this study, we develop a surrogate-based optimization approach for designing such surfaces. The surrogate-based optimization framework employs the Random Forest algorithm and uses a greedy, prediction-based exploration strategy to identify the laser fabrication parameters that minimize the discrepancy relative to a user-defined target optical characteristics. We demonstrate the approach on two synthetic benchmarks and two specific cases of photonic surface inverse design targets. It exhibits superior performance when compared to other optimization algorithms across all benchmarks. Additionally, we demonstrate a technique of inverse design warm starting for changed target optical characteristics which enhances the performance of the introduced approach.

It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as, for example, in the situation of constant learning rates). Numerical simulations often use human-tuned deterministic learning rate schedules or small constant learning rates. The default learning rate schedules for SGD optimization methods in machine learning implementation frameworks such as TensorFlow and Pytorch are constant learning rates. In this work we propose and study a learning-rate-adaptive approach for SGD optimization methods in which the learning rate is adjusted based on empirical estimates for the values of the objective function of the considered optimization problem (the function that one intends to minimize). In particular, we propose a learning-rate-adaptive variant of the Adam optimizer and implement it in case of several neural network learning problems, particularly, in the context of deep learning approximation methods for partial differential equations such as deep Kolmogorov methods, physics-informed neural networks, and deep Ritz methods. In each of the presented learning problems the proposed learning-rate-adaptive variant of the Adam optimizer faster reduces the value of the objective function than the Adam optimizer with the default learning rate. For a simple class of quadratic minimization problems we also rigorously prove that a learning-rate-adaptive variant of the SGD optimization method converges to the minimizer of the considered minimization problem. Our convergence proof is based on an analysis of the laws of invariant measures of the SGD method as well as on a more general convergence analysis for SGD with random but predictable learning rates which we develop in this work.

We study the potential of using large language models (LLMs) as an interactive optimizer for solving maximization problems in a text space using natural language and numerical feedback. Inspired by the classical optimization literature, we classify the natural language feedback into directional and non-directional, where the former is a generalization of the first-order feedback to the natural language space. We find that LLMs are especially capable of optimization when they are provided with {directional feedback}. Based on this insight, we design a new LLM-based optimizer that synthesizes directional feedback from the historical optimization trace to achieve reliable improvement over iterations. Empirically, we show our LLM-based optimizer is more stable and efficient in solving optimization problems, from maximizing mathematical functions to optimizing prompts for writing poems, compared with existing techniques.

Achieving control stability is one of the key design challenges of scalable Wireless Networked Control Systems (WNCS) under limited communication and computing resources. This paper explores the use of an alternative control concept defined as tail-based control, which extends the classical Linear Quadratic Regulator (LQR) cost function for multiple dynamic control systems over a shared wireless network. We cast the control of multiple control systems as a network-wide optimization problem and decouple it in terms of sensor scheduling, plant state prediction, and control policies. Toward this, we propose a solution consisting of a scheduling algorithm based on Lyapunov optimization for sensing, a mechanism based on Gaussian Process Regression (GPR) for state prediction and uncertainty estimation, and a control policy based on Reinforcement Learning (RL) to ensure tail-based control stability. A set of discrete time-invariant mountain car control systems is used to evaluate the proposed solution and is compared against four variants that use state-of-the-art scheduling, prediction, and control methods. The experimental results indicate that the proposed method yields 22% reduction in overall cost in terms of communication and control resource utilization compared to state-of-the-art methods.

Fair supervised learning algorithms assigning labels with little dependence on a sensitive attribute have attracted great attention in the machine learning community. While the demographic parity (DP) notion has been frequently used to measure a model's fairness in training fair classifiers, several studies in the literature suggest potential impacts of enforcing DP in fair learning algorithms. In this work, we analytically study the effect of standard DP-based regularization methods on the conditional distribution of the predicted label given the sensitive attribute. Our analysis shows that an imbalanced training dataset with a non-uniform distribution of the sensitive attribute could lead to a classification rule biased toward the sensitive attribute outcome holding the majority of training data. To control such inductive biases in DP-based fair learning, we propose a sensitive attribute-based distributionally robust optimization (SA-DRO) method improving robustness against the marginal distribution of the sensitive attribute. Finally, we present several numerical results on the application of DP-based learning methods to standard centralized and distributed learning problems. The empirical findings support our theoretical results on the inductive biases in DP-based fair learning algorithms and the debiasing effects of the proposed SA-DRO method.

Meta-Reinforcement Learning (Meta-RL) aims to acquire meta-knowledge for quick adaptation to diverse tasks. However, applying these policies in real-world environments presents a significant challenge in balancing rapid adaptability with adherence to environmental constraints. Our novel approach, Constraint Model Agnostic Meta Learning (C-MAML), merges meta learning with constrained optimization to address this challenge. C-MAML enables rapid and efficient task adaptation by incorporating task-specific constraints directly into its meta-algorithm framework during the training phase. This fusion results in safer initial parameters for learning new tasks. We demonstrate the effectiveness of C-MAML in simulated locomotion with wheeled robot tasks of varying complexity, highlighting its practicality and robustness in dynamic environments.

Bi-level optimization (BO) has become a fundamental mathematical framework for addressing hierarchical machine learning problems. As deep learning models continue to grow in size, the demand for scalable bi-level optimization solutions has become increasingly critical. Traditional gradient-based bi-level optimization algorithms, due to their inherent characteristics, are ill-suited to meet the demands of large-scale applications. In this paper, we introduce $\textbf{F}$orward $\textbf{G}$radient $\textbf{U}$nrolling with $\textbf{F}$orward $\textbf{F}$radient, abbreviated as $(\textbf{FG})^2\textbf{U}$, which achieves an unbiased stochastic approximation of the meta gradient for bi-level optimization. $(\text{FG})^2\text{U}$ circumvents the memory and approximation issues associated with classical bi-level optimization approaches, and delivers significantly more accurate gradient estimates than existing large-scale bi-level optimization approaches. Additionally, $(\text{FG})^2\text{U}$ is inherently designed to support parallel computing, enabling it to effectively leverage large-scale distributed computing systems to achieve significant computational efficiency. In practice, $(\text{FG})^2\text{U}$ and other methods can be strategically placed at different stages of the training process to achieve a more cost-effective two-phase paradigm. Further, $(\text{FG})^2\text{U}$ is easy to implement within popular deep learning frameworks, and can be conveniently adapted to address more challenging zeroth-order bi-level optimization scenarios. We provide a thorough convergence analysis and a comprehensive practical discussion for $(\text{FG})^2\text{U}$, complemented by extensive empirical evaluations, showcasing its superior performance in diverse large-scale bi-level optimization tasks.

For many years now, reinforcement learning (RL) has succeeded in solving a wide variety of decision-making problems and control for robotics [1, 2, 3, 4, 5]. Generally speaking, modelfree methods [6, 7] often suffer from high sample complexity that can require an inordinate amount of samples, making them unsuitable for robotic applications where collecting large amounts of data is time-consuming, costly and potentially dangerous for the system and its surroundings [8, 9, 10, 11, 12]. On the other hand, model-based RL methods have been successful in demonstrating significantly reduced sample complexity and in outperforming model-free approaches for various decision making under uncertainty problems (see, e.g., [13, 14]). However, such modelbased approaches can suffer from the difficulty of learning an appropriate model and from worse asymptotic performance than model-free approaches due to model bias from inherently assuming the learned system dynamics model accurately represents the true system environment (see, e.g., [15, 16, 17]). In this paper we propose a novel form of RL that seeks to directly learn an optimal control policy for a general underlying (unknown) dynamical system and to directly apply the corresponding learned optimal control policy within the dynamical system. This general approach is in strong contrast to many traditional model-based RL methods that, after learning the system dynamics model which is often of high complexity and dimensionality, then use this system dynamics model to compute an approximate solution of a corresponding (stochastic) dynamic programming problem, often applying model predictive control (see, e.g., [18]). Our control-based RL (CBRL) approach instead directly learns the unknown parameters that derive, through control-theoretic means, an optimal control policy function from a family of control policy functions, often of much lower complexity and dimensionality, from which the optimal control policy is directly obtained. The theoretical foundation and analysis of our CRBL approach is presented within the context of a general Markov decision process (MDP) framework that extends the family of policies associated with the classical Bellman operator to a family of control-policy functions mapping a vector of (unknown) parameters from a corresponding parameter set to a control policy which is optimal under those parameters, and that extends the domain of these control policies from a single state to span across all (or a large subset of) states, with the (unknown) parameter vector encoding global and local information that needs to be learned. Within the context of this MDP framework and our general CBRL approach, we establish theoretical results on convergence and optimality with respect to (w.r.t.) a CBRL contraction operator, analogous to the Bellman operator.

Preferential Bayesian optimization (PBO) is a framework for optimizing a decision-maker's latent preferences over available design choices. While preferences often involve multiple conflicting objectives, existing work in PBO assumes that preferences can be encoded by a single objective function. For example, in robotic assistive devices, technicians often attempt to maximize user comfort while simultaneously minimizing mechanical energy consumption for longer battery life. Similarly, in autonomous driving policy design, decision-makers wish to understand the trade-offs between multiple safety and performance attributes before committing to a policy. To address this gap, we propose the first framework for PBO with multiple objectives. Within this framework, we present dueling scalarized Thompson sampling (DSTS), a multi-objective generalization of the popular dueling Thompson algorithm, which may be of interest beyond the PBO setting. We evaluate DSTS across four synthetic test functions and two simulated exoskeleton personalization and driving policy design tasks, showing that it outperforms several benchmarks. Finally, we prove that DSTS is asymptotically consistent. As a direct consequence, this result provides, to our knowledge, the first convergence guarantee for dueling Thompson sampling in the PBO setting.