Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a powerful method. Two classical approaches are the Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA) algorithms, which estimate gradients using just two samples in each iteration to conserve samples. However, this approach yields imprecise gradient estimators, necessitating diminishing step sizes to ensure convergence, often resulting in slow optimization progress. In contrast, FD estimators constructed from batch samples approximate gradients more accurately. While gradient descent algorithms using batch-based FD estimators achieve more precise results in each iteration, they require more samples and permit fewer iterations. This raises a fundamental question: which approach is more effective -- KW-style methods or DFO with batch-based FD estimators? This paper conducts a comprehensive experimental comparison among these approaches, examining the fundamental trade-off between gradient estimation accuracy and iteration steps. Through extensive experiments in both low-dimensional and high-dimensional settings, we demonstrate a surprising finding: when an efficient batch-based FD estimator is applied, its corresponding gradient descent algorithm generally shows better performance compared to classical KW and SPSA algorithms in our tested scenarios.

The large models, as predicted by scaling raw forecasts, have made groundbreaking progress in many fields, particularly in natural language generation tasks, where they have approached or even surpassed human levels. However, the unprecedented scale of their parameters brings significant computational and storage costs. These large models require substantial computational resources and GPU memory to operate. When adapting large models to specific downstream tasks, their massive parameter scale poses a significant challenge in fine-tuning on hardware platforms with limited computational power and GPU memory. To address this issue, Parameter-Efficient Fine-Tuning (PEFT) offers a practical solution by efficiently adjusting the parameters of large pre-trained models to suit various downstream tasks. Specifically, PEFT adjusts the parameters of pre-trained large models to adapt to specific tasks or domains, minimizing the introduction of additional parameters and the computational resources required. This review mainly introduces the preliminary knowledge of PEFT, the core ideas and principles of various PEFT algorithms, the applications of PEFT, and potential future research directions. By reading this review, we believe that interested parties can quickly grasp the PEFT methodology, thereby accelerating its development and innovation.

Many real-world optimization problems can be stated in terms of submodular functions. Furthermore, these real-world problems often involve uncertainties which may lead to the violation of given constraints. A lot of evolutionary multi-objective algorithms following the Pareto optimization approach have recently been analyzed and applied to submodular problems with different types of constraints. We present a first runtime analysis of evolutionary multi-objective algorithms based on Pareto optimization for chance-constrained submodular functions. Here the constraint involves stochastic components and the constraint can only be violated with a small probability of alpha. We investigate the classical GSEMO algorithm for two different bi-objective formulations using tail bounds to determine the feasibility of solutions. We show that the algorithm GSEMO obtains the same worst case performance guarantees for monotone submodular functions as recently analyzed greedy algorithms for the case of uniform IID weights and uniformly distributed weights with the same dispersion when using the appropriate bi-objective formulation. As part of our investigations, we also point out situations where the use of tail bounds in the first bi-objective formulation can prevent GSEMO from obtaining good solutions in the case of uniformly distributed weights with the same dispersion if the objective function is submodular but non-monotone due to a single element impacting monotonicity. Furthermore, we investigate the behavior of the evolutionary multi-objective algorithms GSEMO, NSGA-II and SPEA2 on different submodular chance-constrained network problems. Our experimental results show that the use of evolutionary multi-objective algorithms leads to significant performance improvements compared to state-of-the-art greedy algorithms for submodular optimization.

Conventional methods for Bayesian optimization (BO) primarily involve one-step optimal decisions (e.g., maximizing expected improvement of the next step). To avoid myopic behavior, multi-step lookahead BO algorithms such as rollout strategies consider the sequential decision-making nature of BO, i.e., as a stochastic dynamic programming (SDP) problem, demonstrating promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues, e.g., being limited to two-step lookahead. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the SDP of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and employ off-policy learning to accelerate its initial training. We then propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for Bayesian Optimization), on both synthetic benchmark functions and real-world hyperparameter optimization problems, demonstrating significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.

An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner similar to SVMs and limits their applicability in large-scale scenarios. In this paper, we introduce a novel convex SSLM formulation which has been demonstrated to revert to a convex quadratic programming problem for hyperparameter values of interest. Leveraging the convexity of our method, we derive numerous results that are unattainable with traditional nonconvex approaches. We conduct a thorough analysis of how hyperparameters influence the optimal solution, pointing out scenarios where optimal solutions can be trivially found and identifying instances of ill-posedness. Most notably, we establish connections between our method and traditional approaches, providing a clear determination of when the optimal solution is unique -- a task unachievable with traditional nonconvex methods. We also derive the {\nu}-property to elucidate the interactions between hyperparameters and the fractions of support vectors and margin errors in both positive and negative classes.

Tensegrity robots, characterized by a synergistic assembly of rigid rods and elastic cables, form robust structures that are resistant to impacts. However, this design introduces complexities in kinematics and dynamics, complicating control and state estimation. This work presents a novel proprioceptive state estimator for tensegrity robots. The estimator initially uses the geometric constraints of 3-bar prism tensegrity structures, combined with IMU and motor encoder measurements, to reconstruct the robot's shape and orientation. It then employs a contact-aided invariant extended Kalman filter with forward kinematics to estimate the global position and orientation of the tensegrity robot. The state estimator's accuracy is assessed against ground truth data in both simulated environments and real-world tensegrity robot applications. It achieves an average drift percentage of 4.2%, comparable to the state estimation performance of traditional rigid robots. This state estimator advances the state of the art in tensegrity robot state estimation and has the potential to run in real-time using onboard sensors, paving the way for full autonomy of tensegrity robots in unstructured environments.

The problem of heterogeneous clients in federated learning has recently drawn a lot of attention. Spectral model sharding, i.e., partitioning the model parameters into low-rank matrices based on the singular value decomposition, has been one of the proposed solutions for more efficient on-device training in such settings. In this work, we present two sampling strategies for such sharding, obtained as solutions to specific optimization problems. The first produces unbiased estimators of the original weights, while the second aims to minimize the squared approximation error. We discuss how both of these estimators can be incorporated in the federated learning loop and practical considerations that arise during local training. Empirically, we demonstrate that both of these methods can lead to improved performance on various commonly used datasets.

Operations and maintenance (O&M) is a fundamental problem in wind energy systems with far reaching implications for reliability and profitability. Optimizing O&M is a multi-faceted decision optimization problem that requires a careful balancing act across turbine level failure risks, operational revenues, and maintenance crew logistics. The resulting O&M problems are typically solved using large-scale mixed integer programming (MIP) models, which yield computationally challenging problems that require either long-solution times, or heuristics to reach a solution. To address this problem, we introduce a novel decision-making framework for wind farm O&M that builds on a multi-head attention (MHA) models, an emerging artificial intelligence methods that are specifically designed to learn in rich and complex problem settings. The development of proposed MHA framework incorporates a number of modeling innovations that allows explicit embedding of MIP models within an MHA structure. The proposed MHA model (i) significantly reduces the solution time from hours to seconds, (ii) guarantees feasibility of the proposed solutions considering complex constraints that are omnipresent in wind farm O&M, (iii) results in significant solution quality compared to the conventional MIP formulations, and (iv) exhibits significant transfer learning capability across different problem settings.

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert space (RKHS), thereby enhancing feature representation to an infinite-dimensional space. We demonstrate that a variant of the representer theorem holds for a specific training loss, allowing the reformulation of the problem as a finite-dimensional convex optimization program. To address scalability issues commonly associated with kernel methods, we propose the Sequential Selection Optimization (SSO) algorithm to efficiently train the proposed Kernel Inverse Optimization (KIO) model. Finally, we validate the generalization capabilities of the proposed KIO model and the effectiveness of the SSO algorithm through learning-from-demonstration tasks on the MuJoCo benchmark.

The deployment of ML models on edge devices is challenged by limited computational resources and energy availability. While split computing enables the decomposition of large neural networks (NNs) and allows partial computation on both edge and cloud devices, identifying the most suitable split layer and hardware configurations is a non-trivial task. This process is in fact hindered by the large configuration space, the non-linear dependencies between software and hardware parameters, the heterogeneous hardware and energy characteristics, and the dynamic workload conditions. To overcome this challenge, we propose DynaSplit, a two-phase framework that dynamically configures parameters across both software (i.e., split layer) and hardware (e.g., accelerator usage, CPU frequency). During the Offline Phase, we solve a multi-objective optimization problem with a meta-heuristic approach to discover optimal settings. During the Online Phase, a scheduling algorithm identifies the most suitable settings for an incoming inference request and configures the system accordingly. We evaluate DynaSplit using popular pre-trained NNs on a real-world testbed. Experimental results show a reduction in energy consumption up to 72% compared to cloud-only computation, while meeting ~90% of user request's latency threshold compared to baselines.