Bayesian Optimization (BO) (Shahriari et al., 2015) is a popular sample-efficient optimization technique to solve problems where the objective is expensive. It has been successfully applied in diverse areas (Greenhill et al., 2020) including material discovery (Li et al., 2017), alloy design (Barnett et al., 2020) and molecular design (Gómez-Bombarelli et al., 2018). However, standard BO typically operates tabula rasa, building its model of the objective from minimal priors that do not include domain-specific information. While there has been some progress made incorporating domain-specific knowledge to accelerate BO (Li et al., 2018; Hvarfner et al., 2022) or transfer learning from previous experiments (Shilton et al., 2017), it remains the case that there is a significant corpus of knowledge and expertise that could potentially accelerate BO even further but which remain largely untapped due to the inherent complexities involved in knowledge extraction and exploitation. In particular, this often arises from the fact that experts tend to organize their knowledge in complex schema containing concepts, attributes and relationships (Rousseau, 2001), making the elicitation of relevant expert knowledge, both quantitative and qualitative, a difficult task.

In this work, we develop methods for few-shot image classification from a new perspective of optimal matching between image regions. We employ the Earth Mover's Distance (EMD) as a metric to compute a structural distance between dense image representations to determine image relevance. The EMD generates the optimal matching flows between structural elements that have the minimum matching cost, which is used to calculate the image distance for classification. To generate the important weights of elements in the EMD formulation, we design a cross-reference mechanism, which can effectively alleviate the adverse impact caused by the cluttered background and large intra-class appearance variations. To implement k-shot classification, we propose to learn a structured fully connected layer that can directly classify dense image representations with the EMD. Based on the implicit function theorem, the EMD can be inserted as a layer into the network for end-to-end training. Our extensive experiments validate the effectiveness of our algorithm which outperforms state-of-the-art methods by a significant margin on five widely used few-shot classification benchmarks, namely, miniImageNet, tieredImageNet, Fewshot-CIFAR100 (FC100), Caltech-UCSD Birds-200-2011 (CUB), and CIFAR-FewShot (CIFAR-FS). We also demonstrate the effectiveness of our method on the image retrieval task in our experiments.

Multi-label learning is usually used to mine the correlation between features and labels, and feature selection can retain as much information as possible through a small number of features. $\ell_{2,1}$ regularization method can get sparse coefficient matrix, but it can not solve multicollinearity problem effectively. The model proposed in this paper can obtain the most relevant few features by solving the joint constrained optimization problems of $\ell_{2,1}$ and $\ell_{F}$ regularization.In manifold regularization, we implement random walk strategy based on joint information matrix, and get a highly robust neighborhood graph.In addition, we given the algorithm for solving the model and proved its convergence.Comparative experiments on real-world data sets show that the proposed method outperforms other methods.

This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as the path-tracking control of vehicles. RCTAC has several advantages over existing adaptive dynamic programming algorithms for CT systems. It does not require the ``admissibility" of the initialized policy or the input-affine nature of controlled systems for convergence. Instead, given any initial policy, RCTAC can converge to an admissible, and subsequently nearly optimal policy for a general nonlinear system with a saturated controller. RCTAC consists of two phases: a warm-up phase and a generalized policy iteration phase. The warm-up phase minimizes the square of the Hamiltonian to achieve admissibility, while the generalized policy iteration phase relaxes the update termination conditions for faster convergence. The convergence and optimality of the algorithm are proven through Lyapunov analysis, and its effectiveness is demonstrated through simulations and real-world path-tracking tasks.

Dojo achieves stable simulation at low sample rates and conserves energy and momentum by employing a variational integrator. A nonlinear complementarity problem with second-order cones for friction models hard contact, and is reliably solved using a custom primal-dual interior-point method. Special properties of the interior-point method are exploited using implicit differentiation to efficiently compute smooth gradients that provide useful information through contact events. We demonstrate Dojo with a number of examples including: planning, policy optimization, and system identification, that demonstrate the engine's unique ability to simulate hard contact while providing smooth, analytic gradients.

We formulate the Multiple Kernel Learning (abbreviated as MKL) problem for the support vector machine with the infamous $(0,1)$-loss function. Some first-order optimality conditions are given and then exploited to develop a fast ADMM solver for the nonconvex and nonsmooth optimization problem. A simple numerical experiment on synthetic planar data shows that our MKL-$L_{0/1}$-SVM framework could be promising.

Humans coordinate the abundant degrees of freedom (DoFs) of hands to dexterously perform tasks in everyday life. We imitate human strategies to advance the dexterity of multi-DoF robotic hands. Specifically, we enable a robot hand to grasp multiple objects by exploiting its kinematic redundancy, referring to all its controllable DoFs. We propose a human-like grasp synthesis algorithm to generate grasps using pairwise contacts on arbitrary opposing hand surface regions, no longer limited to fingertips or hand inner surface. To model the available space of the hand for grasp, we construct a reachability map, consisting of reachable spaces of all finger phalanges and the palm. It guides the formulation of a constrained optimization problem, solving for feasible and stable grasps. We formulate an iterative process to empower robotic hands to grasp multiple objects in sequence. Moreover, we propose a kinematic efficiency metric and an associated strategy to facilitate exploiting kinematic redundancy. We validated our approaches by generating grasps of single and multiple objects using various hand surface regions. Such grasps can be successfully replicated on a real robotic hand.

Several decision problems that are encountered in various business domains can be modeled as mathematical programs, i.e. optimization problems. The process of conducting such modeling often requires the involvement of experts trained in operations research and advanced algorithms. Surprisingly, despite the significant advances in the methods for program and code synthesis, AutoML, learning to optimize etc., there has been little or no attention paid to automating the task of synthesizing mathematical programs. We imagine a scenario where the specifications for modeling, i.e. the objective and constraints are expressed in an unstructured form in natural language (NL) and the mathematical program has to be synthesized from such an NL specification. In this work we evaluate the efficacy of employing CodeT5 with data augmentation and post-processing of beams. We utilize GPT-3 with back translation for generation of synthetic examples. Further we apply rules of linear programming to score beams and correct beams based on common error patterns. We observe that with these enhancements CodeT5 base gives an execution accuracy of 0.73 which is significantly better than zero-shot execution accuracy of 0.41 by ChatGPT and 0.36 by Codex.

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization problems, albeit frequently encountered in applications, are quite challenging due to their non-smoothness and non-convexity. To tackle them, we propose an iterative method called the decentralized Riemannian subgradient method (DRSM). The global convergence and an iteration complexity of $\mathcal{O}(\varepsilon^{-2} \log^2(\varepsilon^{-1}))$ for forcing a natural stationarity measure below $\varepsilon$ are established via the powerful tool of proximal smoothness from variational analysis, which could be of independent interest. Besides, we show the local linear convergence of the DRSM using geometrically diminishing stepsizes when the problem at hand further possesses a sharpness property. Numerical experiments are conducted to corroborate our theoretical findings.

This paper presents a novel methodology that uses surrogate models in the form of neural networks to reduce the computation time of simulation-based optimization of a reference trajectory. Simulation-based optimization is necessary when there is no analytical form of the system accessible, only input-output data that can be used to create a surrogate model of the simulation. Like many high-fidelity simulations, this trajectory planning simulation is very nonlinear and computationally expensive, making it challenging to optimize iteratively. Through gradient descent optimization, our approach finds the optimal reference trajectory for landing a hypersonic vehicle. In contrast to the large datasets used to create the surrogate models in prior literature, our methodology is specifically designed to minimize the number of simulation executions required by the gradient descent optimizer. We demonstrated this methodology to be more efficient than the standard practice of hand-tuning the inputs through trial-and-error or randomly sampling the input parameter space. Due to the intelligently selected input values to the simulation, our approach yields better simulation outcomes that are achieved more rapidly and to a higher degree of accuracy. Optimizing the hypersonic vehicle's reference trajectory is very challenging due to the simulation's extreme nonlinearity, but even so, this novel approach found a 74% better-performing reference trajectory compared to nominal, and the numerical results clearly show a substantial reduction in computation time for designing future trajectories.