Zeroth order optimization is a central topic in optimization and related fields. Algorithms for zeroth order optimization find important real-world applications, since often times in practice, we cannot directly access the derivatives of the objective function. To optimize the function in such scenarios, one can estimate the gradient/Hessian first and deploy first/second order algorithms with the estimated derivatives. Previously, many authors have considered this problem. Yet stochastic zeroth order methods for Łojasiewicz functions have not been carefully investigated (See Section 2 for more discussion).

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable PDEconstrained layer that can be incorporated into any NN architecture. Our method leverages differentiable optimization and the implicit function theorem to effectively enforce physical constraints. Inspired by dictionary learning, our model learns a family of functions, each of which defines a mapping from PDE parameters to PDE solutions. At inference time, the model finds an optimal linear combination of the functions in the learned family by solving a PDE-constrained optimization problem. Our method provides continuous solutions over the domain of interest that accurately satisfy desired physical constraints. Our results show that incorporating hard constraints directly into the NN architecture achieves much lower test error when compared to training on an unconstrained objective. Methods based on neural networks (NNs) have shown promise in recent years for physics-based problems (Raissi et al., 2019; Li et al., 2020; Lu et al., 2021a; Li et al., 2021). Current NN methods use two main training approaches to solve Equation 1. The first approach is strictly supervised learning, and the NN is trained on PDE solution data using a regression loss (Lu et al., 2021a; Li et al., 2020). In this case, the feasibility problem only appears through the data; it does not appear explicitly in the training algorithm. The second approach (Raissi et al., 2019) aims to solve the feasibility problem in Equation 1 by considering the relaxation, min E This second approach does not require access to any PDE solution data. These two approaches have also been combined by having both a data fitting loss and the PDE residual loss (Li et al., 2021).

Manufacturing advanced materials and products with a specific property or combination of properties is often warranted. To achieve that it is crucial to find out the optimum recipe or processing conditions that can generate the ideal combination of these properties. Most of the time, a sufficient number of experiments are needed to generate a Pareto front. However, manufacturing experiments are usually costly and even conducting a single experiment can be a time-consuming process. So, it's critical to determine the optimal location for data collection to gain the most comprehensive understanding of the process. Sequential learning is a promising approach to actively learn from the ongoing experiments, iteratively update the underlying optimization routine, and adapt the data collection process on the go. This paper presents a novel data-driven Bayesian optimization framework that utilizes sequential learning to efficiently optimize complex systems with multiple conflicting objectives. Additionally, this paper proposes a novel metric for evaluating multi-objective data-driven optimization approaches. This metric considers both the quality of the Pareto front and the amount of data used to generate it. The proposed framework is particularly beneficial in practical applications where acquiring data can be expensive and resource intensive. To demonstrate the effectiveness of the proposed algorithm and metric, the algorithm is evaluated on a manufacturing dataset. The results indicate that the proposed algorithm can achieve the actual Pareto front while processing significantly less data. It implies that the proposed data-driven framework can lead to similar manufacturing decisions with reduced costs and time.

This paper considers the problem of learning safe policies in the context of reinforcement learning (RL). In particular, we consider the notion of probabilistic safety. This is, we aim to design policies that maintain the state of the system in a safe set with high probability. This notion differs from cumulative constraints often considered in the literature. The challenge of working with probabilistic safety is the lack of expressions for their gradients. Indeed, policy optimization algorithms rely on gradients of the objective function and the constraints. To the best of our knowledge, this work is the first one providing such explicit gradient expressions for probabilistic constraints. It is worth noting that the gradient of this family of constraints can be applied to various policy-based algorithms. We demonstrate empirically that it is possible to handle probabilistic constraints in a continuous navigation problem.

Trajectory generation in confined environment is crucial for wide adoption of intelligent robot manipulators. In this paper, we propose a novel motion planning approach for redundant robot arms that uses a hybrid optimization framework to search for optimal trajectories in both the configuration space and null space, generating high-quality trajectories that satisfy task constraints and collision avoidance constraints, while also avoiding local optima for incremental planners. Our approach is evaluated in an onsite polishing scenario with various robot and workpiece configurations, demonstrating significant improvements in trajectory quality compared to existing methods. The proposed approach has the potential for broad applications in industrial tasks involving redundant robot arms.

Backdoors pose a serious threat to machine learning, as they can compromise the integrity of security-critical systems, such as self-driving cars. While different defenses have been proposed to address this threat, they all rely on the assumption that the hardware on which the learning models are executed during inference is trusted. In this paper, we challenge this assumption and introduce a backdoor attack that completely resides within a common hardware accelerator for machine learning. Outside of the accelerator, neither the learning model nor the software is manipulated, so that current defenses fail. To make this attack practical, we overcome two challenges: First, as memory on a hardware accelerator is severely limited, we introduce the concept of a minimal backdoor that deviates as little as possible from the original model and is activated by replacing a few model parameters only. Second, we develop a configurable hardware trojan that can be provisioned with the backdoor and performs a replacement only when the specific target model is processed. We demonstrate the practical feasibility of our attack by implanting our hardware trojan into the Xilinx Vitis AI DPU, a commercial machine-learning accelerator. We configure the trojan with a minimal backdoor for a traffic-sign recognition system. The backdoor replaces only 30 (0.069%) model parameters, yet it reliably manipulates the recognition once the input contains a backdoor trigger. Our attack expands the hardware circuit of the accelerator by 0.24% and induces no run-time overhead, rendering a detection hardly possible. Given the complex and highly distributed manufacturing process of current hardware, our work points to a new threat in machine learning that is inaccessible to current security mechanisms and calls for hardware to be manufactured only in fully trusted environments.

Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem.

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep Reinforcement Learning (DRL) has been increasingly employed to solve TSP due to its high inference efficiency. Nevertheless, most of existing end-to-end DRL algorithms only perform well on small TSP instances and can hardly generalize to large scale because of the drastically soaring memory consumption and computation time along with the enlarging problem scale. In this paper, we propose a novel end-to-end DRL approach, referred to as Pointerformer, based on multi-pointer Transformer. Particularly, Pointerformer adopts both reversible residual network in the encoder and multi-pointer network in the decoder to effectively contain memory consumption of the encoder-decoder architecture. To further improve the performance of TSP solutions, Pointerformer employs both a feature augmentation method to explore the symmetries of TSP at both training and inference stages as well as an enhanced context embedding approach to include more comprehensive context information in the query. Extensive experiments on a randomly generated benchmark and a public benchmark have shown that, while achieving comparative results on most small-scale TSP instances as SOTA DRL approaches do, Pointerformer can also well generalize to large-scale TSPs.

Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the upper and the lower objectives correspond to empirical risk minimization problems and therefore have a sum structure. In this context, we propose a bilevel extension of the celebrated SARAH algorithm. We demonstrate that the algorithm requires $\mathcal{O}((n+m)^{\frac12}\varepsilon^{-1})$ gradient computations to achieve $\varepsilon$-stationarity with $n+m$ the total number of samples, which improves over all previous bilevel algorithms. Moreover, we provide a lower bound on the number of oracle calls required to get an approximate stationary point of the objective function of the bilevel problem. This lower bound is attained by our algorithm, which is therefore optimal in terms of sample complexity.

This paper proposes a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field's current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. As a result, in this work, we take the privilege to perform an early exploration of applying a quantum computing algorithm to this important image enhancement problem, i.e., SISR. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This work demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using quantum annealers accessed via the D-Wave Leap platform. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.