Designing molecules with desirable properties, such as drug-likeliness and high binding affinities towards protein targets, is a challenging problem. In this paper, we propose the Dual-Space Optimization (DSO) method that integrates latent space sampling and data space selection to solve this problem. DSO iteratively updates a latent space generative model and a synthetic dataset in an optimization process that gradually shifts the generative model and the synthetic data towards regions of desired property values. Our generative model takes the form of a Latent Prompt Transformer (LPT) where the latent vector serves as the prompt of a causal transformer. Our extensive experiments demonstrate effectiveness of the proposed method, which sets new performance benchmarks across single-objective, multi-objective and constrained molecule design tasks.

We investigate the vulnerability of computer-vision-based signal classifiers to adversarial perturbations of their inputs, where the signals and perturbations are subject to physical constraints. We consider a scenario in which a source and interferer emit signals that propagate as waves to a detector, which attempts to classify the source by analyzing the spectrogram of the signal it receives using a pre-trained neural network. By solving PDE-constrained optimization problems, we construct interfering signals that cause the detector to misclassify the source even though the perturbations to the spectrogram of the received signal are nearly imperceptible. Though such problems can have millions of decision variables, we introduce methods to solve them efficiently. Our experiments demonstrate that one can compute effective and physically realizable adversarial perturbations for a variety of machine learning models under various physical conditions.

Bayesian optimization is a popular framework for efficiently finding high-quality solutions to difficult problems based on limited prior information. As a rule, these algorithms operate by iteratively choosing what to try next until some predefined budget has been exhausted. We investigate replacing this de facto stopping rule with an $(\epsilon, \delta)$-criterion: stop when a solution has been found whose value is within $\epsilon > 0$ of the optimum with probability at least $1 - \delta$ under the model. Given access to the prior distribution of problems, we show how to verify this condition in practice using a limited number of draws from the posterior. For Gaussian process priors, we prove that Bayesian optimization with the proposed criterion stops in finite time and returns a point that satisfies the $(\epsilon, \delta)$-criterion under mild assumptions. These findings are accompanied by extensive empirical results which demonstrate the strengths and weaknesses of this approach.

We introduce a framework for benchmarking optimizers according to multiple criteria over various test functions. Based on a recently introduced union-free generic depth function for partial orders/rankings, it fully exploits the ordinal information and allows for incomparability. Our method describes the distribution of all partial orders/rankings, avoiding the notorious shortcomings of aggregation. This permits to identify test functions that produce central or outlying rankings of optimizers and to assess the quality of benchmarking suites. Despite its importance for machine learning research, there is no broad agreement on how to compare optimization algorithms on benchmark suites with regard to multiple criteria, see Hansen et al. (2022) for instance. This is particularly relevant for multi-objective optimization, which has diverse applications ranging from reinforcement learning (Basaklar et al., 2023; Zhu et al., 2023) to representation learning (Gu et al., 2023), neural architecture search (Lu et al., 2019) and large language models (Zhou et al., 2023). But such comparisons also arise when single-objective optimizers are evaluated with respect to several metrics, see Sivaprasad et al. (2020); Mattson et al. (2020); Dahl et al. (2023). A popular example is the duality of fixed-budget (performance) and fixed-target (speed) evaluation of deep learning optimizers, see e.g. In this work, we propose a novel framework for comparing optimizers with respect to multiple criteria over a benchmarking suite of test functions.

In today's information age, the rapidly increasing scale and complexity of data pose unprecedented challenges to traditional data analysis and machine learning algorithms [1-4]. Feature selection, a crucial research area in data mining, aims to identify the optimal subset of features, reducing the dimensionality of high-dimensional datasets and thereby enhancing the performance of learning algorithms [5-7]. Feature selection methods are commonly categorized into three types: filter, wrapper, and embedded methods [8]. Filter methods evaluate features based on predefined rules or criteria without involving learning algorithms [9]. Examples include information gain (IG) [10], maximum relevance minimum redundancy (mRMR) [11], correlation coefficient (CC) [12], Fisher [13], conditional mutual information maximization criterion (CMIM) [14], and ReliefF [15]. Wrapper methods generate various feature subsets and use learning algorithms to evaluate them, aiming to find the globally optimal subset by maximizing or minimizing an objective function [16]. In recent years, embedded methods have gained widespread attention. Wu et al. [17] introduced a supervised feature selection method, Feature Selection with Orthogonal Regression (FSOR), employing Generalized Power Iteration (GPI) and the Augmented Lagrangian Multiplier method to solve the objective function and evaluate features. Nie et al. [18] developed a Robust Feature Selection (RFS) method that uses the 2

Significantly simplifying the creation of optimization models for real-world business problems has long been a major goal in applying mathematical optimization more widely to important business and societal decisions. The recent capabilities of Large Language Models (LLMs) present a timely opportunity to achieve this goal. Therefore, we propose research at the intersection of LLMs and optimization to create a Decision Optimization CoPilot (DOCP) - an AI tool designed to assist any decision maker, interacting in natural language to grasp the business problem, subsequently formulating and solving the corresponding optimization model. This paper outlines our DOCP vision and identifies several fundamental requirements for its implementation. We describe the state of the art through a literature survey and experiments using ChatGPT. We show that a) LLMs already provide substantial novel capabilities relevant to a DOCP, and b) major research challenges remain to be addressed. We also propose possible research directions to overcome these gaps. We also see this work as a call to action to bring together the LLM and optimization communities to pursue our vision, thereby enabling much more widespread improved decision-making.

The advancement in cyber-physical systems has opened a new way in disaster management and rescue operations. The usage of UAVs is very promising in this context. UAVs, mainly quadcopters, are small in size and their payload capacity is limited. A single UAV can not traverse the whole area. Hence multiple UAVs or swarms of UAVs come into the picture managing the entire payload in a modular and equiproportional manner. In this work we have explored a vast topic related to UAVs. Among the UAVs quadcopter is the main focus. We explored the types of quadcopters, their flying strategy,their communication protocols, architecture and controlling techniques, followed by the swarm behaviour in nature and UAVs. Swarm behaviour and a few swarm optimization algorithms has been explored here. Swarm architecture and communication in between swarm UAV networks also got a special attention in our work. In disaster management the UAV swarm network must have to search a large area. And for this proper path planning algorithm is required. We have discussed the existing path planning algorithm, their advantages and disadvantages in great detail. Formation maintenance of the swarm network is an important issue which has been explored through leader-follower technique. The wireless path loss model has been modelled using friis and ground ray reflection model. Using this path loss models we have managed to create the link budget and simulate the variation of communication link performance with the variation of distance.

With the rising popularity of the internet and the widespread use of networks and information systems via the cloud and data centers, the privacy and security of individuals and organizations have become extremely crucial. In this perspective, encryption consolidates effective technologies that can effectively fulfill these requirements by protecting public information exchanges. To achieve these aims, the researchers used a wide assortment of encryption algorithms to accommodate the varied requirements of this field, as well as focusing on complex mathematical issues during their work to substantially complicate the encrypted communication mechanism. as much as possible to preserve personal information while significantly reducing the possibility of attacks. Depending on how complex and distinct the requirements established by these various applications are, the potential of trying to break them continues to occur, and systems for evaluating and verifying the cryptographic algorithms implemented continue to be necessary. The best approach to analyzing an encryption algorithm is to identify a practical and efficient technique to break it or to learn ways to detect and repair weak aspects in algorithms, which is known as cryptanalysis. Experts in cryptanalysis have discovered several methods for breaking the cipher, such as discovering a critical vulnerability in mathematical equations to derive the secret key or determining the plaintext from the ciphertext. There are various attacks against secure cryptographic algorithms in the literature, and the strategies and mathematical solutions widely employed empower cryptanalysts to demonstrate their findings, identify weaknesses, and diagnose maintenance failures in algorithms.

While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO) optimizers, recently proposed to address this issue, only require forward passes during training, making them more memory-friendly. However, the quality of gradient estimates in zeroth order optimization often depends on the data dimensionality, potentially explaining why MeZO still exhibits significant performance drops compared to standard fine-tuning across various tasks. Inspired by the success of Parameter-Efficient Fine-Tuning (PEFT), this paper introduces Sparse MeZO, a novel memory-efficient zeroth-order optimization approach that applies ZO only to a carefully chosen subset of parameters. We propose a simple yet effective parameter selection scheme that yields significant performance gains with Sparse-MeZO. Additionally, we develop a memory-optimized implementation for sparse masking, ensuring the algorithm requires only inference-level memory consumption, allowing Sparse-MeZO to fine-tune LLaMA-30b on a single A100 GPU. Experimental results illustrate that Sparse-MeZO consistently improves both performance and convergence speed over MeZO without any overhead. For example, it achieves a 9\% absolute accuracy improvement and 3.5x speedup over MeZO on the RTE task.

Constrained Markov decision processes (CMDPs) are a common way to model safety constraints in reinforcement learning. State-of-the-art methods for efficiently solving CMDPs are based on primal-dual algorithms. For these algorithms, all currently known regret bounds allow for error cancellations -- one can compensate for a constraint violation in one round with a strict constraint satisfaction in another. This makes the online learning process unsafe since it only guarantees safety for the final (mixture) policy but not during learning. As Efroni et al. (2020) pointed out, it is an open question whether primal-dual algorithms can provably achieve sublinear regret if we do not allow error cancellations. In this paper, we give the first affirmative answer. We first generalize a result on last-iterate convergence of regularized primal-dual schemes to CMDPs with multiple constraints. Building upon this insight, we propose a model-based primal-dual algorithm to learn in an unknown CMDP. We prove that our algorithm achieves sublinear regret without error cancellations.