Heuristics are commonly used to tackle diverse search and optimization problems. Design heuristics usually require tedious manual crafting with domain knowledge. Recent works have incorporated large language models (LLMs) into automatic heuristic search leveraging their powerful language and coding capacity. However, existing research focuses on the optimal performance on the target problem as the sole objective, neglecting other criteria such as efficiency and scalability, which are vital in practice. To tackle this challenge, we propose to model heuristic search as a multi-objective optimization problem and consider introducing other practical criteria beyond optimal performance. Due to the complexity of the search space, conventional multi-objective optimization methods struggle to effectively handle multi-objective heuristic search. We propose the first LLM-based multi-objective heuristic search framework, Multi-objective Evolution of Heuristic (MEoH), which integrates LLMs in a zero-shot manner to generate a non-dominated set of heuristics to meet multiple design criteria. We design a new dominance-dissimilarity mechanism for effective population management and selection, which incorporates both code dissimilarity in the search space and dominance in the objective space. MEoH is demonstrated in two well-known combinatorial optimization problems: the online Bin Packing Problem (BPP) and the Traveling Salesman Problem (TSP). Results indicate that a variety of elite heuristics are automatically generated in a single run, offering more trade-off options than existing methods. It successfully achieves competitive or superior performance while improving efficiency up to 10 times. Moreover, we also observe that the multi-objective search introduces novel insights into heuristic design and leads to the discovery of diverse heuristics.

In many cases, adversarial attacks are based on specialized algorithms specifically dedicated to attacking automatic image classifiers. These algorithms perform well, thanks to an excellent ad hoc distribution of initial attacks. However, these attacks are easily detected due to their specific initial distribution. We therefore consider other black-box attacks, inspired from generic black-box optimization tools, and in particular the log-normal algorithm. We apply the log-normal method to the attack of fake detectors, and get successful attacks: importantly, these attacks are not detected by detectors specialized on classical adversarial attacks. Then, combining these attacks and deep detection, we create improved fake detectors.

This paper addresses the capacitated periodic review inventory control problem, focusing on a retailer managing multiple products with limited shared resources, such as storage or inbound labor at a facility. Specifically, this paper is motivated by the questions of (1) what does it mean to backtest a capacity control mechanism, (2) can we devise and backtest a capacity control mechanism that is compatible with recent advances in deep reinforcement learning for inventory management? First, because we only have a single historic sample path of Amazon's capacity limits, we propose a method that samples from a distribution of possible constraint paths covering a space of real-world scenarios. This novel approach allows for more robust and realistic testing of inventory management strategies. Second, we extend the exo-IDP (Exogenous Decision Process) formulation of Madeka et al. 2022 to capacitated periodic review inventory control problems and show that certain capacitated control problems are no harder than supervised learning. Third, we introduce a `neural coordinator', designed to produce forecasts of capacity prices, guiding the system to adhere to target constraints in place of a traditional model predictive controller. Finally, we apply a modified DirectBackprop algorithm for learning a deep RL buying policy and a training the neural coordinator. Our methodology is evaluated through large-scale backtests, demonstrating RL buying policies with a neural coordinator outperforms classic baselines both in terms of cumulative discounted reward and capacity adherence (we see improvements of up to 50% in some cases).

We consider the problem of finding the ``best'' approximation of an $n$-dimensional probability measure $\rho$ using a measure $\nu$ whose support is parametrized by $f : \mathbb{R}^m \to \mathbb{R}^n$ where $m < n$. We quantify the performance of the approximation with the Monge-Kantorovich $p$-cost (also called the Wasserstein $p$-cost) $\mathbb{W}_p^p(\rho, \nu)$, and constrain the complexity of the approximation by bounding the $W^{k,q}$ Sobolev norm of $f$, which acts as a ``budget.'' We may then reformulate the problem as minimizing a functional $\mathscr{J}_p(f)$ under a constraint on the Sobolev budget. We treat general $k \geq 1$ for the Sobolev differentiability order (though $q, m$ are chosen to restrict $W^{k,q}$ to the supercritical regime $k q > m$ to guarantee existence of optimizers). The problem is closely related to (but distinct from) principal curves with length constraints when $m=1, k = 1$ and smoothing splines when $k > 1$. New aspects and challenges arise from the higher order differentiability condition. We study the gradient of $\mathscr{J}_p$, which is given by a vector field along $f$ we call the barycenter field. We use it to construct improvements to a given $f$, which gives a nontrivial (almost) strict monotonicty relation between the functional $\mathscr{J}_p$ and the Sobolev budget. We also provide a natural discretization scheme and establish its consistency. We use this scheme to model a generative learning task; in particular, we demonstrate that adding a constraint like ours as a soft penalty yields substantial improvement in training a GAN to produce images of handwritten digits, with performance competitive with weight-decay.

Federated learning (FL) is a popular machine learning technique that enables multiple users to collaboratively train a model while maintaining the user data privacy. A significant challenge in FL is the communication bottleneck in the upload direction, and thus the corresponding energy consumption of the devices, attributed to the increasing size of the model/gradient. In this paper, we address this issue by proposing a zero-order (ZO) optimization method that requires the upload of a quantized single scalar per iteration by each device instead of the whole gradient vector. We prove its theoretical convergence and find an upper bound on its convergence rate in the non-convex setting, and we discuss its implementation in practical scenarios. Our FL method and the corresponding convergence analysis take into account the impact of quantization and packet dropping due to wireless errors. We show also the superiority of our method, in terms of communication overhead and energy consumption, as compared to standard gradient-based FL methods.

Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multi-qubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic methods such as Trotterization, variational quantum compilation (VQC) methods employ variational optimization to reduce gate costs while maintaining high accuracy. In this work, we explore the potential of a VQC scheme by making use of out-of-distribution generalization results in quantum machine learning (QML): By learning the action of a given many-body dynamics on a small data set of product states, we can obtain a unitary circuit that generalizes to highly entangled states such as the Haar random states. The efficiency in training allows us to use tensor network methods to compress such time-evolved product states by exploiting their low entanglement features. Our approach exceeds state-of-the-art compilation results in both system size and accuracy in one dimension ($1$D). For the first time, we extend VQC to systems on two-dimensional (2D) strips with a quasi-1D treatment, demonstrating a significant resource advantage over standard Trotterization methods, highlighting the method's promise for advancing quantum simulation tasks on near-term quantum processors.

The Problem-oriented AutoML in Clustering (PoAC) framework introduces a novel, flexible approach to automating clustering tasks by addressing the shortcomings of traditional AutoML solutions. Conventional methods often rely on predefined internal Clustering Validity Indexes (CVIs) and static meta-features, limiting their adaptability and effectiveness across diverse clustering tasks. In contrast, PoAC establishes a dynamic connection between the clustering problem, CVIs, and meta-features, allowing users to customize these components based on the specific context and goals of their task. At its core, PoAC employs a surrogate model trained on a large meta-knowledge base of previous clustering datasets and solutions, enabling it to infer the quality of new clustering pipelines and synthesize optimal solutions for unseen datasets. Unlike many AutoML frameworks that are constrained by fixed evaluation metrics and algorithm sets, PoAC is algorithm-agnostic, adapting seamlessly to different clustering problems without requiring additional data or retraining. Experimental results demonstrate that PoAC not only outperforms state-of-the-art frameworks on a variety of datasets but also excels in specific tasks such as data visualization, and highlight its ability to dynamically adjust pipeline configurations based on dataset complexity.

Novel, functional structures at the nanoscale could be crucial for transforming a broad spectrum of economically significant processes into greener and more sustainable solutions. For instance, nanostructured materials hold the potential to significantly enhance the cost-effectiveness of fuel-cell devices [1], enable the creation of highly efficient quantum-dot LEDs [2], and pave the way for generating atom-precise efficient nanocatalysts for studying novel catalytic pathways in electrochemical applications [3, 4]. As performance is highly dependent on specific structural characteristics which often can not easily be resolved in lab experiments, computational chemistry - most often by using Density Functional Theory (DFT) based approaches - can be used to generate in-silico insights. Typical questions range from elucidating which feature of a given nanoparticle might improve catalytic performance to mechanistic explanations for key synthesis procedures, allowing tailored experiments to drive up experimental yields for optimal structures. Commonly, these questions are associated with finding energetically favorable configurations for the potential energy surface (PES) of a system, which is a property relevant to solving a wide range of problems in computational chemistry. The established methodology allows finding "docking" mechanisms between small molecules and large biomolecules, which is relevant for drug development [5]. Additionally, a large area of research revolves around the sensing of harmful gases by novel nanomaterials chosen according to their strength of interactions.

Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Currently, most methods are tailored to specific scenarios, and the efficiency of existing optimization and learning methods applicable to diverse scenarios is hindered by the complexity of modeling and data dependency, which limit their real-world applicability. To address these issues, this paper proposes a universal multi-vehicle cooperative decision-making method in structured roads with game theory. We transform the decision-making problem into a graph path searching problem within a way-point graph framework. The problem is formulated as a mixed-integer linear programming problem (MILP) first and transformed into a mixed-integer potential game (MIPG), which reduces the scope of problem and ensures that no player needs to sacrifice for the overall cost. Two Gauss-Seidel algorithms for cooperative decision-making are presented to solve the MIPG problem and obtain the Nash equilibrium solutions. Specifically, the sequential Gauss-Seidel algorithm for cooperative decision-making considers the varying degrees of CAV interactions and flexibility in adjustment strategies to determine optimization priorities, which reduces the frequency of ineffective optimizations. Experimental evaluations across various urban traffic scenarios with different topological structures demonstrate the effectiveness and efficiency of the proposed method compared with MILP and comparisons of different optimization sequences validate the efficiency of the sequential Gauss-Seidel algorithm for cooperative decision-making.

Human intelligence, the most evident and accessible form of source of reasoning, hosted by biological hardware, has evolved and been refined over thousands of years, positioning itself today to create new artificial forms and preparing to self--design their evolutionary path forward. Beginning with the advent of foundation models, the rate at which human and artificial intelligence interact with each other has surpassed any anticipated quantitative figures. The close engagement led to both bits of intelligence to be impacted in various ways, which naturally resulted in complex confluences that warrant close scrutiny. In the sequel, we shall explore the interplay between human and machine intelligence, focusing on the crucial role humans play in developing ethical, responsible, and robust intelligent systems. We slightly delve into interesting aspects of implementation inspired by the mechanisms underlying neuroscience and human cognition. Additionally, we propose future perspectives, capitalizing on the advantages of symbiotic designs to suggest a human-centered direction for next-generation AI development. We finalize this evolving document with a few thoughts and open questions yet to be addressed by the broader community.