Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.

Artificial Intelligence Generated Content (AIGC) has gained significant popularity for creating diverse content. Current AIGC models primarily focus on content quality within a centralized framework, resulting in a high service delay and negative user experiences. However, not only does the workload of an AIGC task depend on the AIGC model's complexity rather than the amount of data, but the large model and its multi-layer encoder structure also result in a huge demand for computational and memory resources. These unique characteristics pose new challenges in its modeling, deployment, and scheduling at edge networks. Thus, we model an offloading problem among edges for providing real AIGC services and propose LAD-TS, a novel Latent Action Diffusion-based Task Scheduling method that orchestrates multiple edge servers for expedited AIGC services. The LAD-TS generates a near-optimal offloading decision by leveraging the diffusion model's conditional generation capability and the reinforcement learning's environment interaction ability, thereby minimizing the service delays under multiple resource constraints. Meanwhile, a latent action diffusion strategy is designed to guide decision generation by utilizing historical action probability, enabling rapid achievement of near-optimal decisions. Furthermore, we develop DEdgeAI, a prototype edge system with a refined AIGC model deployment to implement and evaluate our LAD-TS method. DEdgeAI provides a real AIGC service for users, demonstrating up to 29.18% shorter service delays than the current five representative AIGC platforms. We release our open-source code at https://github.com/ChangfuXu/DEdgeAI/.

We present a novel approach to enhance the performance of sampling-based Model Predictive Control (MPC) in constrained optimization by leveraging products of experts. Our methodology divides the main problem into two components: one focused on optimality and the other on feasibility. By combining the solutions from each component, represented as distributions, we apply products of experts to implement a project-then-sample strategy. In this strategy, the optimality distribution is projected into the feasible area, allowing for more efficient sampling. This approach contrasts with the traditional sample-then-project method, leading to more diverse exploration and reducing the accumulation of samples on the boundaries. We demonstrate an effective implementation of this principle using a tensor train-based distribution model, which is characterized by its non-parametric nature, ease of combination with other distributions at the task level, and straightforward sampling technique. We adapt existing tensor train models to suit this purpose and validate the efficacy of our approach through experiments in various tasks, including obstacle avoidance, non-prehensile manipulation, and tasks involving staying on manifolds. Our experimental results demonstrate that the proposed method consistently outperforms known baselines, providing strong empirical support for its effectiveness.

Modular autonomous vehicles (MAVs) represent a transformative paradigm in the rapidly advancing field of autonomous vehicle technology. The integration of modularity offers numerous advantages, poised to reshape urban mobility systems and foster innovation in this emerging domain. Although publications on MAVs have only gained traction in the past five years, these pioneering efforts are critical for envisioning the future of modular mobility. This work provides a comprehensive review of industry and academic contributions to MAV development up to 2024, encompassing conceptualization, design, and applications in both passenger and logistics transport. The review systematically defines MAVs and outlines their technical framework, highlighting groundbreaking efforts in vehicular conceptualization, system design, and business models by the automotive industry and emerging mobility service providers. It also synthesizes academic research on key topics, including passenger and logistics transport, and their integration within future mobility ecosystems. The review concludes by identifying challenges, summarizing the current state of the art, and proposing future research directions to advance the development of modular autonomous mobility systems.

Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic principle introduced in our earlier work--in order to adapt coupling arguments to the Kullback-Leibler (KL) divergence. Our framework combine the strengths of two previously disparate approaches: local error analysis and Girsanov's theorem. Akin to the former, it yields tight bounds by incorporating the so-called weak error, and is user-friendly in that it only requires easily verified local assumptions; and akin to the latter, it yields KL divergence guarantees and applies beyond Wasserstein contractivity. We apply this framework to the problem of sampling from a target distribution $\pi$. Here, the two stochastic processes are the Langevin diffusion and an algorithmic discretization thereof. Our framework provides a unified analysis when $\pi$ is assumed to be strongly log-concave (SLC), weakly log-concave (WLC), or to satisfy a log-Sobolev inequality (LSI). Among other results, this yields KL guarantees for the randomized midpoint discretization of the Langevin diffusion. Notably, our result: (1) yields the optimal $\tilde O(\sqrt d/\epsilon)$ rate in the SLC and LSI settings; (2) is the first result to hold beyond the 2-Wasserstein metric in the SLC setting; and (3) is the first result to hold in \emph{any} metric in the WLC and LSI settings.

We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the Gaussian-smoothed $f_N$ with stochastic approximations. Under mild conditions on $f$, for any $\delta>0$, we prove that with a sufficiently large power $N_\delta$, this method converges to a solution in the $\delta$-neighborhood of $f$'s global optimum point. The convergence rate is $O(d^2\sigma^4\varepsilon^{-2})$, which is faster than both the standard and single-loop homotopy methods if $\sigma$ is pre-selected to be in $(0,1)$. In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.

This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM is applied to black-box combinatorial optimization problems using factorization machine with quantum annealing (FMQA). It is anticipated that the optimization performance of FMQA will be enhanced through an implementation of the warm-start method. Nevertheless, the optimal initialization method for leveraging the warm-start approach in FMQA remains undetermined. Consequently, the present study compares initialization methods based on random initialization and low-rank approximation, and then identifies a suitable one for use with warm-start in FMQA through numerical experiments. Furthermore, the properties of the initialization method by the low-rank approximation for the FM are analyzed using random matrix theory, demonstrating that the approximation accuracy of the proposed method is not significantly influenced by the specific Ising model under consideration. The findings of this study will facilitate advancements of research in the field of black-box combinatorial optimization through the use of Ising machines.

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

The exponential increase in orbital debris and active satellites will lead to congested orbits, necessitating more frequent collision avoidance maneuvers by satellites. To minimize fuel consumption while ensuring the safety of satellites, enforcing a chance constraint, which poses an upper bound in collision probability with debris, can serve as an intuitive safety measure. However, accurately evaluating collision probability, which is critical for the effective implementation of chance constraints, remains a non-trivial task. This difficulty arises because uncertainty propagation in nonlinear orbit dynamics typically provides only limited information, such as finite samples or moment estimates about the underlying arbitrary non-Gaussian distributions. Furthermore, even if the full distribution were known, it remains unclear how to effectively compute chance constraints with such non-Gaussian distributions. To address these challenges, we propose a distributionally robust chance-constrained collision avoidance algorithm that provides a sufficient condition for collision probabilities under limited information about the underlying non-Gaussian distribution. Our distributionally robust approach satisfies the chance constraint for all debris position distributions sharing a given mean and covariance, thereby enabling the enforcement of chance constraints with limited distributional information. To achieve computational tractability, the chance constraint is approximated using a Conditional Value-at-Risk (CVaR) constraint, which gives a conservative and tractable approximation of the distributionally robust chance constraint. We validate our algorithm on a real-world inspired satellite-debris conjunction scenario with different uncertainty propagation methods and show that our controller can effectively avoid collisions.

To operate autonomously, such systems and agents often rely on automated controllers, which are designed to translate a stream of sensor observations or system states into a stream of commands (controls) to execute, in order to maintain a safe behavior, or robustly perform a specified task. Traditionally, controllers had to be expertly designed, e.g., by meticulously considering physical and mechanical aspects of the system. In recent years, however, computational Neural-Network (NN) controllers have been experiencing tremendous popularity. These can handle complex, highdimensional sensor observations, such as images, and enable effective control of highly-complex dynamical systems, such as racing cars, snake robots, high Degree-of-Freedom (DoF) manipulators, and dexterous robot hands, which have been a great challenge in the controls and robotics communities. Such controllers are typically built ("trained") by compressing numerous examples ("training data") using statistical machine learning techniques, in an attempt to yield a certain behavior. Common techniques include Reinforcement Learning (RL) [2], from repeated trial-and-error control attempts, until apparent convergence to a desired behavior, and Imitation Learning [3], from demonstrations of either a human operator or a traditional controller. Unfortunately, such learning methods generally do not provide a guarantee that the resulting controller will robustly exhibit the desired behavior; hence, relying on these controllers can cause the system to suffer from unpredictable or unsafe behavior on edge cases. While there has been a recent efforts to advance controller synthesis [4-6]--that is, the automated creation of controllers that are guaranteed to comply to given specification by design--these usually fail to scale beyond simple scenarios; and, more importantly, are only certified in relation to the assumed (and often simplified) system models.