Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for general conic optimization remain underdeveloped. To fill this gap, we introduce a stochastic interior-point method (SIPM) framework for general conic optimization, along with four novel SIPM variants leveraging distinct stochastic gradient estimators. Under mild assumptions, we establish the global convergence rates of our proposed SIPMs, which, up to a logarithmic factor, match the best-known rates in stochastic unconstrained optimization. Finally, our numerical experiments on robust linear regression, multi-task relationship learning, and clustering data streams demonstrate the effectiveness and efficiency of our approach.

Foundation model (FM) powered agent services are regarded as a promising solution to develop intelligent and personalized applications for advancing toward Artificial General Intelligence (AGI). To achieve high reliability and scalability in deploying these agent services, it is essential to collaboratively optimize computational and communication resources, thereby ensuring effective resource allocation and seamless service delivery. In pursuit of this vision, this paper proposes a unified framework aimed at providing a comprehensive survey on deploying FM-based agent services across heterogeneous devices, with the emphasis on the integration of model and resource optimization to establish a robust infrastructure for these services. Particularly, this paper begins with exploring various low-level optimization strategies during inference and studies approaches that enhance system scalability, such as parallelism techniques and resource scaling methods. The paper then discusses several prominent FMs and investigates research efforts focused on inference acceleration, including techniques such as model compression and token reduction. Moreover, the paper also investigates critical components for constructing agent services and highlights notable intelligent applications. Finally, the paper presents potential research directions for developing real-time agent services with high Quality of Service (QoS).

Safe reinforcement learning (RL) is a popular and versatile paradigm to learn reward-maximizing policies with safety guarantees. Previous works tend to express the safety constraints in an expectation form due to the ease of implementation, but this turns out to be ineffective in maintaining safety constraints with high probability. To this end, we move to the quantile-constrained RL that enables a higher level of safety without any expectation-form approximations. We directly estimate the quantile gradients through sampling and provide the theoretical proofs of convergence. Then a tilted update strategy for quantile gradients is implemented to compensate the asymmetric distributional density, with a direct benefit of return performance. Experiments demonstrate that the proposed model fully meets safety requirements (quantile constraints) while outperforming the state-of-the-art benchmarks with higher return.

Online advertising has become one of the most successful business models of the internet era. Impression opportunities are typically allocated through real-time auctions, where advertisers bid to secure advertisement slots. Deciding the best bid for an impression opportunity is challenging, due to the stochastic nature of user behavior and the variability of advertisement traffic over time. In this work, we propose a framework for training auto-bidding agents in multi-slot second-price auctions to maximize acquisitions (e.g., clicks, conversions) while adhering to budget and cost-per-acquisition (CPA) constraints. We exploit the insight that, after an advertisement campaign concludes, determining the optimal bids for each impression opportunity can be framed as a multiple-choice knapsack problem (MCKP) with a nonlinear objective. We propose an "oracle" algorithm that identifies a near-optimal combination of impression opportunities and advertisement slots, considering both past and future advertisement traffic data. This oracle solution serves as a training target for a student network which bids having access only to real-time information, a method we term Oracle Imitation Learning (OIL). Through numerical experiments, we demonstrate that OIL achieves superior performance compared to both online and offline reinforcement learning algorithms, offering improved sample efficiency. Notably, OIL shifts the complexity of training auto-bidding agents from crafting sophisticated learning algorithms to solving a nonlinear constrained optimization problem efficiently.

How emotions are expressed depends on the context and domain. On X (formerly Twitter), for instance, an author might simply use the hashtag #anger, while in a news headline, emotions are typically written in a more polite, indirect manner. To enable conditional text generation models to create emotionally connotated texts that fit a domain, users need to have access to a parameter that allows them to choose the appropriate way to express an emotion. To achieve this, we introduce MOPO, a Multi-Objective Prompt Optimization methodology. MOPO optimizes prompts according to multiple objectives (which correspond here to the output probabilities assigned by emotion classifiers trained for different domains). In contrast to single objective optimization, MOPO outputs a set of prompts, each with a different weighting of the multiple objectives. Users can then choose the most appropriate prompt for their context. We evaluate MOPO using three objectives, determined by various domain-specific emotion classifiers. MOPO improves performance by up to 15 pp across all objectives with a minimal loss (1-2 pp) for any single objective compared to single-objective optimization. These minor performance losses are offset by a broader generalization across multiple objectives - which is not possible with single-objective optimization. Additionally, MOPO reduces computational requirements by simultaneously optimizing for multiple objectives, eliminating separate optimization procedures for each objective.

When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional BO methods still suffer from the curse of dimensionality, highlighting the need for further improvements. In this work, we introduce BOIDS, a novel high-dimensional BO algorithm that guides optimization by a sequence of one-dimensional direction lines using a novel tailored line-based optimization procedure. To improve the efficiency, we also propose an adaptive selection technique to identify most optimal lines for each round of line-based optimization. Additionally, we incorporate a subspace embedding technique for better scaling to high-dimensional spaces. We further provide theoretical analysis of our proposed method to analyze its convergence property. Our extensive experimental results show that BOIDS outperforms state-of-the-art baselines on various synthetic and real-world benchmark problems.

Geomagnetic navigation leverages the ubiquitous Earth's magnetic signals to navigate missions, without dependence on GPS services or pre-stored geographic maps. It has drawn increasing attention and is promising particularly for long-range navigation into unexplored areas. Current geomagnetic navigation studies are still in the early stages with simulations and computational validations, without concrete efforts to develop cost-friendly test platforms that can empower deployment and experimental analysis of the developed approaches. This paper presents a hardware-in-the-loop simulation testbed to support geomagnetic navigation experimentation. Our testbed is dedicated to synthesizing geomagnetic field environment for the navigation. We develop the software in the testbed to simulate the dynamics of the navigation environment, and we build the hardware to generate the physical magnetic field, which follows and aligns with the simulated environment. The testbed aims to provide controllable magnetic field that can be used to experiment with geomagnetic navigation in labs, thus avoiding real and expensive navigation experiments, e.g., in the ocean, for validating navigation prototypes. We build the testbed with off-the-shelf hardware in an unshielded environment to reduce cost. We also develop the field generation control and hardware parameter optimization for quality magnetic field generation. We conduct a detailed performance analysis to show the quality of the field generation by the testbed, and we report the experimental results on performance indicators, including accuracy, uniformity, stability, and convergence of the generated field towards the target geomagnetic environment.

Artificial intelligence (AI) is driving transformative changes across numerous fields, revolutionizing conventional processes and creating new opportunities for innovation. The development of mechatronic systems is undergoing a similar transformation. Over the past decade, modeling, simulation, and optimization techniques have become integral to the design process, paving the way for the adoption of AI-based methods. In this paper, we examine the potential for integrating AI into the engineering design process, using the V-model from the VDI guideline 2206, considered the state-of-the-art in product design, as a foundation. We identify and classify AI methods based on their suitability for specific stages within the engineering product design workflow. Furthermore, we present a series of application examples where AI-assisted design has been successfully implemented by the authors. These examples, drawn from research projects within the DFG Priority Program \emph{SPP~2353: Daring More Intelligence - Design Assistants in Mechanics and Dynamics}, showcase a diverse range of applications across mechanics and mechatronics, including areas such as acoustics and robotics.

Data rebalancing techniques, including oversampling and undersampling, are a common approach to addressing the challenges of imbalanced data. To tackle unresolved problems related to both oversampling and undersampling, we propose a new undersampling approach that: (i) avoids the pitfalls of noise and overlap caused by synthetic data and (ii) avoids the pitfall of under-fitting caused by random undersampling. Instead of undersampling majority data randomly, our method undersamples datapoints based on their ability to improve model loss. Using improved model loss as a proxy measurement for classification performance, our technique assesses a datapoint's impact on loss and rejects those unable to improve it. In so doing, our approach rejects majority datapoints redundant to datapoints already accepted and, thereby, finds an optimal subset of majority training data for classification. The accept/reject component of our algorithm is motivated by a bilevel optimization problem uniquely formulated to identify the optimal training set we seek. Experimental results show our proposed technique with F1 scores up to 10% higher than state-of-the-art methods.

We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum up to 1 condition; and (C4) the only min or only max oerator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions.