In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.

The goal of multi-objective optimization (MOO) is to learn under multiple, potentially conflicting, objectives. One widely used technique to tackle MOO is through linear scalarization, where one fixed preference vector is used to combine the objectives into a single scalar value for optimization. However, recent work (Hu et al., 2024) has shown linear scalarization often fails to capture the non-convex regions of the Pareto Front, failing to recover the complete set of Pareto optimal solutions. In light of the above limitations, this paper focuses on Tchebycheff scalarization that optimizes for the worst-case objective. In particular, we propose an online mirror descent algorithm for Tchebycheff scalarization, which we call OMD-TCH. We show that OMD-TCH enjoys a convergence rate of $O(\sqrt{\log m/T})$ where $m$ is the number of objectives and $T$ is the number of iteration rounds. We also propose a novel adaptive online-to-batch conversion scheme that significantly improves the practical performance of OMD-TCH while maintaining the same convergence guarantees. We demonstrate the effectiveness of OMD-TCH and the adaptive conversion scheme on both synthetic problems and federated learning tasks under fairness constraints, showing state-of-the-art performance.

Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to identify models with optimal convergence rates and pinpoint essential parameters. Utilizing this model, we propose a Samplet-based approach to efficiently construct and train the Gaussian Processes, reducing the cubic computational complexity to a log-linear scale. This method facilitates optimal regression while maintaining efficient performance.

Passivity-based control is a cornerstone of control theory and an established design approach in robotics. Its strength is based on the passivity theorem, which provides a powerful interconnection framework for robotics. However, the design of passivity-based controllers and their optimal tuning remain challenging. We propose here an intuitive design approach for fully actuated robots, where the control action is determined by a `virtual-mechanism' as in classical virtual model control. The result is a robot whose controlled behavior can be understood in terms of physics. We achieve optimal tuning by applying algorithmic differentiation to ODE simulations of the rigid body dynamics. Overall, this leads to a flexible design and optimization approach: stability is proven by passivity of the virtual mechanism, while performance is obtained by optimization using algorithmic differentiation.

Optimizing the learning rate remains a critical challenge in machine learning, essential for achieving model stability and efficient convergence. The Vector Auxiliary Variable (VAV) algorithm introduces a novel energy-based self-adjustable learning rate optimization method designed for unconstrained optimization problems. It incorporates an auxiliary variable $r$ to facilitate efficient energy approximation without backtracking while adhering to the unconditional energy dissipation law. Notably, VAV demonstrates superior stability with larger learning rates and achieves faster convergence in the early stage of the training process. Comparative analyses demonstrate that VAV outperforms Stochastic Gradient Descent (SGD) across various tasks. This paper also provides rigorous proof of the energy dissipation law and establishes the convergence of the algorithm under reasonable assumptions. Additionally, $r$ acts as an empirical lower bound of the training loss in practice, offering a novel scheduling approach that further enhances algorithm performance.

Machine learning models deployed in sensitive areas such as healthcare must be interpretable to ensure accountability and fairness. However, learning such rule lists presents significant challenges. Existing methods based on combinatorial optimization require feature pre-discretization and impose restrictions on rule size. Neuro-symbolic methods use more scalable continuous optimization yet place similar pre-discretization constraints and suffer from unstable optimization. We formulate a continuous relaxation of the rule list learning problem that converges to a strict rule list through temperature annealing. Machine learning models are increasingly used in high-stakes applications such as healthcare (Deo, 2015), credit risk evaluation (Bhatore et al., 2020), and criminal justice (Lakkaraju & Rudin, 2017), where it is vital that each decision is fair and reasonable. Proxy measures such as Shapley values can give the illusion of interpretability, but are highly problematic as they can not faithfully represent a non-additive models decision process (Gosiewska & Biecek, 2019). Instead, Rudin (2019) argues that it is crucial to use inherently interpretable models, to create systems with human supervision in the loop (Kleinberg et al., 2018). For particularly sensitive domains such as stroke prediction or recidivism, so called Rule Lists are a popular choice (Letham et al., 2015) due to their fully transparent decision making. A rule list predicts based on nested "if-then-else" statements and naturally aligns with the human-decision making process. Each rule is active if its conditions are met, e.g. " if Thalassemia = normal Resting bps < 151 ", and carries a respective prediction, i.e. " then P ( Disease) = 10% ".

This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model predictive control. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Maximum Principle. The proposed framework allows for customization of transient behavior, addressing limitations of existing methods. The Taylored Multi-Faceted Approach for Neural ODE and Optimal Control (T-mano) architecture facilitates training and ensures accurate state estimation. Optimal control strategies are demonstrated for both linear and non-linear dynamical systems.

Glitch tokens in Large Language Models (LLMs) can trigger unpredictable behaviors, threatening model reliability and safety. Existing detection methods rely on predefined patterns, limiting their adaptability across diverse LLM architectures. We propose GlitchMiner, a gradient-based discrete optimization framework that efficiently identifies glitch tokens by introducing entropy as a measure of prediction uncertainty and employing a local search strategy to explore the token space. Experiments across multiple LLM architectures demonstrate that GlitchMiner outperforms existing methods in detection accuracy and adaptability, achieving over 10% average efficiency improvement. This method enhances vulnerability assessment in LLMs, contributing to the development of more robust and reliable applications.

To tackle the twin challenges of limited battery life and lengthy charging durations in electric vehicles (EVs), this paper introduces an Energy-efficient Hybrid Model Predictive Planner (EHMPP), which employs an energy-saving optimization strategy. EHMPP focuses on refining the design of the motion planner to be seamlessly integrated with the existing automatic driving algorithms, without additional hardware. It has been validated through simulation experiments on the Prescan, CarSim, and Matlab platforms, demonstrating that it can increase passive recovery energy by 11.74\% and effectively track motor speed and acceleration at optimal power. To sum up, EHMPP not only aids in trajectory planning but also significantly boosts energy efficiency in autonomous EVs.

This paper presents a hierarchical, performance-based framework for the design optimization of multi-fingered soft grippers. To address the need for systematically defined performance indices, the framework structures the optimization process into three integrated layers: Task Space, Motion Space, and Design Space. In the Task Space, performance indices are defined as core objectives, while the Motion Space interprets these into specific movement primitives. Finally, the Design Space applies parametric and topological optimization techniques to refine the geometry and material distribution of the system, achieving a balanced design across key performance metrics. The framework's layered structure enhances SG design, ensuring balanced performance and scalability for complex tasks and contributing to broader advancements in soft robotics.