We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

High-fidelity personalized human musculoskeletal models are crucial for simulating realistic behavior of physically coupled human-robot interactive systems and verifying their safety-critical applications in simulations before actual deployment, such as human-robot co-transportation and rehabilitation through robotic exoskeletons. Identifying subject-specific Hill-type muscle model parameters and bone dynamic parameters is essential for a personalized musculoskeletal model, but very challenging due to the difficulty of measuring the internal biomechanical variables in vivo directly, especially the joint torques. In this paper, we propose using Differentiable MusculoSkeletal Model (Diff-MSM) to simultaneously identify its muscle and bone parameters with an end-to-end automatic differentiation technique differentiating from the measurable muscle activation, through the joint torque, to the resulting observable motion without the need to measure the internal joint torques. Through extensive comparative simulations, the results manifested that our proposed method significantly outperformed the state-of-the-art baseline methods, especially in terms of accurate estimation of the muscle parameters (i.e., initial guess sampled from a normal distribution with the mean being the ground truth and the standard deviation being 10% of the ground truth could end up with an average of the percentage errors of the estimated values as low as 0.05%). In addition to human musculoskeletal modeling and simulation, the new parameter identification technique with the Diff-MSM has great potential to enable new applications in muscle health monitoring, rehabilitation, and sports science.

Many control problems require repeated tuning and adaptation of controllers across distinct closed-loop tasks, where data efficiency and adaptability are critical. We propose a hierarchical Bayesian optimization (BO) framework that is tailored to efficient controller parameter learning in sequential decision-making and control scenarios for distinct tasks. Instead of treating the closed-loop cost as a black-box, our method exploits structural knowledge of the underlying problem, consisting of a dynamical system, a control law, and an associated closed-loop cost function. We construct a hierarchical surrogate model using Gaussian processes that capture the closed-loop state evolution under different parameterizations, while the task-specific weighting and accumulation into the closed-loop cost are computed exactly via known closed-form expressions. This allows knowledge transfer and enhanced data efficiency between different closed-loop tasks. The proposed framework retains sublinear regret guarantees on par with standard black-box BO, while enabling multi-task or transfer learning. Simulation experiments with model predictive control demonstrate substantial benefits in both sample efficiency and adaptability when compared to purely black-box BO approaches.

This paper introduces two novel modifications to the Dynamic sAmpling Policy Optimization (DAPO) algorithm [1], approached from a mixed-policy perspective. Standard policy gradient methods can suffer from instability and sample inefficiency, particularly in sparse reward settings. To address this, we first propose a method that incorporates a pre-trained, stable guiding policy ($\piphi$) to provide off-policy experience, thereby regularizing the training of the target policy ($\pion$). This approach improves training stability and convergence speed by adaptively adjusting the learning step size. Secondly, we extend this idea to re-utilize zero-reward samples, which are often discarded by dynamic sampling strategies like DAPO's. By treating these samples as a distinct batch guided by the expert policy, we further enhance sample efficiency. We provide a theoretical analysis for both methods, demonstrating that their objective functions converge to the optimal solution within the established theoretical framework of reinforcement learning. The proposed mixed-policy framework effectively balances exploration and exploitation, promising more stable and efficient policy optimization.

Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing for different models to address each part, making them well-suited for problems with inherent hierarchical structure. However, typical H-GP models do not fully take advantage of this structure, only sending information up or down the hierarchy. This one-way coupling limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), an efficient H-GP framework that establishes bidirectional information exchange between parent and child models in H-GPs for online training. BIF retains the modular structure of hierarchical models - the parent combines subtask knowledge from children GPs - while introducing top-down feedback to continually refine children models during online learning. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. BIF outperforms conventional H-GP Bayesian Optimization methods, achieving up to 4x and 3x higher $R^2$ scores for the parent and children respectively, on synthetic and real-world neurostimulation optimization tasks.

In this paper, we address the problem of Column Generation (CG) using Reinforcement Learning (RL). Specifically, we use a RL model based on the attention-mechanism architecture to find the columns with most negative reduced cost in the Pricing Problem (PP). Unlike previous Machine Learning (ML) applications for CG, our model deploys an end-to-end mechanism as it independently solves the pricing problem without the help of any heuristic. We consider a variant of Vehicle Routing Problem (VRP) as a case study for our method. Through a set of experiments where our method is compared against a Dynamic Programming (DP)-based heuristic for solving the PP, we show that our method solves the linear relaxation up to a reasonable objective gap in significantly shorter running times.

The longest run subsequence (LRS) problem is an NP-hard combinatorial optimization problem belonging to the class of subsequence problems from bioinformatics. In particular, the problem plays a role in genome reassembly. In this paper, we present a solution to the LRS problem using a Biased Random Key Genetic Algorithm (BRKGA). Our approach places particular focus on the computational efficiency of evaluating individuals, which involves converting vectors of gray values into valid solutions to the problem. For comparison purposes, a Max-Min Ant System is developed and implemented. This is in addition to the application of the integer linear programming solver CPLEX for solving all considered problem instances. The computation results show that the proposed BRKGA is currently a state-of-the-art technique for the LRS problem. Nevertheless, the results also show that there is room for improvement, especially in the context of input strings based on large alphabet sizes.

Recent multi-task learning studies suggest that linear scalarization, when using well-chosen fixed task weights, can achieve comparable to or even better performance than complex multi-task optimization (MTO) methods. It remains unclear why certain weights yield optimal performance and how to determine these weights without relying on exhaustive hyperparameter search. This paper establishes a direct connection between linear scalarization and MTO methods, revealing through extensive experiments that well-performing scalarization weights exhibit specific trends in key MTO metrics, such as high gradient magnitude similarity. Building on this insight, we introduce AutoScale, a simple yet effective two-phase framework that uses these MTO metrics to guide weight selection for linear scalarization, without expensive weight search. AutoScale consistently shows superior performance with high efficiency across diverse datasets including a new large-scale benchmark.

Combined Algorithm Selection and Hyperparameter Optimization (CASH) has been fundamental to traditional AutoML systems. However, with the advancements of pre-trained models, modern ML workflows go beyond hyperparameter optimization and often require fine-tuning, ensembling, and other adaptation techniques. While the core challenge of identifying the best-performing model for a downstream task remains, the increasing heterogeneity of ML pipelines demands novel AutoML approaches. This work extends the CASH framework to select and adapt modern ML pipelines. We propose PS-PFN to efficiently explore and exploit adapting ML pipelines by extending Posterior Sampling (PS) to the max k -armed bandit problem setup. PS-PFN leverages prior-data fitted networks (PFNs) to efficiently estimate the posterior distribution of the maximal value via in-context learning. We show how to extend this method to consider varying costs of pulling arms and to use different PFNs to model reward distributions individually per arm. Experimental results on one novel and two existing standard benchmark tasks demonstrate the superior performance of PS-PFN compared to other bandit and AutoML strategies.

Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed optimization problems, where each agent aims to optimize their parameters to maximize a coupled reward function subject to coupled constraints. Prior work either studies a centralized setting, does not consider safety, or struggles with sample efficiency. Since we require sample efficiency and work with unknown and nonconvex rewards and constraints, we solve this optimization problem using safe Bayesian optimization with Gaussian process regression. Moreover, we consider nearest-neighbor communication between the agents. To capture the behavior of non-neighboring agents, we reformulate the static global optimization problem as a time-varying local optimization problem for each agent, essentially introducing time as a latent variable. To this end, we propose a custom spatio-temporal kernel to integrate prior knowledge. We show the successful deployment of our algorithm in simulations.