Developing machine learning models often involves the evaluation of numerous intermediate models. These intermediate models arise during feature engineering, model architecture search, and hyperparam-eter tuning. For instance, during hyperparameter optimization, one might explore various configurations of learning rates, regularization parameters, and network architectures, repeatedly evaluating the model's performance at different training budgets. These accuracy assessments are influenced by the chosen model architecture and parameters, and they change as we alter these factors. Given that these evaluations are often computationally expensive, it is crucial to develop a general framework for optimally allocating resources across the vast space of potential intermediate models.

We propose a \textit{guided multi-fidelity Bayesian optimization} framework for data-efficient controller tuning that integrates corrected digital twin simulations with real-world measurements. The method targets closed-loop systems with limited-fidelity simulations or inexpensive approximations. To address model mismatch, we build a multi-fidelity surrogate with a learned correction model that refines digital twin estimates using real data. An adaptive cost-aware acquisition function balances expected improvement, fidelity, and sampling cost. Our method ensures adaptability as new measurements arrive. The digital twin accuracy is re-estimated, dynamically adapting both cross-source correlations and the acquisition function. This ensures that accurate simulations are used more frequently, while inaccurate simulation data are appropriately downweighted. Experiments on robotic drive hardware and supporting numerical studies demonstrate that our method enhances tuning efficiency compared to standard Bayesian optimization and multi-fidelity methods.

We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selection principle from the theory of differential inclusions transforms the dual lasso problem into the problem of calculating the trajectory of a projected dynamical system that we prove is integrable. Our analysis yields an exact algorithm for the lasso problem, numerically up to machine precision, that is amenable to computing regularization paths and is very fast. Moreover, we show the continuation of solutions to the integrable projected dynamical system in terms of the hyperparameter naturally yields a rigorous homotopy algorithm. Numerical experiments confirm that our algorithm outperforms the state-of-the-art algorithms in both efficiency and accuracy. Beyond this work, we expect our results and analysis can be adapted to compute exact or approximate solutions to a broader class of polyhedral-constrained optimization problems.

For many real-world applications, feedback is essential in translating complex, nuanced, or subjective goals into quantifiable optimization objectives. We propose a language-in-the-loop framework that uses a large language model (LLM) to convert unstructured feedback in the form of natural language into scalar utilities to conduct BO over a numeric search space. Unlike preferential BO, which only accepts restricted feedback formats and requires customized models for each domain-specific problem, our approach leverages LLMs to turn varied types of textual feedback into consistent utility signals and to easily include flexible user priors without manual kernel design. At the same time, our method maintains the sample efficiency and principled uncertainty quantification of BO. We show that this hybrid method not only provides a more natural interface to the decision maker but also outperforms conventional BO baselines and LLM-only optimizers, particularly in feedback-limited regimes.

In safety-critical domains such as robotics, navigation and power systems, constrained optimization problems arise where maximizing performance must be carefully balanced with associated constraints. Safe reinforcement learning provides a framework to address these challenges, with Lagrangian methods being a popular choice. However, the effectiveness of Lagrangian methods crucially depends on the choice of the Lagrange multiplier $λ$, which governs the trade-off between return and constraint cost. A common approach is to update the multiplier automatically during training. Although this is standard in practice, there remains limited empirical evidence on the robustness of an automated update and its influence on overall performance. Therefore, we analyze (i) optimality and (ii) stability of Lagrange multipliers in safe reinforcement learning across a range of tasks. We provide $λ$-profiles that give a complete visualization of the trade-off between return and constraint cost of the optimization problem. These profiles show the highly sensitive nature of $λ$ and moreover confirm the lack of general intuition for choosing the optimal value $λ^*$. Our findings additionally show that automated multiplier updates are able to recover and sometimes even exceed the optimal performance found at $λ^*$ due to the vast difference in their learning trajectories. Furthermore, we show that automated multiplier updates exhibit oscillatory behavior during training, which can be mitigated through PID-controlled updates. However, this method requires careful tuning to achieve consistently better performance across tasks. This highlights the need for further research on stabilizing Lagrangian methods in safe reinforcement learning. The code used to reproduce our results can be found at https://github.com/lindsayspoor/Lagrangian_SafeRL.

Swarm trajectory optimization problems are a well-recognized class of multi-agent optimal control problems with strong nonlinearity. However, the heuristic nature of needing to set the final time for agents beforehand and the time-consuming limitation of the significant number of iterations prohibit the application of existing methods to large-scale swarm of Unmanned Aerial Vehicles (UAVs) in practice. In this paper, we propose a spatial-temporal trajectory optimization framework that accomplishes multi-UAV consensus based on the Alternating Direction Multiplier Method (ADMM) and uses Differential Dynamic Programming (DDP) for fast local planning of individual UAVs. The introduced framework is a two-level architecture that employs Parameterized DDP (PDDP) as the trajectory optimizer for each UAV, and ADMM to satisfy the local constraints and accomplish the spatial-temporal parameter consensus among all UAVs. This results in a fully distributed algorithm called Distributed Parameterized DDP (D-PDDP). In addition, an adaptive tuning criterion based on the spectral gradient method for the penalty parameter is proposed to reduce the number of algorithmic iterations. Several simulation examples are presented to verify the effectiveness of the proposed algorithm.

We consider the strategyproof facility location problem on a circle. We focus on the case of 5 agents, and find a tight bound for the PCD strategyproof mechanism, which selects the reported location of an agent in proportion to the length of the arc in front of it. We methodically "reduce" the size of the instance space and then use standard optimization techniques to find and prove the bound is tight. Moreover we hypothesize the approximation ratio of PCD for general odd $n$.

Amazon FAR (Frontier AI & Robotics)Figure 1: We present a Cross-Entropy Method (CEM) with reward model (CEM-RM) framework that optimizes block-wise, finger-wise, and tendon-routing design distributions of a soft robotic hand using pre-collected teleoperation data. Hardware experiments demonstrate that CEM-RM achieves effective design optimization with significantly fewer samples than pure optimization, enabling robust grasping of challenging objects. Abstract-- Soft robotic hands promise to provide compliant and safe interaction with objects and environments. However, designing soft hands to be both compliant and functional across diverse use cases remains challenging. Although co-design of hardware and control better couples morphology to behavior [1], the resulting search space is high-dimensional, and even simulation-based evaluation is computationally expensive. In this paper, we propose a Cross-Entropy Method with Reward Model (CEM-RM) framework that efficiently optimizes tendon-driven soft robotic hands based on teleoperation control policy, reducing design evaluations by more than half compared to pure optimization while learning a distribution of optimized hand designs from pre-collected teleoperation data. We derive a design space for a soft robotic hand composed of flexural soft fingers and implement parallelized training in simulation.

Existing adversarial attacks often neglect perturbation sparsity, limiting their ability to model structural changes and to explain how deep neural networks (DNNs) process meaningful input patterns. We propose ATOS (Attack Through Overlapping Sparsity), a differentiable optimization framework that generates structured, sparse adversarial perturbations in element-wise, pixel-wise, and group-wise forms. For white-box attacks on image classifiers, we introduce the Overlapping Smoothed L0 (OSL0) function, which promotes convergence to a stationary point while encouraging sparse, structured perturbations. By grouping channels and adjacent pixels, ATOS improves interpretability and helps identify robust versus non-robust features. We approximate the L-infinity gradient using the logarithm of the sum of exponential absolute values to tightly control perturbation magnitude. On CIFAR-10 and ImageNet, ATOS achieves a 100% attack success rate while producing significantly sparser and more structurally coherent perturbations than prior methods. The structured group-wise attack highlights critical regions from the network's perspective, providing counterfactual explanations by replacing class-defining regions with robust features from the target class.

Vision-Language-Action (VLA) models trained on large robot datasets promise general-purpose, robust control across diverse domains and embodiments. However, existing approaches often fail out-of-the-box when deployed in novel environments, embodiments, or tasks. We introduce Mixture of Skills VLA (MoS-VLA), a framework that represents robot manipulation policies as linear combinations of a finite set of learned basis functions. During pretraining, MoS-VLA jointly learns these basis functions across datasets from the Open X-Embodiment project, producing a structured skill space. At test time, adapting to a new task requires only a single expert demonstration. The corresponding skill representation is then inferred via a lightweight convex optimization problem that minimizes the L1 action error, without requiring gradient updates. Empirically, MoS-VLA achieves lower action-prediction error on five out of five unseen datasets and succeeds in both simulation and real-robot tasks where a pretrained VLA model fails outright. Inspired by the success of large language models, modern robotics aims to achieve generalization and human-like performance through the use of internet-scale data and large, attention-based architectures. To this end, researchers have collected enormous datasets of robotic arm trajectories (Open X-Embodiment Collaboration et al., 2023) and trained so-called vision-language-action foundation models to map natural language task descriptions and state observations to robot actions (Kim et al., 2024; Octo Model Team et al., 2024; Brohan et al., 2023b;a; Ma et al., 2024).