Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization problems, practical implementations are often hindered by soft constraints that either slow down mixing when too strong, or fail to enforce feasibility when too weak. We introduce a two-dimensional extension of the powerful parallel tempering algorithm (PT) that addresses this challenge by adding a second dimension of replicas interpolating the penalty strengths. This scheme ensures constraint satisfaction in the final replicas, analogous to low-energy states at low temperature. The resulting two-dimensional parallel tempering algorithm (2D-PT) improves mixing in heavily constrained replicas and eliminates the need to explicitly tune the penalty strength. In a representative example of graph sparsification with copy constraints, 2D-PT achieves near-ideal mixing, with Kullback-Leibler divergence decaying as O(1/t). When applied to sparsified Wishart instances, 2D-PT yields orders of magnitude speedup over conventional PT with the same number of replicas. The method applies broadly to constrained Ising problems and can be deployed on existing Ising machines.

--We consider the phase retrieval problem, which involves recovering a rank-one positive semidefinite matrix from rank-one measurements. A recently proposed algorithm based on Bures-Wasserstein gradient descent (BWGD) exhibits superlinear convergence, but it is unstable, and existing theory can only prove local linear convergence for higher rank matrix recovery. We resolve this gap by revealing that BWGD implements Newton's method with a nonsmooth and nonconvex objective. We develop a smoothing framework that regularizes the objective, enabling a stable method with rigorous superlinear convergence guarantees. Experiments on synthetic data demonstrate this superior stability while maintaining fast convergence. Phase retrieval--the problem of recovering a real or complex signal from magnitude-only measurements--is a fundamental problem in signal processing. Its applications range from X-ray crystallography to astronomical imaging, where measurement systems capture a form of intensity [Harrison, 1993, Fienup, 1982, Fienup and Dainty, 1987, Miao et al., 1998]. The seemingly simple constraint of measuring magnitudes transforms what would be a linear problem into a challenging nonlinear and nonconvex optimization problem. More critically, the direct optimization formulation using least squares yields a nonconvex objective function, making it difficult to solve effectively. The phase retrieval problem is a specific instance of a broader class of low-rank matrix sensing problems that arise throughout signal processing [Recht et al., 2010].

Individualized treatment rules (ITRs) have gained significant attention due to their wide-ranging applications in fields such as precision medicine, ridesharing, and advertising recommendations. However, when ITRs are influenced by sensitive attributes such as race, gender, or age, they can lead to outcomes where certain groups are unfairly advantaged or disadvantaged. To address this gap, we propose a flexible approach based on the optimal transport theory, which is capable of transforming any optimal ITR into a fair ITR that ensures demographic parity. Recognizing the potential loss of value under fairness constraints, we introduce an ``improved trade-off ITR," designed to balance value optimization and fairness while accommodating varying levels of fairness through parameter adjustment. To maximize the value of the improved trade-off ITR under specific fairness levels, we propose a smoothed fairness constraint for estimating the adjustable parameter. Additionally, we establish a theoretical upper bound on the value loss for the improved trade-off ITR. We demonstrate performance of the proposed method through extensive simulation studies and application to the Next 36 entrepreneurial program dataset.

3D Gaussian Splatting (3DGS) has recently gained popularity in SLAM applications due to its fast rendering and high-fidelity representation. However, existing 3DGS-SLAM systems have predominantly focused on indoor environments and relied on active depth sensors, leaving a gap for large-scale outdoor applications. We present BGS-SLAM, the first binocular 3D Gaussian Splatting SLAM system designed for outdoor scenarios. Our approach uses only RGB stereo pairs without requiring LiDAR or active sensors. BGS-SLAM leverages depth estimates from pre-trained deep stereo networks to guide 3D Gaussian optimization with a multi-loss strategy enhancing both geometric consistency and visual quality. Experiments on multiple datasets demonstrate that BGS-SLAM achieves superior tracking accuracy and mapping performance compared to other 3DGS-based solutions in complex outdoor environments.

We present DRACo-SLAM2, a distributed SLAM framework for underwater robot teams equipped with multibeam imaging sonar. This framework improves upon the original DRACo-SLAM by introducing a novel representation of sonar maps as object graphs and utilizing object graph matching to achieve time-efficient inter-robot loop closure detection without relying on prior geometric information. To better-accommodate the needs and characteristics of underwater scan matching, we propose incremental Group-wise Consistent Measurement Set Maximization (GCM), a modification of Pairwise Consistent Measurement Set Maximization (PCM), which effectively handles scenarios where nearby inter-robot loop closures share similar registration errors. The proposed approach is validated through extensive comparative analyses on simulated and real-world datasets.

Anchor point placement is a crucial yet often overlooked aspect of exosuit design since it determines how forces interact with the human body. This work analyzes the impact of different anchor point positions on gait kinematics, muscular activation and energetic consumption. A total of six experiments were conducted with 11 subjects wearing the XoSoft exosuit, which assists hip flexion in five configurations. Subjects were instrumented with an IMU-based motion tracking system, EMG sensors, and a mask to measure metabolic consumption. The results show that positioning the knee anchor point on the posterior side while keeping the hip anchor on the anterior part can reduce muscle activation in the hip flexors by up to 10.21\% and metabolic expenditure by up to 18.45\%. Even if the only assisted joint was the hip, all the configurations introduced changes also in the knee and ankle kinematics. Overall, no single configuration was optimal across all subjects, suggesting that a personalized approach is necessary to transmit the assistance forces optimally. These findings emphasize that anchor point position does indeed have a significant impact on exoskeleton effectiveness and efficiency. However, these optimal positions are subject-specific to the exosuit design, and there is a strong need for future work to tailor musculoskeletal models to individual characteristics and validate these results in clinical populations.

We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality constraint to the shape optimization problem. Central to our method is the computation of adjoint gradients of the design objectives (e.g., drag and lift) with respect to the manifold space. These gradients are derived by first computing shape derivatives with respect to conventional shape design parameters (e.g., Hicks-Henne parameters) and then backpropagating them through the diffusion model to its latent space via automatic differentiation. Our framework preserves mathematical rigor and can be integrated into existing adjoint-based design workflows with minimal modification. Demonstrated on extensive transonic RANS airfoil design cases using off-the-shelf and general-purpose nonlinear optimizers, our approach eliminates ad hoc parameter tuning and variable scaling, maintains robustness across initialization and optimizer choices, and achieves superior aerodynamic performance compared to conventional approaches. This work establishes how AI generated priors integrates effectively with adjoint methods to enable robust, high-fidelity aerodynamic shape optimization through automatic differentiation.

We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian class of algorithms, FilterDDP uses a step filter in conjunction with a line search to handle equality constraints. We identify two important design choices for the step filter criteria which lead to robust numerical performance: 1) we use the Lagrangian instead of the cost as one of the filter criterion and, 2) for the stopping criteria and backward pass Hessians, we replace the value function gradient with an estimated dual variable of the dynamics constraints. Both choices are rigorously justified, for 2) in particular by a formal proof of local quadratic convergence. We validate FilterDDP on three contact implicit trajectory optimisation problems which arise in robotics.

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper- and lower-level objectives are smooth but potentially nonconvex. Due to the absence of additional structural assumptions for the lower-level objective-such as convexity or the Polyak-Łojasiewicz (PL) condition-guaranteeing global optimality is generally intractable. Instead, we introduce a suitable notion of stationarity for this class of problems and aim to design a first-order algorithm that finds such stationary points in polynomial time. Intuitively, stationarity in this setting means the upper-level objective cannot be substantially improved locally without causing a larger deterioration in the lower-level objective. To this end, we show that a simple and implementable variant of the dynamic barrier gradient descent (DBGD) framework can effectively solve the considered nonconvex simple bilevel problems up to stationarity. Specifically, to reach an $(ε_f, ε_g)$-stationary point-where $ε_f$ and $ε_g$ denote the target stationarity accuracies for the upper- and lower-level objectives, respectively-the considered method achieves a complexity of $\mathcal{O}\left(\max\left(ε_f^{-\frac{3+p}{1+p}}, ε_g^{-\frac{3+p}{2}}\right)\right)$, where $p \geq 0$ is an arbitrary constant balancing the terms. To the best of our knowledge, this is the first complexity result for a discrete-time algorithm that guarantees joint stationarity for both levels in general nonconvex simple bilevel problems.

Automatic extrinsic sensor calibration is a fundamental problem for multi-sensor platforms. Reliable and general-purpose solutions should be computationally efficient, require few assumptions about the structure of the sensing environment, and demand little effort from human operators. Since the engineering effort required to obtain accurate calibration parameters increases with the number of sensors deployed, robotics researchers have pursued methods requiring few assumptions about the sensing environment and minimal effort from human operators. In this work, we introduce a fast and certifiably globally optimal algorithm for solving a generalized formulation of the $\textit{robot-world and hand-eye calibration}$ (RWHEC) problem. The formulation of RWHEC presented is "generalized" in that it supports the simultaneous estimation of multiple sensor and target poses, and permits the use of monocular cameras that, alone, are unable to measure the scale of their environments. In addition to demonstrating our method's superior performance over existing solutions, we derive novel identifiability criteria and establish $\textit{a priori}$ guarantees of global optimality for problem instances with bounded measurement errors. We also introduce a complementary Lie-algebraic local solver for RWHEC and compare its performance with our global method and prior art. Finally, we provide a free and open-source implementation of our algorithms and experiments.