Multimedia recommendation involves personalized ranking tasks, where multimedia content is usually represented using a generic encoder. However, these generic representations introduce spurious correlations that fail to reveal users' true preferences. Existing works attempt to alleviate this problem by learning invariant representations, but overlook the balance between independent and identically distributed (IID) and out-of-distribution (OOD) generalization. In this paper, we propose a framework called Pareto Invariant Representation Learning (PaInvRL) to mitigate the impact of spurious correlations from an IID-OOD multi-objective optimization perspective, by learning invariant representations (intrinsic factors that attract user attention) and variant representations (other factors) simultaneously. Specifically, PaInvRL includes three iteratively executed modules: (i) heterogeneous identification module, which identifies the heterogeneous environments to reflect distributional shifts for user-item interactions; (ii) invariant mask generation module, which learns invariant masks based on the Pareto-optimal solutions that minimize the adaptive weighted Invariant Risk Minimization (IRM) and Empirical Risk (ERM) losses; (iii) convert module, which generates both variant representations and item-invariant representations for training a multi-modal recommendation model that mitigates spurious correlations and balances the generalization performance within and cross the environmental distributions. We compare the proposed PaInvRL with state-of-the-art recommendation models on three public multimedia recommendation datasets (Movielens, Tiktok, and Kwai), and the experimental results validate the effectiveness of PaInvRL for both within- and cross-environmental learning.

Navigating dynamic environments requires the robot to generate collision-free trajectories and actively avoid moving obstacles. Most previous works designed path planning algorithms based on one single map representation, such as the geometric, occupancy, or ESDF map. Although they have shown success in static environments, due to the limitation of map representation, those methods cannot reliably handle static and dynamic obstacles simultaneously. To address the problem, this paper proposes a gradient-based B-spline trajectory optimization algorithm utilizing the robot's onboard vision. The depth vision enables the robot to track and represent dynamic objects geometrically based on the voxel map. The proposed optimization first adopts the circle-based guide-point algorithm to approximate the costs and gradients for avoiding static obstacles. Then, with the vision-detected moving objects, our receding-horizon distance field is simultaneously used to prevent dynamic collisions. Finally, the iterative re-guide strategy is applied to generate the collision-free trajectory. The simulation and physical experiments prove that our method can run in real-time to navigate dynamic environments safely.

Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization problems, encompassing a wide class of convex and weakly convex (nonconvex nonsmooth) problems. By utilizing the chain rule of the composite structure properly, we introduce the Randomized Coordinate Subgradient method (RCS) for tackling this problem class. To the best of our knowledge, this is the first coordinate subgradient method for solving general nonsmooth composite optimization problems. In theory, we consider the linearly bounded subgradients assumption for the objective function, which is more general than the traditional Lipschitz continuity assumption, to account for practical scenarios. We then conduct convergence analysis for RCS in both convex and weakly convex cases based on this generalized Lipschitz-type assumption. Specifically, we establish the $\widetilde{\mathcal{O}}$$(1/\sqrt{k})$ convergence rate in expectation and the $\tilde o(1/\sqrt{k})$ almost sure asymptotic convergence rate in terms of the suboptimality gap when $f$ is convex. For the case when $f$ is weakly convex and its subdifferential satisfies the global metric subregularity property, we derive the $\mathcal{O}(\varepsilon^{-4})$ iteration complexity in expectation. We also establish an asymptotic convergence result. To justify the global metric subregularity property utilized in the analysis, we establish this error bound condition for the concrete (real-valued) robust phase retrieval problem. We also provide a convergence lemma and the relationship between the global metric subregularity properties of a weakly convex function and its Moreau envelope. Finally, we conduct several experiments to demonstrate the possible superiority of RCS over the subgradient method.

Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete optimization models in the literature address the optimality problem but only work well on relatively small datasets. \cite{firat2020column} proposed a column-generation-based heuristic approach for learning decision trees. This approach improves scalability and can work with large datasets. In this paper, we describe improvements to this column generation approach. First, we modify the subproblem model to significantly reduce the number of subproblems in multiclass classification instances. Next, we show that the data-dependent constraints in the master problem are implied, and use them as cutting planes. Furthermore, we describe a separation model to generate data points for which the linear programming relaxation solution violates their corresponding constraints. We conclude by presenting computational results that show that these modifications result in better scalability.

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression and image reconstruction. We introduce an $\ell_2$ regularized formulation of CS which we reformulate as a mixed integer second order cone program. We derive a second order cone relaxation of this problem and show that under mild conditions on the regularization parameter, the resulting relaxation is equivalent to the well studied basis pursuit denoising problem. We present a semidefinite relaxation that strengthens the second order cone relaxation and develop a custom branch-and-bound algorithm that leverages our second order cone relaxation to solve instances of CS to certifiable optimality. Our numerical results show that our approach produces solutions that are on average $6.22\%$ more sparse than solutions returned by state of the art benchmark methods on synthetic data in minutes. On real world ECG data, for a given $\ell_2$ reconstruction error our approach produces solutions that are on average $9.95\%$ more sparse than benchmark methods, while for a given sparsity level our approach produces solutions that have on average $10.77\%$ lower reconstruction error than benchmark methods in minutes.

3D scene graphs hierarchically represent the environment appropriately organizing different environmental entities in various layers. Our previous work on situational graphs extends the concept of 3D scene graph to SLAM by tightly coupling the robot poses with the scene graph entities, achieving state-of-the-art results. Though, one of the limitations of S-Graphs is scalability in really large environments due to the increased graph size over time, increasing the computational complexity. To overcome this limitation in this work we present an initial research of an improved version of S-Graphs exploiting the hierarchy to reduce the graph size by marginalizing redundant robot poses and their connections to the observations of the same structural entities. Firstly, we propose the generation and optimization of room-local graphs encompassing all graph entities within a room-like structure. These room-local graphs are used to compress the S-Graphs marginalizing the redundant robot keyframes within the given room. We then perform windowed local optimization of the compressed graph at regular time-distance intervals. A global optimization of the compressed graph is performed every time a loop closure is detected. We show similar accuracy compared to the baseline while showing a 39.81% reduction in the computation time with respect to the baseline.

Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling patterns following various strategies, e.g., variable density sampling or radial trajectories. In this work, we propose a method that directly learns the undersampling masks from data points, thereby also providing task- and domain-specific patterns. To solve the resulting discrete optimization problem, we propose a general optimization routine called ProM: A fully probabilistic, differentiable, versatile, and model-free framework for mask optimization that enforces acceleration factors through a convex constraint. Analyzing knee, brain, and cardiac MRI datasets with our method, we discover that different anatomic regions reveal distinct optimal undersampling masks, demonstrating the benefits of using custom masks, tailored for a downstream task. For example, ProM can create undersampling masks that maximize performance in downstream tasks like segmentation with networks trained on fully-sampled MRIs. Even with extreme acceleration factors, ProM yields reasonable performance while being more versatile than existing methods, paving the way for data-driven all-purpose mask generation.

With the electrification of transportation, the rising uptake of electric vehicles (EVs) might stress distribution networks significantly, leaving their performance degraded and stability jeopardized. To accommodate these new loads cost-effectively, modern power grids require coordinated or ``smart'' charging strategies capable of optimizing EV charging scheduling in a scalable and efficient fashion. With this in view, the present work focuses on reservation management programs for large-scale, networked EV charging stations. We formulate a time-coupled binary optimization problem that maximizes EV users' total welfare gain while accounting for the network's available power capacity and stations' occupancy limits. To tackle the problem at scale while retaining high solution quality, a data-driven optimization framework combining techniques from the fields of Deep Learning and Approximation Algorithms is introduced. The framework's key ingredient is a novel input-output processing scheme for neural networks that allows direct extrapolation to problem sizes substantially larger than those included in the training set. Extensive numerical simulations based on synthetic and real-world data traces verify the effectiveness and superiority of the presented approach over two representative scheduling algorithms. Lastly, we round up the contributions by listing several immediate extensions to the proposed framework and outlining the prospects for further exploration.

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. The existing methods leverages the optimality conditions and implicit function theorem to obtain the Jacobian matrix of the output, which increases the computational cost and limits the application of differentiable optimization. In addition, some non-differentiable constraints lead to more challenges when using prior differentiable optimization layers. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe Layer (DFWLayer), by rolling out the Frank-Wolfe method, a well-known optimization algorithm which can solve constrained optimization problems without projections and Hessian matrix computations, thus leading to a efficient way of dealing with large-scale problems. Theoretically, we establish a bound on the suboptimality gap of the DFWLayer in the context of l1-norm constraints. Experimental assessments demonstrate that the DFWLayer not only attains competitive accuracy in solutions and gradients but also consistently adheres to constraints. Moreover, it surpasses the baselines in both forward and backward computational speeds.

Since wearable linkage mechanisms could control the moment transmission from actuator(s) to wearers, they can help ensure that even low-cost wearable systems provide advanced functionality tailored to users' needs. For example, if a hip mechanism transforms an input torque into a spatially-varying moment, a wearer can get effective assistance both in the sagittal and frontal planes during walking, even with an affordable single-actuator system. However, due to the combinatorial nature of the linkage mechanism design space, the topologies of such nonlinear-moment-generating mechanisms are challenging to determine, even with significant computational resources and numerical data. Furthermore, on-premise production development and interactive design are nearly impossible in conventional synthesis approaches. Here, we propose an innovative autonomous computational approach for synthesizing such wearable robot mechanisms, eliminating the need for exhaustive searches or numerous data sets. Our method transforms the synthesis problem into a gradient-based optimization problem with sophisticated objective and constraint functions while ensuring the desired degree of freedom, range of motion, and force transmission characteristics. To generate arbitrary mechanism topologies and dimensions, we employed a unified ground model. By applying the proposed method for the design of hip joint mechanisms, the topologies and dimensions of non-series-type hip joint mechanisms were obtained. Biomechanical simulations validated its multi-moment assistance capability, and its wearability was verified via prototype fabrication. The proposed design strategy can open a new way to design various wearable robot mechanisms, such as shoulders, knees, and ankles.