We consider a general inference setting for discrete probabilistic graphical models where we seek maximum a posteriori (MAP) estimates for a subset of the random variables (max nodes), marginalizing over the rest (sum nodes). We present a hybrid message-passing algorithm to accomplish this. The hybrid algorithm passes a mix of sum and max messages depending on the type of source node (sum or max). We derive our algorithm by showing that it falls out as the solution of a particular relaxation of a variational framework. We further show that the Expectation Maximization algorithm can be seen as an approximation to our algorithm. Experimental results on synthetic and real-world datasets, against several baselines, demonstrate the efficacy of our proposed algorithm.

Budgeted optimization involves optimizing an unknown function that is costly to evaluate by requesting a limited number of function evaluations at intelligently selected inputs. Typical problem formulations assume that experiments are selected one at a time with a limited total number of experiments, which fail to capture important aspects of many real-world problems. This paper defines a novel problem formulation with the following important extensions: 1) allowing for concurrent experiments; 2) allowing for stochastic experiment durations; and 3) placing constraints on both the total number of experiments and the total experimental time. We develop both offline and online algorithms for selecting concurrent experiments in this new setting and provide experimental results on a number of optimization benchmarks. The results show that our algorithms produce highly effective schedules compared to natural baselines.

We consider large matrices of low rank. We address the problem of recovering such matrices when most of the entries are unknown. Matrix completion finds applications in recommender systems. In this setting, the rows of the matrix may correspond to items and the columns may correspond to users. The known entries are the ratings given by users to some items.

In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, called the trace Lasso, uses the trace norm of the selected covariates, which is a convex surrogate of their rank, as the criterion of model complexity. We analyze the properties of our norm, describe an optimization algorithm based on reweighted least-squares, and illustrate the behavior of this norm on synthetic data, showing that it is more adapted to strong correlations than competing methods such as the elastic net.

Latent variable mixture models are a powerful tool for exploring the structure in large datasets. A common challenge for interpreting such models is a desire to impose sparsity, the natural assumption that each data point only contains few latent features.

Optimization-based approaches are widely employed to generate optimal robot motions while considering various constraints, such as robot dynamics, collision avoidance, and physical limitations. It is crucial to efficiently solve the optimization problems in practice, yet achieving rapid computations remains a great challenge for optimization-based approaches with nonlinear constraints. In this paper, we propose a geometric projector for dynamic obstacle avoidance based on velocity obstacle (GeoPro-VO) by leveraging the projection feature of the velocity cone set represented by VO. Furthermore, with the proposed GeoPro-VO and the augmented Lagrangian spectral projected gradient descent (ALSPG) algorithm, we transform an initial mixed integer nonlinear programming problem (MINLP) in the form of constrained model predictive control (MPC) into a sub-optimization problem and solve it efficiently. Numerical simulations are conducted to validate the fast computing speed of our approach and its capability for reliable dynamic obstacle avoidance.

Emergency relief operations are essential in disaster aftermaths, necessitating effective resource allocation to minimize negative impacts and maximize benefits. In prolonged crises or extensive disasters, a systematic, multi-cycle approach is key for timely and informed decision-making. Leveraging advancements in IoT and spatio-temporal data analytics, we've developed the Multi-Objective Shuffled Gray-Wolf Frog Leaping Model (MSGW-FLM). This multi-constraint, multi-objective resource allocation model has been rigorously tested against 28 diverse challenges, showing superior performance in comparison to established models such as NSGA-II, IBEA, and MOEA/D. MSGW-FLM's effectiveness is particularly notable in complex, multi-cycle emergency rescue scenarios, which involve numerous constraints and objectives. This model represents a significant step forward in optimizing resource distribution in emergency response situations.

Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a promising solution to handle the enormous growth in data and model sizes in deep learning. A fundamental problem in distributed nonconvex optimization is avoiding convergence to saddle points, which significantly degrade optimization accuracy. We discover that the process of quantization, which is necessary for all digital communications, can be exploited to enable saddle-point avoidance. More specifically, we propose a stochastic quantization scheme and prove that it can effectively escape saddle points and ensure convergence to a second-order stationary point in distributed nonconvex optimization. With an easily adjustable quantization granularity, the approach allows a user to control the number of bits sent per iteration and, hence, to aggressively reduce the communication overhead. Numerical experimental results using distributed optimization and learning problems on benchmark datasets confirm the effectiveness of the approach.

LiDAR-based localization is valuable for applications like mining surveys and underground facility maintenance. However, existing methods can struggle when dealing with uninformative geometric structures in challenging scenarios. This paper presents RELEAD, a LiDAR-centric solution designed to address scan-matching degradation. Our method enables degeneracy-free point cloud registration by solving constrained ESIKF updates in the front end and incorporates multisensor constraints, even when dealing with outlier measurements, through graph optimization based on Graduated Non-Convexity (GNC). Additionally, we propose a robust Incremental Fixed Lag Smoother (rIFL) for efficient GNC-based optimization. RELEAD has undergone extensive evaluation in degenerate scenarios and has outperformed existing state-of-the-art LiDAR-Inertial odometry and LiDAR-Visual-Inertial odometry methods.

Submodular functions, crucial for various applications, often lack practical learning methods for their acquisition. Seemingly unrelated, learning a scaling from oracles offering graded pairwise preferences (GPC) is underexplored, despite a rich history in psychometrics. In this paper, we introduce deep submodular peripteral networks (DSPNs), a novel parametric family of submodular functions, and methods for their training using a contrastive-learning inspired GPC-ready strategy to connect and then tackle both of the above challenges. We introduce newly devised GPC-style "peripteral" loss which leverages numerically graded relationships between pairs of objects (sets in our case). Unlike traditional contrastive learning, our method utilizes graded comparisons, extracting more nuanced information than just binary-outcome comparisons, and contrasts sets of any size (not just two). We also define a novel suite of automatic sampling strategies for training, including active-learning inspired submodular feedback. We demonstrate DSPNs' efficacy in learning submodularity from a costly target submodular function showing superiority in downstream tasks such as experimental design and streaming applications.