Plug-and-play (PnP) denoising is a popular iterative framework for solving imaging inverse problems using off-the-shelf image denoisers. Their empirical success has motivated a line of research that seeks to understand the convergence of PnP iterates under various assumptions on the denoiser. While a significant amount of research has gone into establishing the convergence of the PnP iteration for different regularity conditions on the denoisers, not much is known about the asymptotic properties of the converged solution as the noise level in the measurement tends to zero, i.e., whether PnP methods are provably convergent regularization schemes under reasonable assumptions on the denoiser. This paper serves two purposes: first, we provide an overview of the classical regularization theory in inverse problems and survey a few notable recent data-driven methods that are provably convergent regularization schemes. We then continue to discuss PnP algorithms and their established convergence guarantees. Subsequently, we consider PnP algorithms with linear denoisers and propose a novel spectral filtering technique to control the strength of regularization arising from the denoiser. Further, by relating the implicit regularization of the denoiser to an explicit regularization functional, we rigorously show that PnP with linear denoisers leads to a convergent regularization scheme. More specifically, we prove that in the limit as the noise vanishes, the PnP reconstruction converges to the minimizer of a regularization potential subject to the solution satisfying the noiseless operator equation. The theoretical analysis is corroborated by numerical experiments for the classical inverse problem of tomographic image reconstruction.

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is to estimate the $p \times p$ inverse covariance matrix (aka precision matrix), assuming it is sparse (i.e., has a few nonzero entries). We propose GraphL0BnB, a new estimator based on an $\ell_0$-penalized version of the pseudolikelihood function, while most earlier approaches are based on the $\ell_1$-relaxation. Our estimator can be formulated as a convex mixed integer program (MIP) which can be difficult to compute at scale using off-the-shelf commercial solvers. To solve the MIP, we propose a custom nonlinear branch-and-bound (BnB) framework that solves node relaxations with tailored first-order methods. As a by-product of our BnB framework, we propose large-scale solvers for obtaining good primal solutions that are of independent interest. We derive novel statistical guarantees (estimation and variable selection) for our estimator and discuss how our approach improves upon existing estimators. Our numerical experiments on real/synthetic datasets suggest that our method can solve, to near-optimality, problem instances with $p = 10^4$ -- corresponding to a symmetric matrix of size $p \times p$ with $p^2/2$ binary variables. We demonstrate the usefulness of GraphL0BnB versus various state-of-the-art approaches on a range of datasets.

As an efficient distributed machine learning approach, Federated learning (FL) can obtain a shared model by iterative local model training at the user side and global model aggregating at the central server side, thereby protecting privacy of users. Mobile users in FL systems typically communicate with base stations (BSs) via wireless channels, where training performance could be degraded due to unreliable access caused by user mobility. However, existing work only investigates a static scenario or random initialization of user locations, which fail to capture mobility in real-world networks. To tackle this issue, we propose a practical model for user mobility in FL across multiple BSs, and develop a user scheduling and resource allocation method to minimize the training delay with constrained communication resources. Specifically, we first formulate an optimization problem with user mobility that jointly considers user selection, BS assignment to users, and bandwidth allocation to minimize the latency in each communication round. This optimization problem turned out to be NP-hard and we proposed a delay-aware greedy search algorithm (DAGSA) to solve it. Simulation results show that the proposed algorithm achieves better performance than the state-of-the-art baselines and a certain level of user mobility could improve training performance.

Recently, the expert-crafted neural architectures is increasing overtaken by the utilization of neural architecture search (NAS) and automatic generation (and tuning) of network structures which has a close relation to the Hyperparameter Optimization and Auto Machine Learning (AutoML). After the earlier NAS attempts to optimize only the prediction accuracy, Multi-Objective Neural architecture Search (MONAS) has been attracting attentions which considers more goals such as computational complexity, power consumption, and size of the network for optimization, reaching a trade-off between the accuracy and other features like the computational cost. In this paper, we present an overview of principal and state-of-the-art works in the field of MONAS. Starting from a well-categorized taxonomy and formulation for the NAS, we address and correct some miscategorizations in previous surveys of the NAS field. We also provide a list of all known objectives used and add a number of new ones and elaborate their specifications. We have provides analyses about the most important objectives and shown that the stochastic properties of some the them should be differed from deterministic ones in the multi-objective optimization procedure of NAS. We finalize this paper with a number of future directions and topics in the field of MONAS.

This paper presents a framework for computing the Gromov-Wasserstein problem between two sets of points in low dimensional spaces, where the discrepancy is the squared Euclidean norm. The Gromov-Wasserstein problem is a generalization of the optimal transport problem that finds the assignment between two sets preserving pairwise distances as much as possible. This can be used to quantify the similarity between two formations or shapes, a common problem in AI and machine learning. The problem can be formulated as a Quadratic Assignment Problem (QAP), which is in general computationally intractable even for small problems. Our framework addresses this challenge by reformulating the QAP as an optimization problem with a low-dimensional domain, leveraging the fact that the problem can be expressed as a concave quadratic optimization problem with low rank. The method scales well with the number of points, and it can be used to find the global solution for large-scale problems with thousands of points. We compare the computational complexity of our approach with state-of-the-art methods on synthetic problems and apply it to a near-symmetrical problem which is of particular interest in computational biology.

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs. In this paper, we introduce a scalable neural architecture and loss function dedicated to learning the constraints and criteria of NP-hard reasoning problems expressed as discrete Graphical Models. Our loss function solves one of the main limitations of Besag's pseudo-loglikelihood, enabling learning of high energies. We empirically show it is able to efficiently learn how to solve NP-hard reasoning problems from natural inputs as the symbolic, visual or many-solutions Sudoku problems as well as the energy optimization formulation of the protein design problem, providing data efficiency, interpretability, and \textit{a posteriori} control over predictions.

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed efficiently. With this in mind, we take a distributional approach and introduce a novel dominance criterion relating return distributions of policies directly. Based on this criterion, we present the distributional undominated set and show that it contains optimal policies otherwise ignored by the Pareto front. In addition, we propose the convex distributional undominated set and prove that it comprises all policies that maximise expected utility for multivariate risk-averse decision makers. We propose a novel algorithm to learn the distributional undominated set and further contribute pruning operators to reduce the set to the convex distributional undominated set. Through experiments, we demonstrate the feasibility and effectiveness of these methods, making this a valuable new approach for decision support in real-world problems.

This work developed collaborative bimanual manipulation for reliable and safe human-robot collaboration, which allows remote and local human operators to work interactively for bimanual tasks. We proposed an optimal motion adaptation to retarget arbitrary commands from multiple human operators into feasible control references. The collaborative manipulation framework has three main modules: (1) contact force modulation for compliant physical interactions with objects via admittance control; (2) task-space sequential equilibrium and inverse kinematics optimization, which adapts interactive commands from multiple operators to feasible motions by satisfying the task constraints and physical limits of the robots; and (3) an interaction controller adopted from the fractal impedance control, which is robust to time delay and stable to superimpose multiple control efforts for generating desired joint torques and controlling the dual-arm robots. Extensive experiments demonstrated the capability of the collaborative bimanual framework, including (1) dual-arm teleoperation that adapts arbitrary infeasible commands that violate joint torque limits into continuous operations within safe boundaries, compared to failures without the proposed optimization; (2) robust maneuver of a stack of objects via physical interactions in presence of model inaccuracy; (3) collaborative multi-operator part assembly, and teleoperated industrial connector insertion, which validate the guaranteed stability of reliable human-robot co-manipulation.

This work is dedicated to the study of how uncertainty estimation of the human motion prediction can be embedded into constrained optimization techniques, such as Model Predictive Control (MPC) for the social robot navigation. We propose several cost objectives and constraint functions obtained from the uncertainty of predicting pedestrian positions and related to the probability of the collision that can be applied to the MPC, and all the different variants are compared in challenging scenes with multiple agents. The main question this paper tries to answer is: what are the most important uncertainty-based criteria for social MPC? For that, we evaluate the proposed approaches with several social navigation metrics in an extensive set of scenarios of different complexity in reproducible synthetic environments. The main outcome of our study is a foundation for a practical guide on when and how to use uncertainty-aware approaches for social robot navigation in practice and what are the most effective criteria.

This paper presents RAYEN, a framework to impose hard convex constraints on the output or latent variable of a neural network. RAYEN guarantees that, for any input or any weights of the network, the constraints are satisfied at all times. Compared to other approaches, RAYEN does not perform a computationally-expensive orthogonal projection step onto the feasible set, does not rely on soft constraints (which do not guarantee the satisfaction of the constraints at test time), does not use conservative approximations of the feasible set, and does not perform a potentially slow inner gradient descent correction to enforce the constraints. RAYEN supports any combination of linear, convex quadratic, second-order cone (SOC), and linear matrix inequality (LMI) constraints, achieving a very small computational overhead compared to unconstrained networks. For example, it is able to impose 1K quadratic constraints on a 1K-dimensional variable with an overhead of less than 8 ms, and an LMI constraint with 300x300 dense matrices on a 10K-dimensional variable in less than 12 ms. When used in neural networks that approximate the solution of constrained optimization problems, RAYEN achieves computation times between 20 and 7468 times faster than state-of-the-art algorithms, while guaranteeing the satisfaction of the constraints at all times and obtaining a cost very close to the optimal one.