This paper presents a collaborative implicit neural simultaneous localization and mapping (SLAM) system with RGB-D image sequences, which consists of complete front-end and back-end modules including odometry, loop detection, sub-map fusion, and global refinement. In order to enable all these modules in a unified framework, we propose a novel neural point based 3D scene representation in which each point maintains a learnable neural feature for scene encoding and is associated with a certain keyframe. Moreover, a distributed-to-centralized learning strategy is proposed for the collaborative implicit SLAM to improve consistency and cooperation. A novel global optimization framework is also proposed to improve the system accuracy like traditional bundle adjustment. Experiments on various datasets demonstrate the superiority of the proposed method in both camera tracking and mapping.

Recent advances in constrained reinforcement learning (RL) have endowed reinforcement learning with certain safety guarantees. However, deploying existing constrained RL algorithms in continuous control tasks with general hard constraints remains challenging, particularly in those situations with non-convex hard constraints. Inspired by the generalized reduced gradient (GRG) algorithm, a classical constrained optimization technique, we propose a reduced policy optimization (RPO) algorithm that combines RL with GRG to address general hard constraints.

Learning to optimize has emerged as a powerful framework for various optimization and machine learning tasks. Current such meta-optimizers often learn in the space of continuous optimization algorithms that are point-based and uncertainty-unaware. To overcome the limitations, we propose a meta-optimizer that learns in the algorithmic space of both point-based and population-based optimization algorithms.

Choosing the optimal hyperparameters, including learning rate and momentum, for specific optimization instances is a significant yet non-convex challenge. This makes conventional iterative techniques such as hypergradient descent \cite{baydin2017online} insufficient in obtaining global optimality guarantees.We consider the more general task of meta-optimization -- online learning of the best optimization algorithm given problem instances, and introduce a novel approach based on control theory. We show how meta-optimization can be formulated as an optimal control problem, departing from existing literature that use stability-based methods to study optimization. Our approach leverages convex relaxation techniques in the recently-proposed nonstochastic control framework to overcome the challenge of nonconvexity, and obtains regret guarantees vs. the best offline solution. This guarantees that in meta-optimization, we can learn a method that attains convergence comparable to that of the best optimization method in hindsight from a class of methods.

This paper explores the challenges of implementing Federated Learning (FL) in practical scenarios featuring isolated nodes with data heterogeneity, which can only be connected to the server through wireless links in an infrastructure-less environment. To overcome these challenges, we propose a novel mobilizing personalized FL approach, which aims to facilitate mobility and resilience. Specifically, we develop a novel optimization algorithm called Random Walk Stochastic Alternating Direction Method of Multipliers (RWSADMM). RWSADMM capitalizes on the server's random movement toward clients and formulates local proximity among their adjacent clients based on hard inequality constraints rather than requiring consensus updates or introducing bias via regularization methods. To mitigate the computational burden on the clients, an efficient stochastic solver of the approximated optimization problem is designed in RWSADMM, which provably converges to the stationary point almost surely in expectation. Our theoretical and empirical results demonstrate the provable fast convergence and substantial accuracy improvements achieved by RWSADMM compared to baseline methods, along with its benefits of reduced communication costs and enhanced scalability.

We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For such a problem, we construct a sequence of surrogate convex constrained optimization problems by replacing the nonconvex functions locally with convex quadratic functions obtained from policy gradient estimators. We prove that the solutions to these surrogate problems converge to a stationary point of the original nonconvex problem. Furthermore, to extend our theoretical results, we apply our algorithm to examples of optimal control and multi-agent reinforcement learning with safety constraints.

For several problems of interest, there are natural constraints which exist over the output label space. For example, for the joint task of NER and POS labeling, these constraints might specify that the NER label'organization' is consistent only with the POS labels'noun' and'preposition'. These constraints can be a great way of injecting prior knowledge into a deep learning model, thereby improving overall performance. In this paper, we present a constrained optimization formulation for training a deep network with a given set of hard constraints on output labels. Our novel approach first converts the label constraints into soft logic constraints over probability distributions outputted by the network. It then converts the constrained optimization problem into an alternating min-max optimization with Lagrangian variables defined for each constraint. Since the constraints are independent of the target labels, our framework easily generalizes to semi-supervised setting.

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization variables. A remedy is non-alternating schemes. However, due to a lack of Lipschitz continuity of the gradient in matrix factorization problems, convergence cannot be guaranteed. A recently developed approach relies on the concept of Bregman distances, which generalizes the standard Euclidean distance. We exploit this theory by proposing a novel Bregman distance for matrix factorization problems, which, at the same time, allows for simple/closed form update steps. Therefore, for non-alternating schemes, such as the recently introduced Bregman Proximal Gradient (BPG) method and an inertial variant Convex--Concave Inertial BPG (CoCaIn BPG), convergence of the whole sequence to a stationary point is proved for Matrix Factorization. In several experiments, we observe a superior performance of our non-alternating schemes in terms of speed and objective value at the limit point.

Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist known impossibility results for approximating the optimal solution when constraints for covering SDPs arrive in an online fashion. In this paper, we study online covering linear and semidefinite programs in which the algorithm is augmented with advice from a possibly erroneous predictor. We show that if the predictor is accurate, we can efficiently bypass these impossibility results and achieve a constant-factor approximation to the optimal solution, i.e., consistency. On the other hand, if the predictor is inaccurate, under some technical conditions, we achieve results that match both the classical optimal upper bounds and the tight lower bounds up to constant factors, i.e., robustness. More broadly, we introduce a framework that extends both (1) the online set cover problem augmented with machine-learning predictors, studied by Bamas, Maggiori, and Svensson (NeurIPS 2020), and (2) the online covering SDP problem, initiated by Elad, Kale, and Naor (ICALP 2016). Specifically, we obtain general online learning-augmented algorithms for covering linear programs with fractional advice and constraints, and initiate the study of learning-augmented algorithms for covering SDP problems. Our techniques are based on the primal-dual framework of Buchbinder and Naor (Mathematics of Operations Research, 34, 2009) and can be further adjusted to handle constraints where the variables lie in a bounded region, i.e., box constraints.

In recent years, machine learning models have been shown to be vulnerable to backdoor attacks. Under such attacks, an adversary embeds a stealthy backdoor into the trained model such that the compromised models will behave normally on clean inputs but will misclassify according to the adversary's control on maliciously constructed input with a trigger. While these existing attacks are very effective, the adversary's capability is limited: given an input, these attacks can only cause the model to misclassify toward a single pre-defined or target class. In contrast, this paper exploits a novel backdoor attack with a much more powerful payload, denoted as Marksman, where the adversary can arbitrarily choose which target class the model will misclassify given any input during inference. To achieve this goal, we propose to represent the trigger function as a class-conditional generative model and to inject the backdoor in a constrained optimization framework, where the trigger function learns to generate an optimal trigger pattern to attack any target class at will while simultaneously embedding this generative backdoor into the trained model. Given the learned trigger-generation function, during inference, the adversary can specify an arbitrary backdoor attack target class, and an appropriate trigger causing the model to classify toward this target class is created accordingly. We show empirically that the proposed framework achieves high attack performance (e.g., 100% attack success rates in several experiments) while preserving the clean-data performance in several benchmark datasets, including MNIST, CIFAR10, GTSRB, and TinyImageNet. The proposed Marksman backdoor attack can also easily bypass existing backdoor defenses that were originally designed against backdoor attacks with a single target class. Our work takes another significant step toward understanding the extensive risks of backdoor attacks in practice.