The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this algorithm are mainly derived for Lipschitz continuous objective functions. In this work, we first extend the typical complexity results for the subgradient method to convex and weakly convex minimization without assuming Lipschitz continuity. Specifically, we establish $\mathcal{O}(1/\sqrt{T})$ bound in terms of the suboptimality gap ``$f(x) - f^*$'' for convex case and $\mathcal{O}(1/{T}^{1/4})$ bound in terms of the gradient of the Moreau envelope function for weakly convex case. Furthermore, we provide convergence results for non-Lipschitz convex and weakly convex objective functions using proper diminishing rules on the step sizes. In particular, when $f$ is convex, we show $\mathcal{O}(\log(k)/\sqrt{k})$ rate of convergence in terms of the suboptimality gap. With an additional quadratic growth condition, the rate is improved to $\mathcal{O}(1/k)$ in terms of the squared distance to the optimal solution set. When $f$ is weakly convex, asymptotic convergence is derived. The central idea is that the dynamics of properly chosen step sizes rule fully controls the movement of the subgradient method, which leads to boundedness of the iterates, and then a trajectory-based analysis can be conducted to establish the desired results. To further illustrate the wide applicability of our framework, we extend the complexity results to the truncated subgradient, the stochastic subgradient, the incremental subgradient, and the proximal subgradient methods for non-Lipschitz functions.

Deploying Deep Neural Networks (DNNs) on tiny devices is a common trend to process the increasing amount of sensor data being generated. Multi-objective optimization approaches can be used to compress DNNs by applying network pruning and weight quantization to minimize the memory footprint (RAM), the number of parameters (ROM) and the number of floating point operations (FLOPs) while maintaining the predictive accuracy. In this paper, we show that existing multi-objective Bayesian optimization (MOBOpt) approaches can fall short in finding optimal candidates on the Pareto front and propose a novel solver based on an ensemble of competing parametric policies trained using an Augmented Random Search Reinforcement Learning (RL) agent. Our methodology aims at finding feasible tradeoffs between a DNN's predictive accuracy, memory consumption on a given target system, and computational complexity. Our experiments show that we outperform existing MOBOpt approaches consistently on different data sets and architectures such as ResNet-18 and MobileNetV3.

We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on the task performance, and incorporate the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer programming approach, which gives optimal solutions for small instances of the problem but is computationally expensive. We also develop a greedy heuristic algorithm as a baseline. Our modeling and solution approaches result in task plans that leverage task precedence relationships and robot coordination and cooperation to achieve high mission performance, even in large missions with many agents.

Autonomous parking (AP) is an emering technique to navigate an intelligent vehicle to a parking space without any human intervention. Existing AP methods based on mathematical optimization or machine learning may lead to potential failures due to either excessive execution time or lack of generalization. To fill this gap, this paper proposes an integrated constrained optimization and imitation learning (iCOIL) approach to achieve efficient and reliable AP. The iCOIL method has two candidate working modes, i.e., CO and IL, and adopts a hybrid scenario analysis (HSA) model to determine the better mode under various scenarios. We implement and verify iCOIL on the Macao Car Racing Metaverse (MoCAM) platform. Results show that iCOIL properly adapts to different scenarios during the entire AP procedure, and achieves significantly larger success rates than other benchmarks.

Tasks for autonomous robotic systems commonly require stabilization to a desired region while maintaining safety specifications. However, solving this multi-objective problem is challenging when the dynamics are nonlinear and high-dimensional, as traditional methods do not scale well and are often limited to specific problem structures. To address this issue, we propose a novel approach to solve the stabilize-avoid problem via the solution of an infinite-horizon constrained optimal control problem (OCP). We transform the constrained OCP into epigraph form and obtain a two-stage optimization problem that optimizes over the policy in the inner problem and over an auxiliary variable in the outer problem. We then propose a new method for this formulation that combines an on-policy deep reinforcement learning algorithm with neural network regression. Our method yields better stability during training, avoids instabilities caused by saddle-point finding, and is not restricted to specific requirements on the problem structure compared to more traditional methods. We validate our approach on different benchmark tasks, ranging from low-dimensional toy examples to an F16 fighter jet with a 17-dimensional state space. Simulation results show that our approach consistently yields controllers that match or exceed the safety of existing methods while providing ten-fold increases in stability performance from larger regions of attraction.

In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best approximates the given distribution on average. Our algorithm is based on a linear program that we solve using the ellipsoid method. Given that its corresponding separation oracle problem is NP-hard, we devise an approximate separation oracle that can be viewed as a generalization of the weighted feedback arc set problem to hypergraphs. Our theoretical result can also be made practical: we obtain a heuristic that is effective and scales to real-world datasets.

This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as semidefinite programming (SDP). Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not properly deal with the configuration space of the 3D rigid body; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space in our formulation and apply the variational integrator to formulate the forced rigid body systems as quadratic polynomials. Then we leverage Lasserre's hierarchy to obtain the globally optimal solution via SDP. By constructing the motion planning problem in a sparse manner, the results show that the proposed algorithm has \emph{linear} complexity with respect to the planning horizon. This paper demonstrates the proposed method can provide rank-one optimal solutions at relaxation order two for most of the testing cases of 1) 3D drone landing using the full dynamics model and 2) inverse kinematics for serial manipulators.

Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This problem has attracted a lot of attention recently, but most existing methods with strong theoretical guarantees are restricted to finite-horizon or tabular settings. In constrast, few algorithms for infinite-horizon settings with function approximation and minimal assumptions on the dataset are both sample and computationally efficient. Another gap in the current literature is the lack of theoretical analysis for the average-reward setting, which is more challenging than the discounted setting. In this paper, we address both of these issues by proposing a primal-dual optimization method based on the linear programming formulation of RL. Our key contribution is a new reparametrization that allows us to derive low-variance gradient estimators that can be used in a stochastic optimization scheme using only samples from the behavior policy. Our method finds an $\varepsilon$-optimal policy with $O(\varepsilon^{-4})$ samples, improving on the previous $O(\varepsilon^{-5})$, while being computationally efficient for infinite-horizon discounted and average-reward MDPs with realizable linear function approximation and partial coverage. Moreover, to the best of our knowledge, this is the first theoretical result for average-reward offline RL.

With emerging topics (e.g., COVID-19) on social media as a source for the spreading misinformation, overcoming the distributional shifts between the original training domain (i.e., source domain) and such target domains remains a non-trivial task for misinformation detection. This presents an elusive challenge for early-stage misinformation detection, where a good amount of data and annotations from the target domain is not available for training. To address the data scarcity issue, we propose MetaAdapt, a meta learning based approach for domain adaptive few-shot misinformation detection. MetaAdapt leverages limited target examples to provide feedback and guide the knowledge transfer from the source to the target domain (i.e., learn to adapt). In particular, we train the initial model with multiple source tasks and compute their similarity scores to the meta task. Based on the similarity scores, we rescale the meta gradients to adaptively learn from the source tasks. As such, MetaAdapt can learn how to adapt the misinformation detection model and exploit the source data for improved performance in the target domain. To demonstrate the efficiency and effectiveness of our method, we perform extensive experiments to compare MetaAdapt with state-of-the-art baselines and large language models (LLMs) such as LLaMA, where MetaAdapt achieves better performance in domain adaptive few-shot misinformation detection with substantially reduced parameters on real-world datasets.

The visual simultaneous localization and mapping(vSLAM) is widely used in GPS-denied and open field environments for ground and surface robots. However, due to the frequent perception failures derived from lacking visual texture or the {swing} of robot view direction on rough terrains, the accuracy and robustness of vSLAM are still to be enhanced. The study develops a novel view planning approach of actively perceiving areas with maximal information to address the mentioned problem; a gimbal camera is used as the main sensor. Firstly, a map representation based on feature distribution-weighted Fisher information is proposed to completely and effectively represent environmental information richness. With the map representation, a continuous environmental information model is further established to convert the discrete information space into a continuous one for numerical optimization in real-time. Subsequently, the receding horizon optimization is utilized to obtain the optimal informative viewpoints with simultaneously considering the robotic perception, exploration and motion cost based on the continuous environmental model. Finally, several simulations and outdoor experiments are performed to verify the improvement of localization robustness and accuracy by the proposed approach.