In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.

In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods. Specifically, the traditional approach requires numerically computing the gradient (first-order information). However, the sampling approach directly reduces the expensive gradient (first-order information) by the objective value (zeroth-order information), which also avoids using the adjoint technique that requires large amounts of storage and is unusable for many atmosphere and ocean models. We present an intuitive analysis for the sampling algorithm and a rigorous Chernoff-type concentration inequality to probabilistically approximate the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial structures, objective values, computation times and nonlinear error growth. Compared with the performance of the three approaches, the CNOPs' spatial structures, objective values, and nonlinear error growth is nearly consistent, while the computation time using the sampling approach with fewer samples is extremely shorter. In other words, the new sampling approach from state-of-the-art statistical machine learning techniques shortens the computation time to the utmost at the cost of losing little accuracy.

Online footstep planning is essential for bipedal walking robots, allowing them to walk in the presence of disturbances and sensory noise. Most of the literature on the topic has focused on optimizing the footstep placement while keeping the step timing constant. In this work, we introduce a footstep planner capable of optimizing footstep placement and step time online. The proposed planner, consisting of an Interior Point Optimizer (IPOPT) and an optimizer based on Augmented Lagrangian (AL) method with analytical gradient descent, solves the full dynamics of the Linear Inverted Pendulum (LIP) model in real time to optimize for footstep location as well as step timing at the rate of 200~Hz. We show that such asynchronous real-time optimization with the AL method (ARTO-AL) provides the required robustness and speed for successful online footstep planning. Furthermore, ARTO-AL can be extended to plan footsteps in 3D, allowing terrain-aware footstep planning on uneven terrains. Compared to an algorithm with no footstep time adaptation, our proposed ARTO-AL demonstrates increased stability in simulated walking experiments as it can resist pushes on flat ground and on a $10^{\circ}$ ramp up to 120 N and 100 N respectively. For the video, see https://youtu.be/ABdnvPqCUu4. For code, see https://github.com/WangKeAlchemist/ARTO-AL/tree/master.

In this paper, we look into the minimum obstacle displacement (MOD) planning problem from a mobile robot motion planning perspective. This problem finds an optimal path to goal by displacing movable obstacles when no path exists due to collision with obstacles. However this problem is computationally expensive and grows exponentially in the size of number of movable obstacles. This work looks into approximate solutions that are computationally less intensive and differ from the optimal solution by a factor of the optimal cost.

Federated Learning (FL) is a communication-efficient and privacy-preserving distributed machine learning framework that has gained a significant amount of research attention recently. Despite the different forms of FL algorithms (e.g., synchronous FL, asynchronous FL) and the underlying optimization methods, nearly all existing works implicitly assumed the existence of a communication infrastructure that facilitates the direct communication between the server and the clients for the model data exchange. This assumption, however, does not hold in many real-world applications that can benefit from distributed learning but lack a proper communication infrastructure (e.g., smart sensing in remote areas). In this paper, we propose a novel FL framework, named FedEx (short for FL via Model Express Delivery), that utilizes mobile transporters (e.g., Unmanned Aerial Vehicles) to establish indirect communication channels between the server and the clients. Two algorithms, called FedEx-Sync and FedEx-Async, are developed depending on whether the transporters adopt a synchronized or an asynchronized schedule. Even though the indirect communications introduce heterogeneous delays to clients for both the global model dissemination and the local model collection, we prove the convergence of both versions of FedEx. The convergence analysis subsequently sheds lights on how to assign clients to different transporters and design the routes among the clients. The performance of FedEx is evaluated through experiments in a simulated network on two public datasets.

Recent trends in robotic services propose offloading robot functionalities to the Edge to meet the strict latency requirements of networked robotics. However, the Edge is typically an expensive resource and sometimes the Cloud is also an option, thus, decreasing the cost. Following this idea, we propose Don't Let Me Down! (DLMD), an algorithm that promotes offloading robot functions to the Cloud when possible to minimize the consumption of Edge resources. Additionally, DLMD takes the appropriate migration, traffic steering, and radio handover decisions to meet robotic service requirements as strict latency constraints. In the paper, we formulate the optimization problem that DLMD aims to solve, compare DLMD performance against state of art, and perform stress tests to assess DLMD performance in small & large networks. Results show that DLMD (i) always finds solutions in less than 30ms; (ii) is optimal in a local warehousing use case, and (iii) consumes only 5% of the Edge resources upon network stress.

This paper presents Deep-PANTHER, a learning-based perception-aware trajectory planner for unmanned aerial vehicles (UAVs) in dynamic environments. Given the current state of the UAV, and the predicted trajectory and size of the obstacle, Deep-PANTHER generates multiple trajectories to avoid a dynamic obstacle while simultaneously maximizing its presence in the field of view (FOV) of the onboard camera. To obtain a computationally tractable real-time solution, imitation learning is leveraged to train a Deep-PANTHER policy using demonstrations provided by a multimodal optimization-based expert. Extensive simulations show replanning times that are two orders of magnitude faster than the optimization-based expert, while achieving a similar cost. By ensuring that each expert trajectory is assigned to one distinct student trajectory in the loss function, Deep-PANTHER can also capture the multimodality of the problem and achieve a mean squared error (MSE) loss with respect to the expert that is up to 18 times smaller than state-of-the-art (Relaxed) Winner-Takes-All approaches. Deep-PANTHER is also shown to generalize well to obstacle trajectories that differ from the ones used in training.

We present the principled design of a control pipeline for the synthesis of policies from examples data. The pipeline, based on a discretized design which we term as discrete fully probabilistic design, expounds an algorithm recently introduced in Gagliardi and Russo (2021) to synthesize policies from examples for constrained, stochastic and nonlinear systems. Contrary to other approaches, the pipeline we present: (i) does not need the constraints to be fulfilled in the possibly noisy example data; (ii) enables control synthesis even when the data are collected from an example system that is different from the one under control. The design is benchmarked numerically on an example that involves controlling an inverted pendulum with actuation constraints starting from data collected from a physically different pendulum that does not satisfy the system-specific actuation constraints. We also make our fully documented code openly available.

Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the continuous-time trajectory by fixed-lag smoothing within a factor-graph optimization framework. With the continuous-time formulation, we can query poses at any time instants corresponding to the sensor measurements. To bound the computation complexity of the continuous-time fixed-lag smoother, we maintain temporal and keyframe sliding windows with constant size, and probabilistically marginalize out control points of the trajectory and other states, which allows preserving prior information for future sliding-window optimization. Based on continuous-time fixed-lag smoothing, we design tightly-coupled multi-modal SLAM algorithms with a variety of sensor combinations, like the LiDAR-inertial and LiDAR-inertial-camera SLAM systems, in which online timeoffset calibration is also naturally supported. More importantly, benefiting from the marginalization and our derived analytical Jacobians for optimization, the proposed continuous-time SLAM systems can achieve real-time performance regardless of the high complexity of continuous-time formulation. The proposed multi-modal SLAM systems have been widely evaluated on three public datasets and self-collect datasets. The results demonstrate that the proposed continuous-time SLAM systems can achieve high-accuracy pose estimations and outperform existing state-of-the-art methods. To benefit the research community, we will open source our code at ~\url{https://github.com/APRIL-ZJU/clic}.

Generating safe motion plans in real-time is a key requirement for deploying robot manipulators to assist humans in collaborative settings. In particular, robots must satisfy strict safety requirements to avoid self-damage or harming nearby humans. Satisfying these requirements is particularly challenging if the robot must also operate in real-time to adjust to changes in its environment.This paper addresses these challenges by proposing Reachability-based Signed Distance Functions (RDFs) as a neural implicit representation for robot safety. RDF, which can be constructed using supervised learning in a tractable fashion, accurately predicts the distance between the swept volume of a robot arm and an obstacle. RDF's inference and gradient computations are fast and scale linearly with the dimension of the system; these features enable its use within a novel real-time trajectory planning framework as a continuous-time collision-avoidance constraint. The planning method using RDF is compared to a variety of state-of-the-art techniques and is demonstrated to successfully solve challenging motion planning tasks for high-dimensional systems faster and more reliably than all tested methods.