This paper studies the cost-performance tradeoffs in cloud robotics with heterogeneous cloud service providers, which have complex pricing models and varying application requirements. We present FogROS2-Sky, a cost-efficient open source robotics platform that offloads unmodified ROS2 applications to multiple cloud providers and enables fine-grained cost analysis for ROS2 applications' communication with multiple cloud providers. As each provider offers different options for CPU, GPU, memory, and latency, it can be very difficult for users to decide which to choose. FogROS2-Sky includes an optimization algorithm, which either finds the best available hardware specification that fulfills the user's latency and cost constraints or reports that such a specification does not exist. We use FogROS2-Sky to perform time-cost analysis on three robotics applications: visual SLAM, grasp planning, and motion planning. We are able to sample different hardware setups at nearly half the cost while still create cost and latency functions suitable for the optimizer. We also evaluate the optimizer's efficacy for these applications with the Pareto frontier and show that the optimizer selects efficient hardware configurations to balance cost and latency. Videos and code are available on the website https://sites.google.com/view/fogros2-sky

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this inconsistency. We present the first tractable inference algorithm for PDGs with discrete variables, making the asymptotic complexity of PDG inference similar that of the graphical models they generalize. The key components are: (1) the observation that, in many cases, the distribution a PDG specifies can be formulated as a convex optimization problem (with exponential cone constraints), (2) a construction that allows us to express these problems compactly for PDGs of boundeed treewidth, (3) contributions to the theory of PDGs that justify the construction, and (4) an appeal to interior point methods that can solve such problems in polynomial time. We verify the correctness and complexity of our approach, and provide an implementation of it. We then evaluate our implementation, and demonstrate that it outperforms baseline approaches. Our code is available at http://github.com/orichardson/pdg-infer-uai.

Model-based optimization (MBO) is increasingly applied to design problems in science and engineering. A common scenario involves using a fixed training set to train models, with the goal of designing new samples that outperform those present in the training data. A major challenge in this setting is distribution shift, where the distributions of training and design samples are different. While some shift is expected, as the goal is to create better designs, this change can negatively affect model accuracy and subsequently, design quality. Despite the widespread nature of this problem, addressing it demands deep domain knowledge and artful application. To tackle this issue, we propose a straightforward method for design practitioners that detects distribution shifts. This method trains a binary classifier using knowledge of the unlabeled design distribution to separate the training data from the design data. The classifier's logit scores are then used as a proxy measure of distribution shift. We validate our method in a real-world application by running offline MBO and evaluate the effect of distribution shift on design quality. We find that the intensity of the shift in the design distribution varies based on the number of steps taken by the optimization algorithm, and our simple approach can identify these shifts. This enables users to constrain their search to regions where the model's predictions are reliable, thereby increasing the quality of designs.

Internet of Things (IoT) involves sensors for monitoring and wireless networks for efficient communication. However, resource-constrained IoT devices and limitations in existing wireless technologies hinder its full potential. Integrating Unmanned Aerial Vehicles (UAVs) into IoT networks can address some challenges by expanding its' coverage, providing security, and bringing computing closer to IoT devices. Nevertheless, effective data collection in UAV-assisted IoT networks is hampered by factors, including dynamic UAV behavior, environmental variables, connectivity instability, and security considerations. In this survey, we first explore UAV-based IoT networks, focusing on communication and networking aspects. Next, we cover various UAV-based data collection methods their advantages and disadvantages, followed by a discussion on performance metrics for data collection. As this article primarily emphasizes reliable and efficient data collection in UAV-assisted IoT networks, we briefly discuss existing research on data accuracy and consistency, network connectivity, and data security and privacy to provide insights into reliable data collection. Additionally, we discuss efficient data collection strategies in UAV-based IoT networks, covering trajectory and path planning, collision avoidance, sensor network clustering, data aggregation, UAV swarm formations, and artificial intelligence for optimization. We also present two use cases of UAVs as a service for enhancing data collection reliability and efficiency. Finally, we discuss future challenges in data collection for UAV-assisted IoT networks.

We study the problem of learning decentralized linear quadratic regulator when the system model is unknown a priori. We propose an online learning algorithm that adaptively designs a control policy as new data samples from a single system trajectory become available. Our algorithm design uses a disturbance-feedback representation of state-feedback controllers coupled with online convex optimization with memory and delayed feedback. We show that our controller enjoys an expected regret that scales as $\sqrt{T}$ with the time horizon $T$ for the case of partially nested information pattern. For more general information patterns, the optimal controller is unknown even if the system model is known. In this case, the regret of our controller is shown with respect to a linear sub-optimal controller. We validate our theoretical findings using numerical experiments.

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that any empirical risk minimizer (ERM) shows good performance on the true population?" This question was proposed by Feldman (2016), who proved that $\Omega(\frac{d}{\epsilon}+\frac{1}{\epsilon^2})$ data points are necessary (where $d$ is the dimension and $\epsilon>0$ is the accuracy parameter). Proving an $\omega(\frac{d}{\epsilon}+\frac{1}{\epsilon^2})$ lower bound was left as an open problem. In this work we show that in fact $\tilde{O}(\frac{d}{\epsilon}+\frac{1}{\epsilon^2})$ data points are also sufficient. This settles the question and yields a new separation between ERMs and uniform convergence. This sample complexity holds for the classical setup of learning bounded convex Lipschitz functions over the Euclidean unit ball. We further generalize the result and show that a similar upper bound holds for all symmetric convex bodies. The general bound is composed of two terms: (i) a term of the form $\tilde{O}(\frac{d}{\epsilon})$ with an inverse-linear dependence on the accuracy parameter, and (ii) a term that depends on the statistical complexity of the class of $\textit{linear}$ functions (captured by the Rademacher complexity). The proof builds a mechanism for controlling the behavior of stochastic convex optimization problems.

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane generator mapping the problem data and previous iterates to cutting planes. We propose a CPL implementation to generate split cuts, and by combining several CPLs, we devise a differentiable cutting-plane algorithm that exploits the repeated nature of parametric instances. In an offline phase, we train our algorithm by updating the internal parameters controlling the CPLs, thus altering cut generation. Once trained, our algorithm computes, with predictable execution times and a fixed number of cuts, solutions with low integrality gaps. Preliminary computational tests show that our algorithm generalizes on unseen instances and captures underlying parametric structures.

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$\beta$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios. The code is available at https://github.com/Raiden-Zhu/ICML-2023-DSGD-and-SAM.

We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem, we propose a Bayesian strategy based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.

We study the convergence behavior of the celebrated temporal-difference (TD) learning algorithm. By looking at the algorithm through the lens of optimization, we first argue that TD can be viewed as an iterative optimization algorithm where the function to be minimized changes per iteration. By carefully investigating the divergence displayed by TD on a classical counter example, we identify two forces that determine the convergent or divergent behavior of the algorithm. We next formalize our discovery in the linear TD setting with quadratic loss and prove that convergence of TD hinges on the interplay between these two forces. We extend this optimization perspective to prove convergence of TD in a much broader setting than just linear approximation and squared loss. Our results provide a theoretical explanation for the successful application of TD in reinforcement learning.