Physics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines in robotics. Over the past decades, several robotic simulators have been developed, each with dedicated contact modeling assumptions and algorithmic solutions. In this article, we survey the main contact models and the associated numerical methods commonly used in robotics for simulating advanced robot motions involving contact interactions. In particular, we recall the physical laws underlying contacts and friction (i.e., Signorini condition, Coulomb's law, and the maximum dissipation principle), and how they are transcribed in current simulators. For each physics engine, we expose their inherent physical relaxations along with their limitations due to the numerical techniques employed. Based on our study, we propose theoretically grounded quantitative criteria on which we build benchmarks assessing both the physical and computational aspects of simulation. We support our work with an open-source and efficient C++ implementation of the existing algorithmic variations. Our results demonstrate that some approximations or algorithms commonly used in robotics can severely widen the reality gap and impact target applications. We hope this work will help motivate the development of new contact models, contact solvers, and robotic simulators in general, at the root of recent progress in motion generation in robotics.

The Frank-Wolfe algorithm is a popular method in structurally constrained machine learning applications, due to its fast per-iteration complexity. However, one major limitation of the method is a slow rate of convergence that is difficult to accelerate due to erratic, zig-zagging step directions, even asymptotically close to the solution. We view this as an artifact of discretization; that is to say, the Frank-Wolfe \emph{flow}, which is its trajectory at asymptotically small step sizes, does not zig-zag, and reducing discretization error will go hand-in-hand in producing a more stabilized method, with better convergence properties. We propose two improvements: a multistep Frank-Wolfe method that directly applies optimized higher-order discretization schemes; and an LMO-averaging scheme with reduced discretization error, and whose local convergence rate over general convex sets accelerates from a rate of $O(1/k)$ to up to $O(1/k^{3/2})$.

This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a consensus-constraint distributed optimization cooperatively via continuous-time dynamics, while the links are subject to strongly sign-preserving odd nonlinear conditions. Logarithmic quantization and clipping (saturation) are two examples of such nonlinearities. In contrast to existing literature that mostly considers ideal links and perfect information exchange over linear channels, we show how general sector-bounded models affect the convergence to the optimizer (i.e., the SVM classifier) over dynamic balanced directed networks. In general, any odd sector-bounded nonlinear mapping can be applied to our dynamics. The main challenge is to show that the proposed system dynamics always have one zero eigenvalue (associated with the consensus) and the other eigenvalues all have negative real parts. This is done by recalling arguments from matrix perturbation theory. Then, the solution is shown to converge to the agreement state under certain conditions. For example, the gradient tracking (GT) step size is tighter than the linear case by factors related to the upper/lower sector bounds. To the best of our knowledge, no existing work in distributed optimization and learning literature considers non-ideal link conditions.

In this paper, we propose a framework for fast trajectory planning for unmanned aerial vehicles (UAVs). Our framework is reformulated from an existing bilevel optimization, in which the lower-level problem solves for the optimal trajectory with a fixed time allocation, whereas the upper-level problem updates the time allocation using analytical gradients. The lower-level problem incorporates the safety-set constraints (in the form of inequality constraints) and is cast as a convex quadratic program (QP). Our formulation modifies the lower-level QP by excluding the inequality constraints for the safety sets, which significantly reduces the computation time. The safety-set constraints are moved to the upper-level problem, where the feasible waypoints are updated together with the time allocation using analytical gradients enabled by the OptNet. We validate our approach in simulations, where our method's computation time scales linearly with respect to the number of safety sets, in contrast to the state-of-the-art that scales exponentially.

Machine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local minima and barren plateaus, which slow-down calculations and lead to non-optimal solutions. In practice, this results in dramatic computational and energy costs for AI applications. In this paper we introduce a generic strategy to accelerate and improve the overall performance of such methods, allowing to alleviate the effect of barren plateaus and local minima. Our method is based on coordinate transformations, somehow similar to variational rotations, adding extra directions in parameter space that depend on the cost function itself, and which allow to explore the configuration landscape more efficiently. The validity of our method is benchmarked by boosting a number of quantum machine learning algorithms, getting a very significant improvement in their performance.

Individual human decision-makers may benefit from different forms of support to improve decision outcomes. However, a key question is which form of support will lead to accurate decisions at a low cost. In this work, we propose learning a decision support policy that, for a given input, chooses which form of support, if any, to provide. We consider decision-makers for whom we have no prior information and formalize learning their respective policies as a multi-objective optimization problem that trades off accuracy and cost. Using techniques from stochastic contextual bandits, we propose $\texttt{THREAD}$, an online algorithm to personalize a decision support policy for each decision-maker, and devise a hyper-parameter tuning strategy to identify a cost-performance trade-off using simulated human behavior. We provide computational experiments to demonstrate the benefits of $\texttt{THREAD}$ compared to offline baselines. We then introduce $\texttt{Modiste}$, an interactive tool that provides $\texttt{THREAD}$ with an interface. We conduct human subject experiments to show how $\texttt{Modiste}$ learns policies personalized to each decision-maker and discuss the nuances of learning decision support policies online for real users.

Certified defense methods against adversarial perturbations have been recently investigated in the black-box setting with a zeroth-order (ZO) perspective. However, these methods suffer from high model variance with low performance on high-dimensional datasets due to the ineffective design of the denoiser and are limited in their utilization of ZO techniques. To this end, we propose a certified ZO preprocessing technique for removing adversarial perturbations from the attacked image in the black-box setting using only model queries. We propose a robust UNet denoiser (RDUNet) that ensures the robustness of black-box models trained on high-dimensional datasets. We propose a novel black-box denoised smoothing (DS) defense mechanism, ZO-RUDS, by prepending our RDUNet to the black-box model, ensuring black-box defense. We further propose ZO-AE-RUDS in which RDUNet followed by autoencoder (AE) is prepended to the black-box model. We perform extensive experiments on four classification datasets, CIFAR-10, CIFAR-10, Tiny Imagenet, STL-10, and the MNIST dataset for image reconstruction tasks. Our proposed defense methods ZO-RUDS and ZO-AE-RUDS beat SOTA with a huge margin of $35\%$ and $9\%$, for low dimensional (CIFAR-10) and with a margin of $20.61\%$ and $23.51\%$ for high-dimensional (STL-10) datasets, respectively.

In today's highly competitive and complex business environment, organizations are under constant pressure to optimize their performance and decision-making processes. According to Herbert Simon, enhancing organizational performance relies on effectively channeling finite human attention towards critical data for decision-making, necessitating the integration of information systems (IS), artificial intelligence (AI) and operations research (OR) insights [1]. Recent OR research provides evidence in support of this proposition, as the discipline has witnessed a transformation due to the abundant availability of rich and voluminous data from various sources coupled with advances in machine learning [2]. As of late, heightened academic attention has been devoted to prescriptive analytics, a discipline that suggests combining the results of predictive analytics with optimization techniques in a probabilistic framework to generate responsive, automated, restricted, time-sensitive, and ideal decisions [3]. The confluence of AI and OR is evident due to their interdependent and complementary nature, as both disciplines strive to augment decision-making processes through computational and mathematical methodologies [4].

Data-driven, learning-based control methods offer the potential to improve operations in complex systems, and model-free deep reinforcement learning represents a popular approach to data-driven control. However, existing classes of algorithms present a trade-off between two important deployment requirements for real-world control: (i) practical performance guarantees and (ii) data efficiency. Off-policy algorithms make efficient use of data through sample reuse but lack theoretical guarantees, while on-policy algorithms guarantee approximate policy improvement throughout training but suffer from high sample complexity. In order to balance these competing goals, we develop a class of Generalized Policy Improvement algorithms that combines the policy improvement guarantees of on-policy methods with the efficiency of sample reuse. We demonstrate the benefits of this new class of algorithms through extensive experimental analysis on a variety of continuous control tasks from the DeepMind Control Suite.

Influence maximization is the problem of finding a set of seed nodes in the network that maximizes the influence spread, which has become an important topic in social network analysis. Conventional influence maximization algorithms cause “unfair" influence spread among different groups in the population, which could lead to severe bias in public opinion dissemination and viral marketing. To address this issue, we formulate the fair influence maximization problem concerning the trade-off between influence maximization and group fairness. For the purpose of solving the fair influence maximization problem in large-scale social networks efficiently, we propose a novel attribute-based reverse influence sampling (ABRIS) framework. This framework intends to estimate influence in specific groups with guarantee through an attribute-based hypergraph so that we can select seed nodes strategically. Therefore, under the ABRIS framework, we design two different node selection algorithms, ABRIS-G and ABRIS-T. ABRIS-G selects nodes in a greedy scheduling way. ABRIS-T adopts a two-phase node selection method. These algorithms run efficiently and achieve a good trade-off between influence maximization and group fairness. Extensive experiments on six real-world social networks show that our algorithms significantly outperform the state-of-the-art approaches. This article appears in the AI & Society track.