The clients' positions may change in complex and unpredictable ways and thus an a priori knowledge

Motion planning and trajectory generation are crucial technologies in various domains including the control of Unmanned Aerial Vehicles (UAV), manipulators, and rockets. However, optimization-based real-time motion planning becomes increasingly challenging due to the problem's probable non-convexity and the inherent limitations of Non-Linear Programming algorithms. Highly nonlinear dynamics, obstacle avoidance constraints, and non-convex inputs can exacerbate these difficulties. To address these hurdles, this paper proposes a two-layer optimization algorithm for 2D vehicles by dynamically reformulating small time horizon convex programming subproblems, aiming to provide real-time guarantees for trajectory optimization. Our approach involves breaking down the original problem into small horizon-based planning cycles with fixed final times, referred to as planning cycles. Each planning cycle is then solved within a series of restricted convex sets identified by our customized search algorithms incrementally. The key benefits of our proposed algorithm include fast computation speeds and lower task time. We demonstrate these advantages through mathematical proofs under some moderate preconditions and experimental results.

Across various sectors such as healthcare, criminal justice, national security, finance, and technology, large-scale machine learning (ML) and artificial intelligence (AI) systems are being deployed to make critical data-driven decisions. Many have asked if we can and should trust these ML systems to be making these decisions. Two critical components are prerequisites for trust in ML systems: interpretability, or the ability to understand why the ML system makes the decisions it does, and fairness, which ensures that ML systems do not exhibit bias against certain individuals or groups. Both interpretability and fairness are important and have separately received abundant attention in the ML literature, but so far, there have been very few methods developed to directly interpret models with regard to their fairness. In this paper, we focus on arguably the most popular type of ML interpretation: feature importance scores. Inspired by the use of decision trees in knowledge distillation, we propose to leverage trees as interpretable surrogates for complex black-box ML models. Specifically, we develop a novel fair feature importance score for trees that can be used to interpret how each feature contributes to fairness or bias in trees, tree-based ensembles, or tree-based surrogates of any complex ML system. Like the popular mean decrease in impurity for trees, our Fair Feature Importance Score is defined based on the mean decrease (or increase) in group bias. Through simulations as well as real examples on benchmark fairness datasets, we demonstrate that our Fair Feature Importance Score offers valid interpretations for both tree-based ensembles and tree-based surrogates of other ML systems.

In this study, we capitalized on a collective dataset repository of 57k accidents from 9 companies belonging to 3 domains and tested whether models trained on multiple datasets (generic models) predicted safety outcomes better than the company-specific models. We experimented with full generic models (trained on all data), per-domain generic models (construction, electric T&D, oil & gas), and with ensembles of generic and specific models. Results are very positive, with generic models outperforming the company-specific models in most cases while also generating finer-grained, hence more useful, forecasts. Successful generic models remove the needs for training company-specific models, saving a lot of time and resources, and give small companies, whose accident datasets are too limited to train their own models, access to safety outcome predictions. It may still however be advantageous to train specific models to get an extra boost in performance through ensembling with the generic models. Overall, by learning lessons from a pool of datasets whose accumulated experience far exceeds that of any single company, and making these lessons easily accessible in the form of simple forecasts, generic models tackle the holy grail of safety cross-organizational learning and dissemination in the construction industry.

Animals inspiring robot design is not a new phenomenon, as robots have commonly been developed to mimic animal movements such as walking and swimming. Now, US researchers are investigating how to design robots that imitate the gliding motion performed by flying snakes. The study, 'Computational analysis of vortex dynamics and aerodynamic performance in flying-snake-like gliding flight with horizontal undulation,' is published in Physics of Fluids. The investigation analysed the lift production mechanism of flying snakes that undulate side-to-side as they travel from the tops of trees to the ground to evade predators or move efficiently. This undulation enables flying snakes to glide for great distances – as far as 25 metres from a 15-metre height.

When sound was first incorporated into movies in the 1920s, it opened up new possibilities for filmmakers such as music and spoken dialogue. Physicists may be on the verge of a similar revolution, thanks to a new device developed at Stanford University that promises to bring an audio dimension to previously silent quantum science experiments. In particular, it could bring sound to a common quantum science setup known as an optical lattice, which uses a crisscrossing mesh of laser beams to arrange atoms in an orderly manner resembling a crystal. This tool is commonly used to study the fundamental characteristics of solids and other phases of matter that have repeating geometries. A shortcoming of these lattices, however, is that they are silent.

Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition --- increasing-differences.

Before deploying autonomous agents in the real world, we need to be confident they will perform safely in novel situations. Ideally, we would expose agents to a very wide range of situations during training, allowing them to learn about every possible danger, but this is often impractical. This paper investigates safety and generalization from a limited number of training environments in deep reinforcement learning (RL). We find RL algorithms can fail dangerously on unseen test environments even when performing perfectly on training environments. Firstly, in a gridworld setting, we show that catastrophes can be significantly reduced with simple modifications, including ensemble model averaging and the use of a blocking classifier. In the more challenging CoinRun environment we find similar methods do not significantly reduce catastrophes. However, we do find that the uncertainty information from the ensemble is useful for predicting whether a catastrophe will occur within a few steps and hence whether human intervention should be requested.

Wasserstein distributionally robust optimization (DRO) estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by the need to identify model parameters (or) decision choices that are robust to model uncertainties and misspecification, the Wasserstein DRO estimators recover a wide range of regularized estimators, including square-root LASSO and support vector machines, among others, as particular cases. This paper studies the asymptotic normality of underlying DRO estimators as well as the properties of an optimal (in a suitable sense) confidence region induced by the Wasserstein DRO formulation.