In this paper, we tackle the problem of flying a quadrotor using time-optimal control policies that can be replanned online when the environment changes or when encountering unknown disturbances. This problem is challenging as the time-optimal trajectories that consider the full quadrotor dynamics are computationally expensive to generate (order of minutes or even hours). We introduce a sampling-based method for efficient generation of time-optimal paths of a point-mass model. These paths are then tracked using a Model Predictive Contouring Control approach that considers the full quadrotor dynamics and the single rotor thrust limits. Our combined approach is able to run in real-time, being the first time-optimal method that is able to adapt to changes on-the-fly. We showcase our approach's adaption capabilities by flying a quadrotor at more than 60 km/h in a racing track where gates are moving. Additionally, we show that our online replanning approach can cope with strong disturbances caused by winds of up to 68 km/h.

Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This perspective enables us to reason about the effects of changes to this process (interventions) and what would have happened in hindsight (counterfactuals). We categorize work in CausalML into five groups according to the problems they address: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, and (5) causal reinforcement learning. We systematically compare the methods in each category and point out open problems. Further, we review data-modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.

Louis is a front-end developer, writer, and author based in Toronto, Canada. In recent years, the web development community has rightfully spread the message widely that images are often the largest resource on any given web page. While many developers spend time optimizing other areas of a web page's performance, reducing the size of images can have a bigger impact on performance than all other areas combined. You might already know that Smashing Magazine has published the book Image Optimization by Addy Osmani, which covers this topic in full detail. But consider this post a compliment to the book, as this will focus purely on different tools available for reducing the size of images.

In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. The training data are generated uniformly in the domain of interest, consisting of the state samples and corresponding affine control laws, based on which the lattice PWA approximations are constructed. Re-sampling of data is also proposed to guarantee that the lattice PWA approximations are identical to explicit MPC control law in the unique order (UO) regions containing the sample points as interior points. Additionally, under mild assumptions, the equivalence of the two lattice PWA approximations guarantees that the approximations are error-free in the domain of interest. The algorithms for deriving statistically error-free approximation to the explicit linear MPC are proposed and the complexity of the entire procedure is analyzed, which is polynomial with respect to the number of samples. The performance of the proposed approximation strategy is tested through two simulation examples, and the result shows that with a moderate number of sample points, we can construct lattice PWA approximations that are equivalent to optimal control law of the explicit linear MPC.

Task allocation using a team or coalition of robots is one of the most important problems in robotics, computer science, operational research, and artificial intelligence. In recent work, research has focused on handling complex objectives and feasibility constraints amongst other variations of the multi-robot task allocation problem. There are many examples of important research progress in these directions. We present a general formulation of the task allocation problem that generalizes several versions that are well-studied. Our formulation includes the states of robots, tasks, and the surrounding environment in which they operate. We describe how the problem can vary depending on the feasibility constraints, objective functions, and the level of dynamically changing information. In addition, we discuss existing solution approaches for the problem including optimization-based approaches, and market-based approaches.

Engineering a high-performance race car requires a direct consideration of the human driver using real-world tests or Human-Driver-in-the-Loop simulations. Apart from that, offline simulations with human-like race driver models could make this vehicle development process more effective and efficient but are hard to obtain due to various challenges. With this work, we intend to provide a better understanding of race driver behavior and introduce an adaptive human race driver model based on imitation learning. Using existing findings and an interview with a professional race engineer, we identify fundamental adaptation mechanisms and how drivers learn to optimize lap time on a new track. Subsequently, we use these insights to develop generalization and adaptation techniques for a recently presented probabilistic driver modeling approach and evaluate it using data from professional race drivers and a state-of-the-art race car simulator. We show that our framework can create realistic driving line distributions on unseen race tracks with almost human-like performance. Moreover, our driver model optimizes its driving lap by lap, correcting driving errors from previous laps while achieving faster lap times. This work contributes to a better understanding and modeling of the human driver, aiming to expedite simulation methods in the modern vehicle development process and potentially supporting automated driving and racing technologies.

With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate rule conflicts, both of which are ubiquitous in practice. It is also desirable for them to be simple and interpretable, so they can be easily verified and implemented. Existing approaches from the literature center around constructing variants of prescriptive decision trees to generate interpretable policies. However, none of the existing methods are able to handle constraints. In this paper, we propose a scalable method that solves the constrained prescriptive policy generation problem. We introduce a novel path-based mixed-integer program (MIP) formulation which identifies a (near) optimal policy efficiently via column generation. The policy generated can be represented as a multiway-split tree which is more interpretable and informative than a binary-split tree due to its shorter rules. We demonstrate the efficacy of our method with extensive experiments on both synthetic and real datasets.

Examples can be found in all areas of engineering and science, for instance plant breeding (Hunter & McClosky, 2016), aircraft maintenance (Mattila & Virtanen, 2014) or electric network planning (Dutrieux et al., 2015b). In this work, we choose to focus on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. One of the classical algorithms for Bayesian deterministic multi-objective optimization is the ParEGO algorithm (Knowles, 2006). It relies on a scalarization approach to extend the very popular single-objective Efficient Global Optimization (EGO) algorithm (Jones et al., 1998), based on the Expected Improvement (EI) criterion. Another scalarization approach, called multi-attribute Knowledge Gradient (Astudillo & Frazier, 2017), uses the Knowledge Gradient (KG) criterion instead of the EI criterion.

Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the self-expressive model which represents the samples as linear combination of other samples. However, these approaches require sufficiently well-spread samples for accurate representation which might not be necessarily accessible in many applications. In this paper, we shed light on this commonly neglected issue and argue that data distribution within each subspace plays a critical role in the success of self-expressive models. Our proposed solution to tackle this issue is motivated by the central role of data augmentation in the generalization power of deep neural networks. We propose two subspace clustering frameworks for both unsupervised and semi-supervised settings that use augmented samples as an enlarged dictionary to improve the quality of the self-expressive representation. We present an automatic augmentation strategy using a few labeled samples for the semi-supervised problem relying on the fact that the data samples lie in the union of multiple linear subspaces. Experimental results confirm the effectiveness of data augmentation, as it significantly improves the performance of general self-expressive models.

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study the convergence properties of a natural alternating update rule for this nonconvex optimization problem starting from a random initialization. We show sharp convergence guarantees for a sample-split version of the algorithm by deriving a deterministic recursion that is accurate even in high-dimensional problems. Notably, while the infinite-sample population update is uninformative and suggests exact recovery in a single step, the algorithm -- and our deterministic prediction -- converges geometrically fast from a random initialization. Our sharp, non-asymptotic analysis also exposes several other fine-grained properties of this problem, including how the nonlinearity and noise level affect convergence behavior. On a technical level, our results are enabled by showing that the empirical error recursion can be predicted by our deterministic sequence within fluctuations of the order $n^{-1/2}$ when each iteration is run with $n$ observations. Our technique leverages leave-one-out tools originating in the literature on high-dimensional $M$-estimation and provides an avenue for sharply analyzing higher-order iterative algorithms from a random initialization in other high-dimensional optimization problems with random data.