Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs from the environment in which the learned policy is applied. To account for the effect of different environments during learning and execution, distributionally robust optimization (DRO) methods have been developed that compute worst-case bounds on the policy values assuming that the distribution of the new environment lies within an uncertainty set. Typically, this uncertainty set is defined based on the KL divergence around the empirical distribution computed from the logging dataset. However, the KL uncertainty set fails to encompass distributions with varying support and lacks awareness of the geometry of the distribution support. As a result, KL approaches fall short in addressing practical environment mismatches and lead to over-fitting to worst-case scenarios. To overcome these limitations, we propose a novel DRO approach that employs the Wasserstein distance instead. While Wasserstein DRO is generally computationally more expensive compared to KL DRO, we present a regularized method and a practical (biased) stochastic gradient descent method to optimize the policy efficiently. We also provide a theoretical analysis of the finite sample complexity and iteration complexity for our proposed method. We further validate our approach using a public dataset that was recorded in a randomized stoke trial.

Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The theoretical formulation of information flow for stochastic dynamical systems provides a general expression and a data-driven statistic for the rate of entropy transfer between different system units. To advance understanding of information flow rate in terms of intuitive concepts and physically meaningful parameters, we investigate statistical properties of the data-driven information flow rate between coupled stochastic processes. We derive relations between the expectation of the information flow rate statistic and properties of the auto- and cross-correlation functions. Thus, we elucidate the dependence of the information flow rate on the analytical properties and characteristic times of the correlation functions. Our analysis provides insight into the influence of the sampling step, the strength of cross-correlations, and the temporal delay of correlations on information flow rate. We support the theoretical results with numerical simulations of correlated Gaussian processes.

Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for comparing foundation models involves evaluating them with aggregate metrics on various benchmark datasets. This method of model comparison is heavily dependent on the chosen evaluation metric, which makes it unsuitable for situations where the ideal metric is either not obvious or unavailable. In this work, we present a methodology for directly comparing the embedding space geometry of foundation models, which facilitates model comparison without the need for an explicit evaluation metric. Our methodology is grounded in random graph theory and enables valid hypothesis testing of embedding similarity on a per-datum basis. Further, we demonstrate how our methodology can be extended to facilitate population level model comparison. In particular, we show how our framework can induce a manifold of models equipped with a distance function that correlates strongly with several downstream metrics. We remark on the utility of this population level model comparison as a first step towards a taxonomic science of foundation models.

The rapid advancement of artificial intelligence (AI) techniques has opened up new opportunities to revolutionize various fields, including operations research (OR). This survey paper explores the integration of AI within the OR process (AI4OR) to enhance its effectiveness and efficiency across multiple stages, such as parameter generation, model formulation, and model optimization. By providing a comprehensive overview of the state-of-the-art and examining the potential of AI to transform OR, this paper aims to inspire further research and innovation in the development of AI-enhanced OR methods and tools. The synergy between AI and OR is poised to drive significant advancements and novel solutions in a multitude of domains, ultimately leading to more effective and efficient decision-making.

Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contact with the environment. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we proposed a hybrid MPC solver based on Generalized Benders Decomposition (GBD). The algorithm enumerates and stores cutting planes online inside a finite buffer. After a short cold-start phase, the stored cuts provide warm-starts for the new problem instances to enhance the solving speed. Despite the disturbance and randomly changing environment, the solving speed maintains. Leveraging on the sparsity of feasibility cuts, we also propose a fast algorithm for Benders master problems. Our solver is validated through controlling a cart-pole system with randomly moving soft contact walls, and a free-flying robot navigating around obstacles. The results show that with significantly less data than previous works, the solver reaches competitive speeds to the off-the-shelf solver Gurobi despite the Python overhead.

The line coverage problem involves finding efficient routes for the coverage of linear features by one or more resource-constrained robots. Linear features model environments like road networks, power lines, and oil and gas pipelines. Two modes of travel are defined for robots: servicing and deadheading. A robot services a feature if it performs task-specific actions, such as taking images, as it traverses the feature; otherwise, it is deadheading. Traversing the environment incurs costs (e.g., travel time) and demands on resources (e.g., battery life). Servicing and deadheading can have different cost and demand functions, which can be direction-dependent. The environment is modeled as a graph, and an integer linear program is provided. As the problem is NP-hard, we design a fast and efficient heuristic algorithm, Merge-Embed-Merge (MEM). Exploiting the constructive property of the MEM algorithm, algorithms for line coverage of large graphs with multiple depots are developed. Furthermore, turning costs and nonholonomic constraints are efficiently incorporated into the algorithm. The algorithms are benchmarked on road networks and demonstrated in experiments with aerial robots.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

The effectiveness of advertising in e-commerce largely depends on the ability of merchants to bid on and win impressions for their targeted users. The bidding procedure is highly complex due to various factors such as market competition, user behavior, and the diverse objectives of advertisers. In this paper we consider the problem at the level of user timelines instead of individual bid requests, manipulating full policies (i.e. pre-defined bidding strategies) and not bid values. In order to optimally allocate policies to users, typical multiple treatments allocation methods solve knapsack-like problems which aim at maximizing an expected value under constraints. In the industrial contexts such as online advertising, we argue that optimizing for the probability of success is a more suited objective than expected value maximization, and we introduce the SuccessProbaMax algorithm that aims at finding the policy allocation which is the most likely to outperform a fixed reference policy. Finally, we conduct comprehensive experiments both on synthetic and real-world data to evaluate its performance. The results demonstrate that our proposed algorithm outperforms conventional expected-value maximization algorithms in terms of success rate.

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics. We propose the first approach for learning neural Lyapunov control in a broad class of discrete-time systems. Three key ingredients enable us to effectively learn provably stable control policies. The first is a novel mixed-integer linear programming approach for verifying the discrete-time Lyapunov stability conditions, leveraging the particular structure of these conditions. The second is a novel approach for computing verified sublevel sets. The third is a heuristic gradient-based method for quickly finding counterexamples to significantly speed up Lyapunov function learning. Our experiments on four standard benchmarks demonstrate that our approach significantly outperforms state-of-the-art baselines. For example, on the path tracking benchmark, we outperform recent neural Lyapunov control baselines by an order of magnitude in both running time and the size of the region of attraction, and on two of the four benchmarks (cartpole and PVTOL), ours is the first automated approach to return a provably stable controller. Our code is available at: https://github.com/jlwu002/nlc_discrete.

Flight Trajectory Prediction (FTP) is an essential task in Air Traffic Control (ATC), which can assist air traffic controllers in managing airspace more safely and efficiently. Existing approaches generally perform multi-horizon FTP tasks in an autoregressive manner, thereby suffering from error accumulation and low-efficiency problems. In this paper, a novel framework, called FlightBERT++, is proposed to i) forecast multi-horizon flight trajectories directly in a non-autoregressive way, and ii) improve the limitation of the binary encoding (BE) representation in the FlightBERT. Specifically, the FlightBERT++ is implemented by a generalized encoder-decoder architecture, in which the encoder learns the temporal-spatial patterns from historical observations and the decoder predicts the flight status for the future horizons. Compared with conventional architecture, an innovative horizon-aware contexts generator is dedicatedly designed to consider the prior horizon information, which further enables non-autoregressive multi-horizon prediction. Moreover, a differential prompted decoder is proposed to enhance the capability of the differential predictions by leveraging the stationarity of the differential sequence. The experimental results on a real-world dataset demonstrated that the FlightBERT++ outperformed the competitive baselines in both FTP performance and computational efficiency.