ANY modern digital platforms involve the acquisition of data over networks, while network data has a stationary process models, ARMA models widely used in typically time-varying structure. For instance, measurements classical signal processing have also been adapted to graph acquired on a sensor network or user data in a social network domains in several recent works [5], [6]. Meanwhile, the often vary over time. Such data can be modeled as timevarying computation of an ARMA process model is a challenging graph signals, or time-vertex signals. In many practical problem in graph domains as it typically involves the solution applications, time-vertex signals may have missing observations of highly nonlinear and nonconvex optimization problems. The due to issues such as sensor failure, connection loss, and problem of learning graph ARMA process models has been partial availability of user statistics. Hence, the spatio-temporal addressed in the previous studies [3], [5], [6]; however, none of interpolation of time-vertex signals arises as an important these studies explicitly aim to capture the specific time-vertex problem of interest.

Reinforcement learning in sparse-reward navigation environments with expensive and limited interactions is challenging and poses a need for effective exploration. Motivated by complex navigation tasks that require real-world training (when cheap simulators are not available), we consider an agent that faces an unknown distribution of environments and must decide on an exploration strategy. It may leverage a series of training environments to improve its policy before it is evaluated in a test environment drawn from the same environment distribution. Most existing approaches focus on fixed exploration strategies, while the few that view exploration as a meta-optimization problem tend to ignore the need for cost-efficient exploration. We propose a cost-aware Bayesian optimization approach that efficiently searches over a class of dynamic subgoal-based exploration strategies. The algorithm adjusts a variety of levers -- the locations of the subgoals, the length of each episode, and the number of replications per trial -- in order to overcome the challenges of sparse rewards, expensive interactions, and noise. An experimental evaluation demonstrates that the new approach outperforms existing baselines across a number of problem domains. We also provide a theoretical foundation and prove that the method asymptotically identifies a near-optimal subgoal design.

As machine learning technology gets applied to actual products and solutions, new challenges have emerged. Models unexpectedly fail to generalize to small changes in the distribution, tend to be confident on novel data they have never seen, or cannot communicate the rationale behind their decisions effectively with the end users. Collectively, we face a trustworthiness issue with the current machine learning technology. This textbook on Trustworthy Machine Learning (TML) covers a theoretical and technical background of four key topics in TML: Out-of-Distribution Generalization, Explainability, Uncertainty Quantification, and Evaluation of Trustworthiness. We discuss important classical and contemporary research papers of the aforementioned fields and uncover and connect their underlying intuitions. The book evolved from the homonymous course at the University of T\"ubingen, first offered in the Winter Semester of 2022/23. It is meant to be a stand-alone product accompanied by code snippets and various pointers to further sources on topics of TML. The dedicated website of the book is https://trustworthyml.io/.

AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time, this work provides an automatic method for approximation analysis on a well-studied problem in theoretical computer science: computing approximate Nash equilibria in two-player games. We observe that such algorithms can be reformulated into a search-and-mix paradigm, which involves a search phase followed by a mixing phase. By doing so, we are able to fully automate the procedure of designing and analyzing the mixing phase. For example, we illustrate how to perform our method with a program to analyze the approximation bounds of all the algorithms in the literature. Same approximation bounds are computed without any hand-written proof. Our automatic method heavily relies on the LP-relaxation structure in approximate Nash equilibria. Since many approximation algorithms and online algorithms adopt the LP relaxation, our approach may be extended to automate the analysis of other algorithms.

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to distinguish samples from two groups. To solve this problem, we propose a framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a group of variables with a pre-specified size that maximizes the variance-regularized MMD statistics. This formulation also corresponds to the minimization of asymptotic type-II error while controlling type-I error, as studied in the literature. We present mixed-integer programming formulations and develop exact and approximation algorithms with performance guarantees for different choices of kernel functions. Furthermore, we provide a statistical testing power analysis of our proposed framework. Experiment results on synthetic and real datasets demonstrate the superior performance of our approach.

Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common scenario in real-world applications such as the design of medical therapies, industrial process optimization, and hyperparameter optimization. One popular approach to handling these complex scenarios is Bayesian Optimization (BO). In terms of theoretical behavior, BO is relatively well understood in the unconstrained setting, where its principles have been well explored and validated. However, when it comes to constrained Bayesian optimization (CBO), the existing framework often relies on heuristics or approximations without the same level of theoretical guarantees. In this paper, we delve into the theoretical and practical aspects of constrained Bayesian optimization, where the objective and constraints can be independently evaluated and are subject to noise. By recognizing that both the objective and constraints can help identify high-confidence regions of interest (ROI), we propose an efficient CBO framework that intersects the ROIs identified from each aspect to determine the general ROI. The ROI, coupled with a novel acquisition function that adaptively balances the optimization of the objective and the identification of feasible regions, enables us to derive rigorous theoretical guarantees for its performance. We showcase the efficiency and robustness of our proposed CBO framework through extensive empirical evidence and discuss the fundamental challenge of deriving practical regret bounds for CBO algorithms.

Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these approaches output a multi-modal distribution of obstacle trajectories instead of a single deterministic prediction to account for the underlying uncertainty. However, existing planners cannot handle the multi-modality based on just sample-level information of the predictions. With this motivation, this paper proposes a trajectory optimizer that can leverage the distributional aspects of the prediction in a computationally tractable and sample-efficient manner. Our optimizer can work with arbitrarily complex distributions and thus can be used with output distribution represented as a deep neural network. The core of our approach is built on embedding distribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage in two ways. First, we propose an RKHS embedding approach to select probable samples from the obstacle trajectory distribution. Second, we rephrase chance-constrained optimization as distribution matching in RKHS and propose a novel sampling-based optimizer for its solution. We validate our approach with hand-crafted and neural network-based predictors trained on real-world datasets and show improvement over the existing stochastic optimization approaches in safety metrics.

Recent developments in offline reinforcement learning have uncovered the immense potential of diffusion modeling, which excels at representing heterogeneous behavior policies. However, sampling from diffusion policies is considerably slow because it necessitates tens to hundreds of iterative inference steps for one action. To address this issue, we propose to extract an efficient deterministic inference policy from critic models and pretrained diffusion behavior models, leveraging the latter to directly regularize the policy gradient with the behavior distribution's score function during optimization. Our method enjoys powerful generative capabilities of diffusion modeling while completely circumventing the computationally intensive and time-consuming diffusion sampling scheme, both during training and evaluation. Extensive results on D4RL tasks show that our method boosts action sampling speed by more than 25 times compared with various leading diffusion-based methods in locomotion tasks, while still maintaining state-of-the-art performance.

In current model-free reinforcement learning (RL) algorithms, stability criteria based on sampling methods are commonly utilized to guide policy optimization. However, these criteria only guarantee the infinite-time convergence of the system's state to an equilibrium point, which leads to sub-optimality of the policy. In this paper, we propose a policy optimization technique incorporating sampling-based Lyapunov stability. Our approach enables the system's state to reach an equilibrium point within an optimal time and maintain stability thereafter, referred to as "optimal-time stability". To achieve this, we integrate the optimization method into the Actor-Critic framework, resulting in the development of the Adaptive Lyapunov-based Actor-Critic (ALAC) algorithm. Through evaluations conducted on ten robotic tasks, our approach outperforms previous studies significantly, effectively guiding the system to generate stable patterns.

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods.