High-level robot skills represent an increasingly popular paradigm in robot programming. However, configuring the skills' parameters for a specific task remains a manual and time-consuming endeavor. Existing approaches for learning or optimizing these parameters often require numerous real-world executions or do not work in dynamic environments. To address these challenges, we propose MuTT, a novel encoder-decoder transformer architecture designed to predict environment-aware executions of robot skills by integrating vision, trajectory, and robot skill parameters. Notably, we pioneer the fusion of vision and trajectory, introducing a novel trajectory projection. Furthermore, we illustrate MuTT's efficacy as a predictor when combined with a model-based robot skill optimizer. This approach facilitates the optimization of robot skill parameters for the current environment, without the need for real-world executions during optimization. Designed for compatibility with any representation of robot skills, MuTT demonstrates its versatility across three comprehensive experiments, showcasing superior performance across two different skill representations.

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models. While various heuristics aim to optimize the distributionally robust risk using the $\infty$-Wasserstein metric, such a notion of robustness frequently encounters computation intractability. To tackle the computational challenge, we develop a novel approach to adversarial training that integrates $\phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We develop stochastic gradient methods with biased oracles to solve this problem efficiently, achieving the near-optimal sample complexity. Moreover, we establish its regularization effects and demonstrate it is asymptotic equivalence to a regularized empirical risk minimization framework, by considering various scaling regimes of the regularization parameter and robustness level. These regimes yield gradient norm regularization, variance regularization, or a smoothed gradient norm regularization that interpolates between these extremes. We numerically validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.

Rule-based neural networks stand out for enabling interpretable classification by learning logical rules for both prediction and interpretation. However, existing models often lack flexibility due to the fixed model structure. Addressing this, we introduce the Normal Form Rule Learner (NFRL) algorithm, leveraging a selective discrete neural network, that treat weight parameters as hard selectors, to learn rules in both Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF) for enhanced accuracy and interpretability. Instead of adopting a deep, complex structure, the NFRL incorporates two specialized Normal Form Layers (NFLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Normal Form Constraint (NFC) to streamline neuron connections. We also show the novel network architecture can be optimized using adaptive gradient update together with Straight-Through Estimator to overcome the gradient vanishing challenge. Through extensive experiments on 11 datasets, NFRL demonstrates superior classification performance, quality of learned rules, efficiency and interpretability compared to 12 state-of-the-art alternatives. Code and data are available at \url{https://anonymous.4open.science/r/NFRL-27B4/}.

This study addresses the challenge of fleet design optimization in the context of heterogeneous multi-robot fleets, aiming to obtain feasible designs that balance performance and costs. In the domain of autonomous multi-robot exploration, reinforcement learning agents play a central role, offering adaptability to complex terrains and facilitating collaboration among robots. However, modifying the fleet composition results in changes in the learned behavior, and training multi-robot systems using multi-agent reinforcement learning is expensive. Therefore, an exhaustive evaluation of each potential fleet design is infeasible. To tackle these hurdles, we introduce Bayesian Optimization for Fleet Design (BOFD), a framework leveraging multi-objective Bayesian Optimization to explore fleets on the Pareto front of performance and cost while accounting for uncertainty in the design space. Moreover, we establish a sub-linear bound for cumulative regret, supporting BOFD's robustness and efficacy. Extensive benchmark experiments in synthetic and simulated environments demonstrate the superiority of our framework over state-of-the-art methods, achieving efficient fleet designs with minimal fleet evaluations.

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. Thus, not only does this model allow for learning stochastic algorithms based on their empirical performance, it also yields results about their actual convergence rate and their actual convergence time. We stress that, since the model is valid in a more general setting than learning-to-optimize, it is of interest for other fields of application, too. Finally, we conduct five practically relevant experiments, showing the validity of our claims.

The ICP registration algorithm has been a preferred method for LiDAR-based robot localization for nearly a decade. However, even in modern SLAM solutions, ICP can degrade and become unreliable in geometrically ill-conditioned environments. Current solutions primarily focus on utilizing additional sources of information, such as external odometry, to either replace the degenerate directions of the optimization solution or add additional constraints in a sensor-fusion setup afterward. In response, this work investigates and compares new and existing degeneracy mitigation methods for robust LiDAR-based localization and analyzes the efficacy of these approaches in degenerate environments for the first time in the literature at this scale. Specifically, this work proposes and investigates i) the incorporation of different types of constraints into the ICP algorithm, ii) the effect of using active or passive degeneracy mitigation techniques, and iii) the choice of utilizing global point cloud registration methods on the ill-conditioned ICP problem in LiDAR degenerate environments. The study results are validated through multiple real-world field and simulated experiments. The analysis shows that active optimization degeneracy mitigation is necessary and advantageous in the absence of reliable external estimate assistance for LiDAR-SLAM. Furthermore, introducing degeneracy-aware hard constraints in the optimization before or during the optimization is shown to perform better in the wild than by including the constraints after. Moreover, with heuristic fine-tuned parameters, soft constraints can provide equal or better results in complex ill-conditioned scenarios. The implementations used in the analysis of this work are made publicly available to the community.

Model merging, which combines multiple models into a single model, has gained increasing popularity in recent years. By efficiently integrating the capabilities of various models without their original training data, this significantly reduces the parameter count and memory usage. However, current methods can only produce one single merged model. This necessitates a performance trade-off due to conflicts among the various models, and the resultant one-size-fits-all model may not align with the preferences of different users who may prioritize certain models over others. To address this issue, we propose preference-aware model merging, and formulate this as a multi-objective optimization problem in which the performance of the merged model on each base model's task is treated as an objective. In only one merging process, the proposed parameter-efficient structure can generate the whole Pareto set of merged models, each representing the Pareto-optimal model for a given user-specified preference. Merged models can also be selected from the learned Pareto set that are tailored to different user preferences. Experimental results on a number of benchmark datasets demonstrate that the proposed preference-aware Pareto Merging can obtain a diverse set of trade-off models and outperforms state-of-the-art model merging baselines.

Google Vizier has performed millions of optimizations and accelerated numerous research and production systems at Google, demonstrating the success of Bayesian optimization as a large-scale service. Over multiple years, its algorithm has been improved considerably, through the collective experiences of numerous research efforts and user feedback. In this technical report, we discuss the implementation details and design choices of the current default algorithm provided by Open Source Vizier. Our experiments on standardized benchmarks reveal its robustness and versatility against well-established industry baselines on multiple practical modes.

Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. This model selection problem can be challenging due to its large combinatorial search space, particularly when dealing with non-parametric causal models. Recent research has sought to bypass the combinatorial search by reformulating causal discovery as a continuous optimization problem, employing constraints that ensure the acyclicity of the graph. In non-parametric settings, existing approaches typically rely on finite-dimensional approximations of the relationships between nodes, resulting in a score-based continuous optimization problem with a smooth acyclicity constraint. In this work, we develop an alternative approximation method by utilizing reproducing kernel Hilbert spaces (RKHS) and applying general sparsity-inducing regularization terms based on partial derivatives. Within this framework, we introduce an extended RKHS representer theorem. To enforce acyclicity, we advocate the log-determinant formulation of the acyclicity constraint and show its stability. Finally, we assess the performance of our proposed RKHS-DAGMA procedure through simulations and illustrative data analyses.

Leverage scores have become essential in statistics and machine learning, aiding regression analysis, randomized matrix computations, and various other tasks. This paper delves into the inverse problem, aiming to recover the intrinsic model parameters given the leverage scores gradient. This endeavor not only enriches the theoretical understanding of models trained with leverage score techniques but also has substantial implications for data privacy and adversarial security. We specifically scrutinize the inversion of the leverage score gradient, denoted as $g(x)$. An innovative iterative algorithm is introduced for the approximate resolution of the regularized least squares problem stated as $\min_{x \in \mathbb{R}^d} 0.5 \|g(x) - c\|_2^2 + 0.5\|\mathrm{diag}(w)Ax\|_2^2$. Our algorithm employs subsampled leverage score distributions to compute an approximate Hessian in each iteration, under standard assumptions, considerably mitigating the time complexity. Given that a total of $T = \log(\| x_0 - x^* \|_2/ \epsilon)$ iterations are required, the cost per iteration is optimized to the order of $O( (\mathrm{nnz}(A) + d^{\omega} ) \cdot \mathrm{poly}(\log(n/\delta))$, where $\mathrm{nnz}(A)$ denotes the number of non-zero entries of $A$.