Fast kinodynamic motion planning is crucial for systems to effectively adapt to dynamically changing environments. Despite some efforts, existing approaches still struggle with rapid planning in high-dimensional, complex problems. Not surprisingly, the primary challenge arises from the high-dimensionality of the search space, specifically the trajectory space. We address this issue with a two-step method: initially, we identify a lower-dimensional trajectory manifold {\it offline}, comprising diverse trajectories specifically relevant to the task at hand while meeting kinodynamic constraints. Subsequently, we search for solutions within this manifold {\it online}, significantly enhancing the planning speed. To encode and generate a manifold of continuous-time, differentiable trajectories, we propose a novel neural network model, {\it Differentiable Motion Manifold Primitives (DMMP)}, along with a practical training strategy. Experiments with a 7-DoF robot arm tasked with dynamic throwing to arbitrary target positions demonstrate that our method surpasses existing approaches in planning speed, task success, and constraint satisfaction.

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of nonsmooth optimization algorithms characterized by the active manifold identification property. This class includes a diverse array of methods such as the proximal point method, proximal gradient method, proximal linear method, proximal coordinate descent method, Douglas-Rachford splitting (or the alternating direction method of multipliers), and the iteratively reweighted $\ell_1$ method, among others. Under the assumption that the optimization problem possesses an active manifold at a stationary point, we establish a local R-linear convergence rate for the Anderson-accelerated algorithm. Our extensive numerical experiments further highlight the robust performance of the proposed Anderson-accelerated methods.

Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $\Phi$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $\Phi$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by $\mathsf{QAC}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.

This paper explores a variation of the Traveling Salesperson Problem, where the agent places a circular obstacle next to each node once it visits it. Referred to as the Traveling Salesperson Problem with Circle Placement (TSP-CP), the aim is to maximize the obstacle radius for which a valid closed tour exists and then minimize the tour cost. The TSP-CP finds relevance in various real-world applications, such as harvesting, quarrying, and open-pit mining. We propose several novel solvers to address the TSP-CP, its variant tailored for Dubins vehicles, and a crucial subproblem known as the Traveling Salesperson Problem on self-deleting graphs (TSP-SD). Our extensive experimental results show that the proposed solvers outperform the current state-of-the-art on related problems in solution quality.

In reinforcement learning, off-policy actor-critic approaches like DDPG and TD3 are based on the deterministic policy gradient. Herein, the Q-function is trained from off-policy environment data and the actor (policy) is trained to maximize the Q-function via gradient ascent. We observe that in complex tasks like dexterous manipulation and restricted locomotion, the Q-value is a complex function of action, having several local optima or discontinuities. This poses a challenge for gradient ascent to traverse and makes the actor prone to get stuck at local optima. To address this, we introduce a new actor architecture that combines two simple insights: (i) use multiple actors and evaluate the Q-value maximizing action, and (ii) learn surrogates to the Q-function that are simpler to optimize with gradient-based methods. We evaluate tasks such as restricted locomotion, dexterous manipulation, and large discrete-action space recommender systems and show that our actor finds optimal actions more frequently and outperforms alternate actor architectures.

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of differentiable programming to computational plasma physics. First, we consider how differentiable programming can be used to simplify and improve stellarator optimization. We introduce a stellarator coil design code (FOCUSADD) that uses gradient-based optimization to produce stellarator coils with finite build. Because we use reverse mode AD, which can compute gradients of scalar functions with the same computational complexity as the function, FOCUSADD is simple, flexible, and efficient. We then discuss two additional applications of AD in stellarator optimization. Second, we explore how machine learning (ML) can be used to improve or replace the numerical methods used to solve partial differential equations (PDEs), focusing on time-dependent PDEs in fluid mechanics relevant to plasma physics. Differentiable programming allows neural networks and other techniques from ML to be embedded within numerical methods. This is a promising, but relatively new, research area. We focus on two basic questions. First, can we design ML-based PDE solvers that have the same guarantees of conservation, stability, and positivity that standard numerical methods do? The answer is yes; we introduce error-correcting algorithms that preserve invariants of time-dependent PDEs. Second, which types of ML-based solvers work best at solving PDEs? We perform a systematic review of the scientific literature on solving PDEs with ML. Unfortunately we discover two issues, weak baselines and reporting biases, that affect the interpretation reproducibility of a significant majority of published research. We conclude that using ML to solve PDEs is not as promising as we initially believed.

Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network's ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. Bayesian OED requires four elements: 1) A likelihood function that describes the distribution of detection and travel time data from the sensor network, 2) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, 3) An algorithm to compute EIG about seismic events over a dataset of hypothetical prior events, 4) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number, and locations influence uncertainty; and how prior models and constraints influence sensor placement.

Recent breakthroughs in preference alignment have significantly improved Large Language Models' ability to generate texts that align with human preferences and values. However, current alignment metrics typically emphasize the post-hoc overall improvement, while overlooking a critical aspect: regression, which refers to the backsliding on previously correctly-handled data after updates. This potential pitfall may arise from excessive fine-tuning on already well-aligned data, which subsequently leads to over-alignment and degeneration. To address this challenge, we propose FlipGuard, a constrained optimization approach to detect and mitigate update regression with focal attention. Specifically, FlipGuard identifies performance degradation using a customized reward characterization and strategically enforces a constraint to encourage conditional congruence with the pre-aligned model during training. Comprehensive experiments demonstrate that FlipGuard effectively alleviates update regression while demonstrating excellent overall performance, with the added benefit of knowledge preservation while aligning preferences.

Sharpness-aware minimization (SAM) has been shown to improve the generalization of neural networks. However, each SAM update requires \emph{sequentially} computing two gradients, effectively doubling the per-iteration cost compared to base optimizers like SGD. We propose a simple modification of SAM, termed SAMPa, which allows us to fully parallelize the two gradient computations. SAMPa achieves a twofold speedup of SAM under the assumption that communication costs between devices are negligible. Empirical results show that SAMPa ranks among the most efficient variants of SAM in terms of computational time. Additionally, our method consistently outperforms SAM across both vision and language tasks. Notably, SAMPa theoretically maintains convergence guarantees even for \emph{fixed} perturbation sizes, which is established through a novel Lyapunov function. We in fact arrive at SAMPa by treating this convergence guarantee as a hard requirement -- an approach we believe is promising for developing SAM-based methods in general. Our code is available at \url{https://github.com/LIONS-EPFL/SAMPa}.

We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract explanatory rules. For global explanations, candidate rules are chosen from the entire trained tree-ensemble models, whereas for local explanations, candidate rules are selected by only considering rules that are relevant to the particular predicted instance. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks.