Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

We propose Diffusion Inference-Time T-Optimization (DITTO), a general-purpose frame-work for controlling pre-trained text-to-music diffusion models at inference-time via optimizing initial noise latents. Our method can be used to optimize through any differentiable feature matching loss to achieve a target (stylized) output and leverages gradient checkpointing for memory efficiency. We demonstrate a surprisingly wide-range of applications for music generation including inpainting, outpainting, and looping as well as intensity, melody, and musical structure control - all without ever fine-tuning the underlying model. When we compare our approach against related training, guidance, and optimization-based methods, we find DITTO achieves state-of-the-art performance on nearly all tasks, including outperforming comparable approaches on controllability, audio quality, and computational efficiency, thus opening the door for high-quality, flexible, training-free control of diffusion models. Sound examples can be found at https://DITTO-Music.github.io/web/.

The burgeoning volume of graph data poses significant challenges in storage, transmission, and particularly the training of graph neural networks (GNNs). To address these challenges, graph condensation (GC) has emerged as an innovative solution. GC focuses on synthesizing a compact yet highly representative graph, on which GNNs can achieve performance comparable to trained on the large original graph. The notable efficacy of GC and its broad prospects have garnered significant attention and spurred extensive research. This survey paper provides an up-to-date and systematic overview of GC, organizing existing research into four categories aligned with critical GC evaluation criteria: effectiveness, generalization, fairness, and efficiency. To facilitate an in-depth and comprehensive understanding of GC, we examine various methods under each category and thoroughly discuss two essential components within GC: optimization strategies and condensed graph generation. Additionally, we introduce the applications of GC in a variety of fields, and highlight the present challenges and novel insights in GC, promoting advancements in future research.

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter. Selection of an appropriate regularization parameter is critical, with various choices leading to very different reconstructions. Classical strategies used to determine a suitable parameter value include the discrepancy principle and the L-curve criterion, and in recent years a supervised machine learning approach called bilevel learning has been employed. Bilevel learning is a powerful framework to determine optimal parameters and involves solving a nested optimization problem. While previous strategies enjoy various theoretical results, the well-posedness of bilevel learning in this setting is still an open question. In particular, a necessary property is positivity of the determined regularization parameter. In this work, we provide a new condition that better characterizes positivity of optimal regularization parameters than the existing theory. Numerical results verify and explore this new condition for both small and high-dimensional problems.

Controlling the interaction forces between a human and an exoskeleton is crucial for providing transparency or adjusting assistance or resistance levels. However, it is an open problem to control the interaction forces of lower-limb exoskeletons designed for unrestricted overground walking. For these types of exoskeletons, it is challenging to implement force/torque sensors at every contact between the user and the exoskeleton for direct force measurement. Moreover, it is important to compensate for the exoskeleton's whole-body gravitational and dynamical forces, especially for heavy lower-limb exoskeletons. Previous works either simplified the dynamic model by treating the legs as independent double pendulums, or they did not close the loop with interaction force feedback. The proposed whole-exoskeleton closed-loop compensation (WECC) method calculates the interaction torques during the complete gait cycle by using whole-body dynamics and joint torque measurements on a hip-knee exoskeleton. Furthermore, it uses a constrained optimization scheme to track desired interaction torques in a closed loop while considering physical and safety constraints. We evaluated the haptic transparency and dynamic interaction torque tracking of WECC control on three subjects. We also compared the performance of WECC with a controller based on a simplified dynamic model and a passive version of the exoskeleton. The WECC controller results in a consistently low absolute interaction torque error during the whole gait cycle for both zero and nonzero desired interaction torques. In contrast, the simplified controller yields poor performance in tracking desired interaction torques during the stance phase.

Optimal control (OC) algorithms such as Differential Dynamic Programming (DDP) take advantage of the derivatives of the dynamics to efficiently control physical systems. Yet, in the presence of nonsmooth dynamical systems, such class of algorithms are likely to fail due, for instance, to the presence of discontinuities in the dynamics derivatives or because of non-informative gradient. On the contrary, reinforcement learning (RL) algorithms have shown better empirical results in scenarios exhibiting non-smooth effects (contacts, frictions, etc). Our approach leverages recent works on randomized smoothing (RS) to tackle non-smoothness issues commonly encountered in optimal control, and provides key insights on the interplay between RL and OC through the prism of RS methods. This naturally leads us to introduce the randomized Differential Dynamic Programming (R-DDP) algorithm accounting for deterministic but non-smooth dynamics in a very sample-efficient way. The experiments demonstrate that our method is able to solve classic robotic problems with dry friction and frictional contacts, where classical OC algorithms are likely to fail and RL algorithms require in practice a prohibitive number of samples to find an optimal solution.

With the recent influx in demand for multi-robot systems throughout industry and academia, there is an increasing need for faster, robust, and generalizable path planning algorithms. Similarly, given the inherent connection between control algorithms and multi-robot path planners, there is in turn an increased demand for fast, efficient, and robust controllers. We propose a scalable joint path planning and control algorithm for multi-robot systems with constrained behaviours based on factor graph optimization. We demonstrate our algorithm on a series of hardware and simulated experiments. Our algorithm is consistently able to recover from disturbances and avoid obstacles while outperforming state-of-the-art methods in optimization time, path deviation, and inter-robot errors. See the code and supplementary video for experiments.

From email, over social networks, to virtual worlds, the way people work and enjoy their free time is changing dramatically. The resulting networks are usually large in scale, involving huge numbers of interactions, and are open for the interacting entities to join or leave at will. People are often supported by software components of different complexity to which some of the corresponding tasks can be delegated. In practice, such systems cannot be built and managed based on rigid, centralised client-server architectures, but call for more flexible and decentralised means of interaction. The field of Agreement Technologies (AT) [1] envisions next-generation open distributed systems, where interactions between software components are based on the concept of agreement, and which enact two key mechanisms: a means to specify the "space" of agreements that the agents can possibly reach, and an interaction model by means of which agreements can be effectively reached. Autonomy, interaction, mobility and openness are key characteristics that are tackled from a theoretical and practical perspective. Coordination in Distributed Systems is often seen as governing the interaction among distributed processes, with the aim of "gluing together" their behaviour, so that the resulting ensemble shows desired characteristics or functionalities [2]. This notion has also been applied to Distributed Systems made up of software agents. Initially, the main purpose of such multiagent systems was to efficiently perform problem-solving in a distributed manner: both the agents and their rules of interaction were designed together, often in a top-down manner and applying a divide-and-Appl.

This paper presents a unique solution to challenges in medical image processing by incorporating an adaptive curve grey wolf optimization (ACGWO) algorithm into neural network backpropagation. Neural networks show potential in medical data but suffer from issues like overfitting and lack of interpretability due to imbalanced and scarce data. Traditional Gray Wolf Optimization (GWO) also has its drawbacks, such as a lack of population diversity and premature convergence. This paper addresses these problems by introducing an adaptive algorithm, enhancing the standard GWO with a sigmoid function. This algorithm was extensively compared to four leading algorithms using six well-known test functions, outperforming them effectively. Moreover, by utilizing the ACGWO, we increase the robustness and generalization of the neural network, resulting in more interpretable predictions. Applied to the publicly accessible Cleveland Heart Disease dataset, our technique surpasses ten other methods, achieving 86.8% accuracy, indicating its potential for efficient heart disease prediction in the clinical setting.

Current advancements in reinforcement learning (RL) have predominantly focused on learning step-based policies that generate actions for each perceived state. While these methods efficiently leverage step information from environmental interaction, they often ignore the temporal correlation between actions, resulting in inefficient exploration and unsmooth trajectories that are challenging to implement on real hardware. Episodic RL (ERL) seeks to overcome these challenges by exploring in parameters space that capture the correlation of actions. However, these approaches typically compromise data efficiency, as they treat trajectories as opaque \emph{black boxes}. In this work, we introduce a novel ERL algorithm, Temporally-Correlated Episodic RL (TCE), which effectively utilizes step information in episodic policy updates, opening the 'black box' in existing ERL methods while retaining the smooth and consistent exploration in parameter space. TCE synergistically combines the advantages of step-based and episodic RL, achieving comparable performance to recent ERL methods while maintaining data efficiency akin to state-of-the-art (SoTA) step-based RL.