The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems. However, AdaMM is not suited for solving black-box optimization problems, where explicit gradient forms are difficult or infeasible to obtain. In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime. We show that the convergence rate of ZO-AdaMM for both convex and nonconvex optimization is roughly a factor of O(\sqrt{d}) worse than that of the first-order AdaMM algorithm, where d is problem size. In particular, we provide a deep understanding on why Mahalanobis distance matters in convergence of ZO-AdaMM and other AdaMM-type methods.

Reward Machines (RMs), originally proposed for specifying problems in Reinforcement Learning (RL), provide a structured, automata-based representation of a reward function that allows an agent to decompose problems into subproblems that can be efficiently learned using off-policy learning. Here we show that RMs can be learned from experience, instead of being specified by the user, and that the resulting problem decomposition can be used to effectively solve partially observable RL problems. We pose the task of learning RMs as a discrete optimization problem where the objective is to find an RM that decomposes the problem into a set of subproblems such that the combination of their optimal memoryless policies is an optimal policy for the original problem. We show the effectiveness of this approach on three partially observable domains, where it significantly outperforms A3C, PPO, and ACER, and discuss its advantages, limitations, and broader potential.

In recent years, many deep learning approaches have incorporated layers that solve optimization problems (e.g., linear, quadratic, and semidefinite programs). Integrating these optimization problems as differentiable layers requires computing the derivatives of the optimization problem's solution with respect to its objective and constraints. This has so far prevented the use of state-of-the-art black-box numerical solvers within neural networks, as they lack a differentiable interface. To address this issue for one of the most common convex optimization problems -- quadratic programming (QP) -- we introduce dQP, a modular framework that enables plug-and-play differentiation for any QP solver, allowing seamless integration into neural networks and bi-level optimization tasks. Our solution is based on the core theoretical insight that knowledge of the active constraint set at the QP optimum allows for explicit differentiation. This insight reveals a unique relationship between the computation of the solution and its derivative, enabling efficient differentiation of any solver, that only requires the primal solution. Our implementation, which will be made publicly available, interfaces with an existing framework that supports over 15 state-of-the-art QP solvers, providing each with a fully differentiable backbone for immediate use as a differentiable layer in learning setups. To demonstrate the scalability and effectiveness of dQP, we evaluate it on a large benchmark dataset of QPs with varying structures. We compare dQP with existing differentiable QP methods, demonstrating its advantages across a range of problems, from challenging small and dense problems to large-scale sparse ones, including a novel bi-level geometry optimization problem.

This paper presents a three-layered architecture that enables stylistic locomotion with online contact location adjustment. Our method combines an autoregressive Deep Neural Network (DNN) acting as a trajectory generation layer with a model-based trajectory adjustment and trajectory control layers. The DNN produces centroidal and postural references serving as an initial guess and regularizer for the other layers. Being the DNN trained on human motion capture data, the resulting robot motion exhibits locomotion patterns, resembling a human walking style. The trajectory adjustment layer utilizes non-linear optimization to ensure dynamically feasible center of mass (CoM) motion while addressing step adjustments. We compare two implementations of the trajectory adjustment layer: one as a receding horizon planner (RHP) and the other as a model predictive controller (MPC). To enhance MPC performance, we introduce a Kalman filter to reduce measurement noise. The filter parameters are automatically tuned with a Genetic Algorithm. Experimental results on the ergoCub humanoid robot demonstrate the system's ability to prevent falls, replicate human walking styles, and withstand disturbances up to 68 Newton. Website: https://sites.google.com/view/dnn-mpc-walking Youtube video: https://www.youtube.com/watch?v=x3tzEfxO-xQ

Federated Edge Learning (FEL), an emerging distributed Machine Learning (ML) paradigm, enables model training in a distributed environment while ensuring user privacy by using physical separation for each user data. However, with the development of complex application scenarios such as the Internet of Things (IoT) and Smart Earth, the conventional resource allocation schemes can no longer effectively support these growing computational and communication demands. Therefore, joint resource optimization may be the key solution to the scaling problem. This paper simultaneously addresses the multifaceted challenges of computation and communication, with the growing multiple resource demands. We systematically review the joint allocation strategies for different resources (computation, data, communication, and network topology) in FEL, and summarize the advantages in improving system efficiency, reducing latency, enhancing resource utilization and enhancing robustness. In addition, we present the potential ability of joint optimization to enhance privacy preservation by reducing communication requirements, indirectly. This work not only provides theoretical support for resource management in federated learning (FL) systems, but also provides ideas for potential optimal deployment in multiple real-world scenarios. By thoroughly discussing the current challenges and future research directions, it also provides some important insights into multi-resource optimization in complex application environments.

Humanoid robots rely on multi-contact planners to navigate a diverse set of environments, including those that are unstructured and highly constrained. To synthesize stable multi-contact plans within a reasonable time frame, most planners assume statically stable motions or rely on reduced order models. However, these approaches can also render the problem infeasible in the presence of large obstacles or when operating near kinematic and dynamic limits. To that end, we propose a new multi-contact framework that leverages recent advancements in relaxing collision-free path planning into a convex optimization problem, extending it to be applicable to humanoid multi-contact navigation. Our approach generates near-feasible trajectories used as guides in a dynamic trajectory optimizer, altogether addressing the aforementioned limitations. We evaluate our computational approach showcasing three different-sized humanoid robots traversing a high-raised naval knee-knocker door using our proposed framework in simulation. Our approach can generate motion plans within a few seconds consisting of several multi-contact states, including dynamic feasibility in joint space.

Lean Methodology for Garment Modernization. This article presents the lean methodology for modernizing garment manufacturing, focusing on lean thinking, lean practices, automation development, VSM, and CRP, and how to integrate them effectively. While isolated automation of specific operations can improve efficiency and reduce cycle time, it does not necessarily enhance overall garment output and efficiency. To achieve these broader improvements, it is essential to consider the entire production line and process using VSM and CRP to optimize production and center balance. This approach can increase efficiency, and reduce manufacturing costs, labor time, and lead time, ultimately adding value to the company and factory.

While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article, we partially close this gap between theory and practice and demonstrate that virtually identical guarantees can be obtained in optimization problems with a `benign' non-convexity. We show that these weaker geometric assumptions are well justified in overparametrized deep learning, at least locally. Variations of this result are obtained for a continuous time model of Nesterov's accelerated gradient descent algorithm (NAG), the classical discrete time version of NAG, and versions of NAG with stochastic gradient estimates with purely additive noise and with noise that exhibits both additive and multiplicative scaling.

Fine-tuning has become a popular approach to adapting large foundational models to specific tasks. As the size of models and datasets grows, parameter-efficient fine-tuning techniques are increasingly important. One of the most widely used methods is Low-Rank Adaptation (LoRA), with adaptation update expressed as the product of two low-rank matrices. While LoRA was shown to possess strong performance in fine-tuning, it often under-performs when compared to full-parameter fine-tuning (FPFT). Although many variants of LoRA have been extensively studied empirically, their theoretical optimization analysis is heavily under-explored. The starting point of our work is a demonstration that LoRA and its two extensions, Asymmetric LoRA and Chain of LoRA, indeed encounter convergence issues. To address these issues, we propose Randomized Asymmetric Chain of LoRA (RAC-LoRA) -- a general optimization framework that rigorously analyzes the convergence rates of LoRA-based methods. Our approach inherits the empirical benefits of LoRA-style heuristics, but introduces several small but important algorithmic modifications which turn it into a provably convergent method. Our framework serves as a bridge between FPFT and low-rank adaptation. We provide provable guarantees of convergence to the same solution as FPFT, along with the rate of convergence. Additionally, we present a convergence analysis for smooth, non-convex loss functions, covering gradient descent, stochastic gradient descent, and federated learning settings. Our theoretical findings are supported by experimental results.

Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on specific problem classes and do not generalize to unseen classes. To address this shortcoming, we take a foundation model training approach, where we train a single deep learning model on a diverse set of MILP problems to generalize across problem classes. As existing datasets for MILP lack diversity and volume, we introduce MILP-Evolve, a novel LLM-based evolutionary framework that is capable of generating a large set of diverse MILP classes with an unlimited amount of instances. We study our methodology on three key learning tasks that capture diverse aspects of MILP: (1) integrality gap prediction, (2) learning to branch, and (3) a new task of aligning MILP instances with natural language descriptions. Our empirical results show that models trained on the data generated by MILP-Evolve achieve significant improvements on unseen problems, including MIPLIB benchmarks. Our work highlights the potential of moving towards a foundation model approach for MILP that can generalize to a broad range of MILP applications. We are committed to fully open-sourcing our work to advance further research.