Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods do not consider using adaptive learning rates. It is well known that adaptive learning rates can accelerate optimization algorithms. To fill this gap, in the paper, we propose a novel fast adaptive bilevel framework to solve stochastic bilevel optimization problems that the outer problem is possibly nonconvex and the inner problem is strongly convex. Our framework uses unified adaptive matrices including many types of adaptive learning rates, and can flexibly use the momentum and variance reduced techniques. In particular, we provide a useful convergence analysis framework for the bilevel optimization. Specifically, we propose a fast single-loop adaptive bilevel optimization (BiAdam) algorithm, which achieves a sample complexity of $\tilde{O}(\epsilon^{-4})$ for finding an $\epsilon$-stationary solution. Meanwhile, we propose an accelerated version of BiAdam algorithm (VR-BiAdam), which reaches the best known sample complexity of $\tilde{O}(\epsilon^{-3})$. To the best of our knowledge, we first study the adaptive bilevel optimization methods with adaptive learning rates. Experimental results on data hyper-cleaning and hyper-representation learning tasks demonstrate the efficiency of our algorithms.

We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics. By converting the problem of minimizing a convex function into an auxiliary problem of solving a min-max game in a sequential fashion, we can consider a range of strategies for each of the two-players who must select their actions one after the other. A common choice for these strategies are so-called no-regret learning algorithms, and we describe a number of such and prove bounds on their regret. We then show that many classical first-order methods for convex optimization -- including average-iterate gradient descent, the Frank-Wolfe algorithm, Nesterov's acceleration methods, and the accelerated proximal method -- can be interpreted as special cases of our framework as long as each player makes the correct choice of no-regret strategy. Proving convergence rates in this framework becomes very straightforward, as they follow from plugging in the appropriate known regret bounds. Our framework also gives rise to a number of new first-order methods for special cases of convex optimization that were not previously known.

A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers' intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot. We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.

The choice of optimization algorithm can depend on several factors, including the specific problem you're trying to solve, the size and complexity of your dataset, and the resources (such as computational power and memory) that you have available.

Future AI applications require performance, reliability and privacy that the existing, cloud-dependant system architectures cannot provide. In this article, we study orchestration in the device-edge-cloud continuum, and focus on edge AI for resource orchestration. We claim that to support the constantly growing requirements of intelligent applications in the device-edge-cloud computing continuum, resource orchestration needs to embrace edge AI and emphasize local autonomy and intelligence. To justify the claim, we provide a general definition for continuum orchestration, and look at how current and emerging orchestration paradigms are suitable for the computing continuum. We describe certain major emerging research themes that may affect future orchestration, and provide an early vision of an orchestration paradigm that embraces those research themes. Finally, we survey current key edge AI methods and look at how they may contribute into fulfilling the vision of future continuum orchestration.

Data-driven materials design often encounters challenges where systems require or possess qualitative (categorical) information. Metal-organic frameworks (MOFs) are an example of such material systems. The representation of MOFs through different building blocks makes it a challenge for designers to incorporate qualitative information into design optimization. Furthermore, the large number of potential building blocks leads to a combinatorial challenge, with millions of possible MOFs that could be explored through time consuming physics-based approaches. In this work, we integrated Latent Variable Gaussian Process (LVGP) and Multi-Objective Batch-Bayesian Optimization (MOBBO) to identify top-performing MOFs adaptively, autonomously, and efficiently without any human intervention. Our approach provides three main advantages: (i) no specific physical descriptors are required and only building blocks that construct the MOFs are used in global optimization through qualitative representations, (ii) the method is application and property independent, and (iii) the latent variable approach provides an interpretable model of qualitative building blocks with physical justification. To demonstrate the effectiveness of our method, we considered a design space with more than 47,000 MOF candidates. By searching only ~1% of the design space, LVGP-MOBBO was able to identify all MOFs on the Pareto front and more than 97% of the 50 top-performing designs for the CO$_2$ working capacity and CO$_2$/N$_2$ selectivity properties. Finally, we compared our approach with the Random Forest algorithm and demonstrated its efficiency, interpretability, and robustness.

Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large and discrete search space. A recent flurry of developments followed NOTEARS[1] recast this combinatorial problem into a continuous optimization problem by leveraging an algebraic equality characterization of acyclicity. However, the continuous optimization methods suffer from obtaining non-spare graphs after the numerical optimization, which leads to the inflexibility to rule out the potentially cycle-inducing edges or false discovery edges with small values. To address this issue, in this paper, we develop a completely data-driven DAG structure learning method without a predefined value to post-threshold small values. We name our method NOTEARS with adaptive Lasso (NOTEARS-AL), which is achieved by applying the adaptive penalty method to ensure the sparsity of the estimated DAG. Moreover, we show that NOTEARS-AL also inherits the oracle properties under some specific conditions. Extensive experiments on both synthetic and a real-world dataset demonstrate that our method consistently outperforms NOTEARS.

Deploying machine learning (ML) models often requires both fairness and privacy guarantees. Both of these objectives present unique trade-offs with the utility (e.g., accuracy) of the model. However, the mutual interactions between fairness, privacy, and utility are less well-understood. As a result, often only one objective is optimized, while the others are tuned as hyper-parameters. Because they implicitly prioritize certain objectives, such designs bias the model in pernicious, undetectable ways. To address this, we adopt impartiality as a principle: design of ML pipelines should not favor one objective over another. We propose impartially-specified models, which provide us with accurate Pareto frontiers that show the inherent trade-offs between the objectives. Extending two canonical ML frameworks for privacy-preserving learning, we provide two methods (FairDP-SGD and FairPATE) to train impartially-specified models and recover the Pareto frontier. Through theoretical privacy analysis and a comprehensive empirical study, we provide an answer to the question of where fairness mitigation should be integrated within a privacy-aware ML pipeline.

The simplest and often most effective way of parallelizing the training of complex machine learning models is to execute several training instances on multiple machines, possibly scanning the hyperparameter space to optimize the underlying statistical model and the learning procedure. Often, such a meta learning procedure is limited by the ability of accessing securely a common database organizing the knowledge of the previous and ongoing trials. Exploiting opportunistic GPUs provided in different environments represents a further challenge when designing such optimization campaigns. In this contribution we discuss how a set of RestAPIs can be used to access a dedicated service based on INFN Cloud to monitor and possibly coordinate multiple training instances, with gradient-less optimization techniques, via simple HTTP requests. The service, named Hopaas (Hyperparameter OPtimization As A Service), is made of web interface and sets of APIs implemented with a FastAPI back-end running through Uvicorn and NGINX in a virtual instance of INFN Cloud. The optimization algorithms are currently based on Bayesian techniques as provided by Optuna. A Python front-end is also made available for quick prototyping. We present applications to hyperparameter optimization campaigns performed combining private, INFN Cloud and CINECA resources.

Due to nonholonomic dynamics, the motion planning of nonholonomic robots is always a difficult problem. This letter presents a Discrete States-based Trajectory Planning(DSTP) algorithm for autonomous nonholonomic robots. The proposed algorithm represents the trajectory as x and y positions, orientation angle, longitude velocity and acceleration, angular velocity, and time intervals. More variables make the expression of optimization and constraints simpler, reduce the error caused by too many approximations, and also handle the gear shifting situation. L-BFGS-B is used to deal with the optimization of many variables and box constraints, thus speeding up the problem solving. Various simulation experiments compared with prior works have validated that our algorithm has an order-of-magnitude efficiency advantage and can generate a smoother trajectory with a high speed and low control effort. Besides, real-world experiments are also conducted to verify the feasibility of our algorithm in real scenes. We will release our codes as ros packages.