Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.

We study the existence and computation of Nash equilibria in continuous static games where the players' admissible strategies are subject to shared coupling constraints, i.e., constraints that depend on their \emph{joint} strategies. Specifically, we focus on a class of games characterized by playerwise concave utilities and playerwise concave constraints. Prior results on the existence of Nash equilibria are not applicable to this class, as they rely on strong assumptions such as joint convexity of the feasible set. By leveraging topological fixed point theory and novel structural insights into the contractibility of feasible sets under playerwise concave constraints, we give an existence proof for Nash equilibria under weaker conditions. Having established existence, we then focus on the computation of Nash equilibria via independent gradient methods under the additional assumption that the utilities admit a potential function. To account for the possibly nonconvex feasible region, we employ a log barrier regularized gradient ascent with adaptive stepsizes. Starting from an initial feasible strategy profile and under exact gradient feedback, the proposed method converges to an $ε$-approximate constrained Nash equilibrium within $\mathcal{O}(ε^{-3})$ iterations.

In robotics, structural design and behavior optimization have long been considered separate processes, resulting in the development of systems with limited capabilities. Recently, co-design methods have gained popularity, where bi-level formulations are used to simultaneously optimize the robot design and behavior for specific tasks. However, most implementations assume a serial or tree-type model of the robot, overlooking the fact that many robot platforms incorporate parallel mechanisms. In this paper, we present a novel co-design approach that explicitly incorporates parallel coupling constraints into the dynamic model of the robot. In this framework, an outer optimization loop focuses on the design parameters, in our case the transmission ratios of a parallel belt-driven manipulator, which map the desired torques from the joint space to the actuation space. An inner loop performs trajectory optimization in the actuation space, thus exploiting the entire dynamic range of the manipulator. We compare the proposed method with a conventional co-design approach based on a simplified tree-type model. By taking advantage of the actuation space representation, our approach leads to a significant increase in dynamic payload capacity compared to the conventional co-design implementation.

This paper introduces an approach to learning of structural SVMs based on a direction method of multipliers. The starting point is to bring the primal form of the learning objective into a dual-decomposed representation (eq. This representation is frequently used for inference in intractable graphical models, and has meanwhile also been exploited successfully for structured learning (e.g. in [13,14]). Basically, the problem is broken down into maximization of individual factors, as well as minimization with respect to the model parameters as well as Lagrange variables coupling the factors. Approaches then differ in how the coupling constraint are handled, and in how the minimization with respect to the model parameters is conducted.

In the field of brain science, data sharing across servers is becoming increasingly challenging due to issues such as industry competition, privacy security, and administrative procedure policies and regulations. Therefore, there is an urgent need to develop new methods for data analysis and processing that enable scientific collaboration without data sharing. In view of this, this study proposes to study and develop a series of efficient non-negative coupled tensor decomposition algorithm frameworks based on federated learning called FCNCP for the EEG data arranged on different servers. It combining the good discriminative performance of tensor decomposition in high-dimensional data representation and decomposition, the advantages of coupled tensor decomposition in cross-sample tensor data analysis, and the features of federated learning for joint modelling in distributed servers. The algorithm utilises federation learning to establish coupling constraints for data distributed across different servers. In the experiments, firstly, simulation experiments are carried out using simulated data, and stable and consistent decomposition results are obtained, which verify the effectiveness of the proposed algorithms in this study. Then the FCNCP algorithm was utilised to decompose the fifth-order event-related potential (ERP) tensor data collected by applying proprioceptive stimuli on the left and right hands. It was found that contralateral stimulation induced more symmetrical components in the activation areas of the left and right hemispheres. The conclusions drawn are consistent with the interpretations of related studies in cognitive neuroscience, demonstrating that the method can efficiently process higher-order EEG data and that some key hidden information can be preserved.

In contrast to conventional robots, accurately modeling the kinematics and statics of continuum robots is challenging due to partially unknown material properties, parasitic effects, or unknown forces acting on the continuous body. Consequentially, state estimation approaches that utilize additional sensor information to predict the shape of continuum robots have garnered significant interest. This paper presents a novel approach to state estimation for systems with multiple coupled continuum robots, which allows estimating the shape and strain variables of multiple continuum robots in an arbitrary coupled topology. Simulations and experiments demonstrate the capabilities and versatility of the proposed method, while achieving accurate and continuous estimates for the state of such systems, resulting in average end-effector errors of 3.3 mm and 5.02{\deg} depending on the sensor setup. It is further shown, that the approach offers fast computation times of below 10 ms, enabling its utilization in quasi-static real-time scenarios with average update rates of 100-200 Hz. An open-source C++ implementation of the proposed state estimation method is made publicly available to the community.

We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

Whereas people learn many different types of knowledge from diverse experiences over many years, and become better learners over time, most current machine learning systems are much more narrow, learning just a single function or data model based on statistical analysis of a single data set. We suggest that people learn better than computers precisely because of this difference, and we suggest a key direction for machine learning research is to develop software architectures that enable intelligent agents to also learn many types of knowledge, continuously over many years, and to become better learners over time. In this paper we define more precisely this never-ending learning paradigm for machine learning, and we present one case study: the Never-Ending Language Learner (NELL), which achieves a number of the desired properties of a never-ending learner. NELL has been learning to read the Web 24hrs/day since January 2010, and so far has acquired a knowledge base with 120mn diverse, confidence-weighted beliefs (e.g., servedWith(tea,biscuits)), while learning thousands of interrelated functions that continually improve its reading competence over time. NELL has also learned to reason over its knowledge base to infer new beliefs it has not yet read from those it has, and NELL is inventing new relational predicates to extend the ontology it uses to represent beliefs. We describe the design of NELL, experimental results illustrating its behavior, and discuss both its successes and shortcomings as a case study in never-ending learning. NELL can be tracked online at http://rtw.ml.cmu.edu, and followed on Twitter at @CMUNELL. Machine learning is a highly successful branch of artificial intelligence (AI), and is now widely used for tasks from spam filtering, to speech recognition, to credit card fraud detection, to face recognition. Despite these successes, the ways in which computers learn today remain surprisingly narrow when compared to human learning. This paper explores an alternative paradigm for machine learning that more closely models the diversity, competence and cumulative nature of human learning.

Whereas people learn many different types of knowledge from diverse experiences over many years, most current machine learning systems acquire just a single function or data model from just a single data set. We propose a never-ending learning paradigm for machine learning, to better reflect the more ambitious and encompassing type of learning performed by humans. As a case study, we describe the Never-Ending Language Learner (NELL), which achieves some of the desired properties of a never-ending learner, and we discuss lessons learned. NELL has been learning to read the web 24 hours/day since January 2010, and so far has acquired a knowledge base with over 80 million confidence-weighted beliefs (e.g., servedWith(tea, biscuits) ). NELL has also learned millions of features and parameters that enable it to read these beliefs from the web. Additionally, it has learned to reason over these beliefs to infer new beliefs, and is able to extend its ontology by synthesizing new relational predicates. NELL can be tracked online at http://rtw.ml.cmu.edu, and followed on Twitter at @CMUNELL.