We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection.

In this paper, a heuristic method based on TabuSearch and TokenRing Search is being used in order to solve the Portfolio Optimization Problem. The seminal mean-variance model of Markowitz is being considered with the addition of cardinality and quantity constraints to better capture the dynamics of the trading procedure, the model becomes an NP-hard problem that can not be solved using an exact method. The combination of three different neighborhood relations is being explored with Tabu Search. In addition, a new constructive method for the initial solution is proposed. Finally, I show how the proposed techniques perform on public benchmarks

Multi-objective feature selection is one of the most significant issues in the field of pattern recognition. It is challenging because it maximizes the classification performance and, at the same time, minimizes the number of selected features, and the mentioned two objectives are usually conflicting. To achieve a better Pareto optimal solution, metaheuristic optimization methods are widely used in many studies. However, the main drawback is the exploration of a large search space. Another problem with multi-objective feature selection approaches is the interaction between features. Selecting correlated features has negative effect on classification performance. To tackle these problems, we present a novel multi-objective feature selection method that has several advantages. Firstly, it considers the interaction between features using an advanced probability scheme. Secondly, it is based on the Pareto Archived Evolution Strategy (PAES) method that has several advantages such as simplicity and its speed in exploring the solution space. However, we improve the structure of PAES in such a way that generates the offsprings, intelligently. Thus, the proposed method utilizes the introduced probability scheme to produce more promising offsprings. Finally, it is equipped with a novel strategy that guides it to find the optimum number of features through the process of evolution. The experimental results show a significant improvement in finding the optimal Pareto front compared to state-of-the-art methods on different real-world datasets.

Despite being responsible for state-of-the-art results in several computer vision and natural language processing tasks, neural networks have faced harsh criticism due to some of their current shortcomings. One of them is that neural networks are correlation machines prone to model biases within the data instead of focusing on actual useful causal relationships. This problem is particularly serious in application domains affected by aspects such as race, gender, and age. To prevent models from incurring on unfair decision-making, the AI community has concentrated efforts in correcting algorithmic biases, giving rise to the research area now widely known as fairness in AI. In this survey paper, we provide an in-depth overview of the main debiasing methods for fairness-aware neural networks in the context of vision and language research. We propose a novel taxonomy to better organize the literature on debiasing methods for fairness, and we discuss the current challenges, trends, and important future work directions for the interested researcher and practitioner.

In this work, we focus on the problem of safe policy transfer in reinforcement learning: we seek to leverage existing policies when learning a new task with specified constraints. This problem is important for safety-critical applications where interactions are costly and unconstrained policies can lead to undesirable or dangerous outcomes, e.g., with physical robots that interact with humans. We propose a Constrained Markov Decision Process (CMDP) formulation that simultaneously enables the transfer of policies and adherence to safety constraints. Our formulation cleanly separates task goals from safety considerations and permits the specification of a wide variety of constraints. Our approach relies on a novel extension of generalized policy improvement to constrained settings via a Lagrangian formulation. We devise a dual optimization algorithm that estimates the optimal dual variable of a target task, thus enabling safe transfer of policies derived from successor features learned on source tasks. Our experiments in simulated domains show that our approach is effective; it visits unsafe states less frequently and outperforms alternative state-of-the-art methods when taking safety constraints into account.

Abstract: We present a novel method to address the problem of multi-vehicle conflict resolution in highly constrained spaces. An optimal control problem is formulated to incorporate nonlinear, non-holonomic vehicle dynamics and exact collision avoidance constraints. A solution to the problem can be obtained by first learning configuration strategies with reinforcement learning (RL) in a simplified discrete environment, and then using these strategies to shape the constraint space of the original problem. Simulation results show that our method can explore efficient actions to resolve conflicts in confined space and generate dexterous maneuvers that are both collision-free and kinematically feasible. Keywords: Trajectory and Path Planning, Multi-vehicle systems, Autonomous Vehicles, Reinforcement learning control, Control problems under conflict 1. INTRODUCTION When conflicts arise in highly constrained spaces such as crowded parking lots, both the optimal control and the RL approaches often fail due to the following reasons: Current autonomous vehicles (AVs) operate reasonably well in environments where traffic rules are well-defined, (i) The vehicles need to plan for combinatorial actions in the surrounding agents are rational, and their actions can order to create spaces for each other to pass through; be easily predicted.

Designing safety-critical control for robotic manipulators is challenging, especially in a cluttered environment. First, the actual trajectory of a manipulator might deviate from the planned one due to the complex collision environments and non-trivial dynamics, leading to collision; Second, the feasible space for the manipulator is hard to obtain since the explicit distance functions between collision meshes are unknown. By analyzing the relationship between the safe set and the controlled invariant set, this paper proposes a data-driven control barrier function (CBF) construction method, which extracts CBF from distance samples. Specifically, the CBF guarantees the controlled invariant property for considering the system dynamics. The data-driven method samples the distance function and determines the safe set. Then, the CBF is synthesized based on the safe set by a scenario-based sum of square (SOS) program. Unlike most existing linearization based approaches, our method reserves the volume of the feasible space for planning without approximation, which helps find a solution in a cluttered environment. The control law is obtained by solving a CBF-based quadratic program in real time, which works as a safe filter for the desired planning-based controller. Moreover, our method guarantees safety with the proven probabilistic result. Our method is validated on a 7-DOF manipulator in both real and virtual cluttered environments. The experiments show that the manipulator is able to execute tasks where the clearance between obstacles is in millimeters.

Machine learning frameworks such as Genetic Programming (GP) and Reinforcement Learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, bench-marking some of their most representative algorithms against global optimization techniques such as Bayesian Optimization (BO) and Lipschitz global optimization (LIPO). First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers' flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between `model capacity' in the control law definition versus `required complexity'. We believe that such a comparison paves the way toward the hybridization of the various methods, and we offer some perspective on their future development in the literature on flow control problems.

This paper studies a model for online job scheduling in green datacenters. In green datacenters, resource availability depends on the power supply from the renewables. Intermittent power supply from renewables leads to intermittent resource availability, inducing job delays (and associated costs). Green datacenter operators must intelligently manage their workloads and available power supply to extract maximum benefits. The scheduler's objective is to schedule jobs on a set of resources to maximize the total value (revenue) while minimizing the overall job delay. A trade-off exists between achieving high job value on the one hand and low expected delays on the other. Hence, the aims of achieving high rewards and low costs are in opposition. In addition, datacenter operators often prioritize multiple objectives, including high system utilization and job completion. To accomplish the opposing goals of maximizing total job value and minimizing job delays, we apply the Proportional-Integral-Derivative (PID) Lagrangian methods in Deep Reinforcement Learning to job scheduling problem in the green datacenter environment. Lagrangian methods are widely used algorithms for constrained optimization problems. We adopt a controls perspective to learn the Lagrange multiplier with proportional, integral, and derivative control, achieving favorable learning dynamics. Feedback control defines cost terms for the learning agent, monitors the cost limits during training, and continuously adjusts the learning parameters to achieve stable performance. Our experiments demonstrate improved performance compared to scheduling policies without the PID Lagrangian methods. Experimental results illustrate the effectiveness of the Constraint Controlled Reinforcement Learning (CoCoRL) scheduler that simultaneously satisfies multiple objectives.

Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem. We present our methodology in a general format and prove that the solution converges to the best estimator in terms of the expected cost of the selected application. Then, we propose two solution methods: an exact method based on the KKT conditions of the second-level problem and a scalable heuristic approach suitable for decomposition methods. The proposed methodology is applied to the relevant problem of defining dynamic reserve requirements and conditional load forecasts, offering an alternative approach to current \emph{ad hoc} procedures implemented in industry practices. We benchmark our methodology with the standard sequential least-squares forecast and dispatch planning process. We apply the proposed methodology to an illustrative system and to a wide range of instances, from dozens of buses to large-scale realistic systems with thousands of buses. Our results show that the proposed methodology is scalable and yields consistently better performance than the standard open-loop approach.