Co-Designing Robots by Differentiating Motion Solvers

We present a novel algorithm for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are based on random sampling or concurrent optimization. A few recently proposed methods explore the relationship between the gradient of the optimal motion and robot design. Inspired by these approaches, we propose a bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (the inner level) without simplifying assumptions on its structure. Our approach can quickly optimize the robot's morphology while considering its full dynamics, joint limits and physical constraints such as friction cones. It has a faster convergence rate and greater scalability for larger design problems than state-of-the-art approaches based on sampling methods. It also allows us to handle constraints such as the actuation limits, which are important for co-designing dynamic maneuvers. We demonstrate these capabilities by studying jumping and trotting gaits under different design metrics and verify our results in a physics simulator. For these cases, our algorithm converges in less than a third of the number of iterations needed for sampling approaches, and the computation time scales linearly.Comment: 8 pages, 7 figures, submitted to IROS 202

Progressive Preference Articulation for Decision Making in Multi-Objective Optimisation Problems

This paper proposes a novel algorithm for addressing multi-objective optimisation problems, by employing a progressive preference articu- lation approach to decision making. This enables the interactive incorporation of problem knowledge and decision maker preferences during the optimisation process. A novel progressive preference articulation mechanism, derived from a statistical technique, is herein proposed and implemented within a multi-objective framework based on evolution strategy search and hypervolume indicator selection. The proposed algo- rithm is named the Weighted Z-score Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (WZ-HAGA). WZ-HAGA is based on a framework that makes use of evolution strategy logic with covariance matrix adaptation to perturb the solutions, and a hypervolume indicator driven algorithm to select successful solutions for the subsequent generation. In order to guide the search towards interesting regions, a preference articulation procedure composed of four phases and based on the weighted z-score approach is employed. The latter procedure cascades into the hypervolume driven algorithm to perform the selection of the solutions at each generation. Numerical results against five modern algorithms representing the state-of-the-art in multi-objective optimisation demonstrate that the pro- posed WZ-HAGA outperforms its competitors in terms of both the hypervolume indicator and pertinence to the regions of interest

Efficient Optimization of Loops and Limits with Randomized Telescoping Sums

We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the solutions to differential equations are all examples of optimization problems with this character. In such problems, it can be expensive to compute the objective function value and its gradient, but truncating the loop or using less accurate approximations can induce biases that damage the overall solution. We propose randomized telescope (RT) gradient estimators, which represent the objective as the sum of a telescoping series and sample linear combinations of terms to provide cheap unbiased gradient estimates. We identify conditions under which RT estimators achieve optimization convergence rates independent of the length of the loop or the required accuracy of the approximation. We also derive a method for tuning RT estimators online to maximize a lower bound on the expected decrease in loss per unit of computation. We evaluate our adaptive RT estimators on a range of applications including meta-optimization of learning rates, variational inference of ODE parameters, and training an LSTM to model long sequences

A Unified Framework for Gradient-based Hyperparameter Optimization and Meta-learning

Machine learning algorithms and systems are progressively becoming part of our societies, leading to a growing need of building a vast multitude of accurate, reliable and interpretable models which should possibly exploit similarities among tasks. Automating segments of machine learning itself seems to be a natural step to undertake to deliver increasingly capable systems able to perform well in both the big-data and the few-shot learning regimes. Hyperparameter optimization (HPO) and meta-learning (MTL) constitute two building blocks of this growing effort. We explore these two topics under a unifying perspective, presenting a mathematical framework linked to bilevel programming that captures existing similarities and translates into procedures of practical interest rooted in algorithmic differentiation. We discuss the derivation, applicability and computational complexity of these methods and establish several approximation properties for a class of objective functions of the underlying bilevel programs. In HPO, these algorithms generalize and extend previous work on gradient-based methods. In MTL, the resulting framework subsumes classic and emerging strategies and provides a starting basis from which to build and analyze novel techniques. A series of examples and numerical simulations offer insight and highlight some limitations of these approaches. Experiments on larger-scale problems show the potential gains of the proposed methods in real-world applications. Finally, we develop two extensions of the basic algorithms apt to optimize a class of discrete hyperparameters (graph edges) in an application to relational learning and to tune online learning rate schedules for training neural network models, an old but crucially important issue in machine learning

A Statistical Analysis of Performance in the 2021 CEC-GECCO-PESGM Competition on Evolutionary Computation in the Energy Domain

Evolutionary algorithms (EAs) have emerged as an efficient alternative to deal with real-world applications with high complexity. However, due to the stochastic nature of the results obtained using EAs, the design of benchmarks and competitions where such approaches can be evaluated and compared is attracting attention in the field. In the energy domain, the “2021 CEC-GECCO-PESGM Competition on Evolutionary Computation in the Energy Domain: Smart Grid Applications” provides a platform to test and compare new EAs to solve complex problems in the field. However, the metric used to rank the algorithms is based solely on the mean fitness value (related to the objective function value only), which does not give statistical significance to the performance of the algorithms. Thus, this paper presents a statistical analysis using the Wilcoxon pair-wise comparison to study the performance of algorithms with statistical grounds. Results suggest that, for track 1 of the competition, only the winner approach (first place) is significantly different and superior to the other algorithms; in contrast, the second place is already statistically comparable to some other contestants. For track 2, all the winner approaches (first, second, and third) are statistically different from each other and the rest of the contestants. This type of analysis is important to have a deeper understanding of the stochastic performance of algorithms.This research has received funding from FEDER funds through the Operational Programme for Competitiveness and Internationalization (COMPETE 2020), under Project POCI01-0145-FEDER-028983; by National Funds through the FCT Portuguese Foundation for Science and Technology, under Projects PTDC/EEI-EEE/28983/2017(CENERGETIC),CEECIND/02814/2017, and UIDB/000760/2020.info:eu-repo/semantics/publishedVersio

Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm.

Real-world problems often involve the optimisation of multiple conflicting objectives. These problems, referred to as multi-objective optimisation problems, are especially challenging when more than three objectives are considered simultaneously. This paper proposes an algorithm to address this class of problems. The proposed algorithm is an evolutionary algorithm based on an evolution strategy framework, and more specifically, on the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES). A novel selection mechanism is introduced and integrated within the framework. This selection mechanism makes use of an adaptive grid to perform a local approximation of the hypervolume indicator which is then used as a selection criterion. The proposed implementation, named Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (CMA-PAES-HAGA), overcomes the limitation of CMA-PAES in handling more than two objectives and displays a remarkably good performance on a scalable test suite in five, seven, and ten-objective problems. The performance of CMA-PAES-HAGA has been compared with that of a competition winning meta-heuristic, representing the state-of-the-art in this sub-field of multi-objective optimisation. The proposed algorithm has been tested in a seven-objective real-world application, i.e. the design of an aircraft lateral control system. In this optimisation problem, CMA-PAES-HAGA greatly outperformed its competitors

Towards Poisoning Fair Representations

Fair machine learning seeks to mitigate model prediction bias against certain demographic subgroups such as elder and female. Recently, fair representation learning (FRL) trained by deep neural networks has demonstrated superior performance, whereby representations containing no demographic information are inferred from the data and then used as the input to classification or other downstream tasks. Despite the development of FRL methods, their vulnerability under data poisoning attack, a popular protocol to benchmark model robustness under adversarial scenarios, is under-explored. Data poisoning attacks have been developed for classical fair machine learning methods which incorporate fairness constraints into shallow-model classifiers. Nonetheless, these attacks fall short in FRL due to notably different fairness goals and model architectures. This work proposes the first data poisoning framework attacking FRL. We induce the model to output unfair representations that contain as much demographic information as possible by injecting carefully crafted poisoning samples into the training data. This attack entails a prohibitive bilevel optimization, wherefore an effective approximated solution is proposed. A theoretical analysis on the needed number of poisoning samples is derived and sheds light on defending against the attack. Experiments on benchmark fairness datasets and state-of-the-art fair representation learning models demonstrate the superiority of our attack