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Are we Forgetting about Compositional Optimisers in Bayesian Optimisation?

arXiv.org Machine Learning

Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional optimisation problem, allowing us to benefit from the extensive literature in this field. We highlight the empirical advantages of the compositional approach to acquisition function maximisation across 3958 individual experiments comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given the generality of the acquisition function maximisation subroutine, we posit that the adoption of compositional optimisers has the potential to yield performance improvements across all domains in which Bayesian optimisation is currently being applied.


Quality-Diversity Optimization: a novel branch of stochastic optimization

arXiv.org Machine Learning

Traditional optimization algorithms search for a single global optimum that maximizes (or minimizes) the objective function. Multimodal optimization algorithms search for the highest peaks in the search space that can be more than one. Quality-Diversity algorithms are a recent addition to the evolutionary computation toolbox that do not only search for a single set of local optima, but instead try to illuminate the search space. In effect, they provide a holistic view of how high-performing solutions are distributed throughout a search space. The main differences with multimodal optimization algorithms are that (1) Quality-Diversity typically works in the behavioral space (or feature space), and not in the genotypic (or parameter) space, and (2) Quality-Diversity attempts to fill the whole behavior space, even if the niche is not a peak in the fitness landscape. In this chapter, we provide a gentle introduction to Quality-Diversity optimization, discuss the main representative algorithms, and the main current topics under consideration in the community. Throughout the chapter, we also discuss several successful applications of Quality-Diversity algorithms, including deep learning, robotics, and reinforcement learning.


Squirrel: A Switching Hyperparameter Optimizer

arXiv.org Machine Learning

In this short note, we describe our submission to the NeurIPS 2020 BBO challenge. Motivated by the fact that different optimizers work well on different problems, our approach switches between different optimizers. Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel, or here, short, Squirrel. The challenge mandated to suggest 16 successive batches of 8 hyperparameter configurations at a time. We chose to only use one optimizer for a given batch, warmstarted with all previous observations.


Solving the Travelling Thief Problem based on Item Selection Weight and Reverse Order Allocation

arXiv.org Artificial Intelligence

The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem (KP). Increasingly algorithms have been proposed for solving this novel problem that combines two interdependent sub-problems. In this paper, TTP is investigated theoretically and empirically. An algorithm based on the score value calculated by our proposed formulation in picking items and sorting items in the reverse order in the light of the scoring value is proposed to solve the problem. Different approaches for solving the TTP are compared and analyzed; the experimental investigations suggest that our proposed approach is very efficient in meeting or beating current state-of-the-art heuristic solutions on a comprehensive set of benchmark TTP instances.


Digital Twins Are Not Monozygotic -- Cross-Replicating ADAS Testing in Two Industry-Grade Automotive Simulators

arXiv.org Artificial Intelligence

The increasing levels of software- and data-intensive driving automation call for an evolution of automotive software testing. As a recommended practice of the Verification and Validation (V&V) process of ISO/PAS 21448, a candidate standard for safety of the intended functionality for road vehicles, simulation-based testing has the potential to reduce both risks and costs. There is a growing body of research on devising test automation techniques using simulators for Advanced Driver-Assistance Systems (ADAS). However, how similar are the results if the same test scenarios are executed in different simulators? We conduct a replication study of applying a Search-Based Software Testing (SBST) solution to a real-world ADAS (PeVi, a pedestrian vision detection system) using two different commercial simulators, namely, TASS/Siemens PreScan and ESI Pro-SiVIC. Based on a minimalistic scene, we compare critical test scenarios generated using our SBST solution in these two simulators. We show that SBST can be used to effectively and efficiently generate critical test scenarios in both simulators, and the test results obtained from the two simulators can reveal several weaknesses of the ADAS under test. However, executing the same test scenarios in the two simulators leads to notable differences in the details of the test outputs, in particular, related to (1) safety violations revealed by tests, and (2) dynamics of cars and pedestrians. Based on our findings, we recommend future V&V plans to include multiple simulators to support robust simulation-based testing and to base test objectives on measures that are less dependant on the internals of the simulators.


Better call Surrogates: A hybrid Evolutionary Algorithm for Hyperparameter optimization

arXiv.org Artificial Intelligence

In this paper, we propose a surrogate-assisted evolutionary algorithm (EA) for hyperparameter optimization of machine learning (ML) models. The proposed STEADE model initially estimates the objective function landscape using RadialBasis Function interpolation, and then transfers the knowledge to an EA technique called Differential Evolution that is used to evolve new solutions guided by a Bayesian optimization framework. We empirically evaluate our model on the hyperparameter optimization problems as a part of the black box optimization challenge at NeurIPS 2020 and demonstrate the improvement brought about by STEADE over the vanilla EA.


From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit

arXiv.org Machine Learning

In this paper we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding mean-field approximation based on Vlasov-Fokker-Planck-type equations. The disadvantage of memory effects induced by the need to store the local best position is overcome by the introduction of an additional differential equation describing the evolution of the local best. A regularization process for the global best permits to formally derive the respective mean-field description. Subsequently, in the small inertia limit, we compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization (CBO) methods. Several numerical examples illustrate the mean field process, the small inertia limit and the potential of this general class of global optimization methods.


Hybrid Quantum Computing -- Tabu Search Algorithm for Partitioning Problems: preliminary study on the Traveling Salesman Problem

arXiv.org Artificial Intelligence

Quantum Computing is considered as the next frontier in computing, and it is attracting a lot of attention from the current scientific community. This kind of computation provides to researchers with a revolutionary paradigm for addressing complex optimization problems, offering a significant speed advantage and an efficient search ability. Anyway, despite hopes placed in this field are high, Quantum Computing is still in an incipient stage of development. For this reason, present architectures show certain limitations in terms of computational capabilities and performance. These limitations have motivated the carrying out of this paper. With this paper, we contribute to the field introducing a novel solving scheme coined as hybrid Quantum Computing - Tabu Search Algorithm. Main pillars of operation of the proposed method are a greater control over the access to quantum resources, and a considerable reduction of non-profitable accesses. For assessing the quality of our method, we have used the well-known TSP as benchmarking problem. Furthermore, the performance of QTA has been compared with QBSolv -- a state-of-the-art decomposing solver -- on a set of 7 different TSP instances. The obtained experimental outcomes support the preliminary conclusion that QTA is an approach which offers promising results for solving partitioning problems, while it drastically reduces the access to QC resources. Furthermore, we also contribute in this paper to the field of Transfer Optimization by developing and using a evolutionary multiform multitasking algorithm as initialization method for the introduced hybrid Quantum Computing - Tabu Search Algorithm. Concretely, the evolutionary multitasking algorithm implemented is a multiform variant of the recently published Coevolutionary Variable Neighborhood Search Algorithm for Discrete Multitasking.


Neural fidelity warping for efficient robot morphology design

arXiv.org Artificial Intelligence

We consider the problem of optimizing a robot morphology to achieve the best performance for a target task, under computational resource limitations. The evaluation process for each morphological design involves learning a controller for the design, which can consume substantial time and computational resources. To address the challenge of expensive robot morphology evaluation, we present a continuous multi-fidelity Bayesian Optimization framework that efficiently utilizes computational resources via low-fidelity evaluations. We identify the problem of non-stationarity over fidelity space. Our proposed fidelity warping mechanism can learn representations of learning epochs and tasks to model non-stationary covariances between continuous fidelity evaluations which prove challenging for off-the-shelf stationary kernels. Various experiments demonstrate that our method can utilize the low-fidelity evaluations to efficiently search for the optimal robot morphology, outperforming state-of-the-art methods.


EvoCraft: A New Challenge for Open-Endedness

arXiv.org Artificial Intelligence

This paper introduces EvoCraft, a framework for Minecraft designed to study open-ended algorithms. We introduce an API that provides an open-source Python interface for communicating with Minecraft to place and track blocks. In contrast to previous work in Minecraft that focused on learning to play the game, the grand challenge we pose here is to automatically search for increasingly complex artifacts in an open-ended fashion. Compared to other environments used to study open-endedness, Minecraft allows the construction of almost any kind of structure, including actuated machines with circuits and mechanical components. We present initial baseline results in evolving simple Minecraft creations through both interactive and automated evolution. While evolution succeeds when tasked to grow a structure towards a specific target, it is unable to find a solution when rewarded for creating a simple machine that moves. Thus, EvoCraft offers a challenging new environment for automated search methods (such as evolution) to find complex artifacts that we hope will spur the development of more open-ended algorithms.