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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.


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.


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.


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.


A Hybrid Pricing and Cutting Approach for the Multi-Shift Full Truckload Vehicle Routing Problem

arXiv.org Artificial Intelligence

Full truckload transportation (FTL) in the form of freight containers represents one of the most important transportation modes in international trade. Due to large volume and scale, in FTL, delivery time is often less critical but cost and service quality are crucial. Therefore, efficiently solving large scale multiple shift FTL problems is becoming more and more important and requires further research. In one of our earlier studies, a set covering model and a three-stage solution method were developed for a multi-shift FTL problem. This paper extends the previous work and presents a significantly more efficient approach by hybridising pricing and cutting strategies with metaheuristics (a variable neighbourhood search and a genetic algorithm). The metaheuristics were adopted to find promising columns (vehicle routes) guided by pricing and cuts are dynamically generated to eliminate infeasible flow assignments caused by incompatible commodities. Computational experiments on real-life and artificial benchmark FTL problems showed superior performance both in terms of computational time and solution quality, when compared with previous MIP based three-stage methods and two existing metaheuristics. The proposed cutting and heuristic pricing approach can efficiently solve large scale real-life FTL problems.


DNA mixture deconvolution using an evolutionary algorithm with multiple populations, hill-climbing, and guided mutation

arXiv.org Machine Learning

DNA samples crime cases analysed in forensic genetics, frequently contain DNA from multiple contributors. These occur as convolutions of the DNA profiles of the individual contributors to the DNA sample. Thus, in cases where one or more of the contributors were unknown, an objective of interest would be the separation, often called deconvolution, of these unknown profiles. In order to obtain deconvolutions of the unknown DNA profiles, we introduced a multiple population evolutionary algorithm (MEA). We allowed the mutation operator of the MEA to utilise that the fitness is based on a probabilistic model and guide it by using the deviations between the observed and the expected value for every element of the encoded individual. This guided mutation operator (GM) was designed such that the larger the deviation the higher probability of mutation. Furthermore, the GM was inhomogeneous in time, decreasing to a specified lower bound as the number of iterations increased. We analysed 102 two-person DNA mixture samples in varying mixture proportions. The samples were quantified using two different DNA prep. kits: (1) Illumina ForenSeq Panel B (30 samples), and (2) Applied Biosystems Precision ID Globalfiler NGS STR panel (72 samples). The DNA mixtures were deconvoluted by the MEA and compared to the true DNA profiles of the sample. We analysed three scenarios where we assumed: (1) the DNA profile of the major contributor was unknown, (2) DNA profile of the minor was unknown, and (3) both DNA profiles were unknown. Furthermore, we conducted a series of sensitivity experiments on the ForenSeq panel by varying the sub-population size, comparing a completely random homogeneous mutation operator to the guided operator with varying mutation decay rates, and allowing for hill-climbing of the parent population.