The main objective of this paper is to outline a theoretical framework to characterise humans' decision-making strategies under uncertainty, in particular active learning in a black-box optimization task and trading-off between information gathering (exploration) and reward seeking (exploitation). Humans' decisions making according to these two objectives can be modelled in terms of Pareto rationality. If a decision set contains a Pareto efficient strategy, a rational decision maker should always select the dominant strategy over its dominated alternatives. A distance from the Pareto frontier determines whether a choice is Pareto rational. To collect data about humans' strategies we have used a gaming application that shows the game field, with previous decisions and observations, as well as the score obtained. The key element in this paper is the representation of behavioural patterns of human learners as a discrete probability distribution. This maps the problem of the characterization of humans' behaviour into a space whose elements are probability distributions structured by a distance between histograms, namely the Wasserstein distance (WST). The distributional analysis gives new insights about human search strategies and their deviations from Pareto rationality. Since the uncertainty is one of the two objectives defining the Pareto frontier, the analysis has been performed for three different uncertainty quantification measures to identify which better explains the Pareto compliant behavioural patterns. Beside the analysis of individual patterns WST has also enabled a global analysis computing the barycenters and WST k-means clustering. A further analysis has been performed by a decision tree to relate non-Paretian behaviour, characterized by exasperated exploitation, to the dynamics of the evolution of the reward seeking process.
The ability to optimize multiple competing objective functions with high sample efficiency is imperative in many applied problems across science and industry. Multi-objective Bayesian optimization (BO) achieves strong empirical performance on such problems, but even with recent methodological advances, it has been restricted to simple, low-dimensional domains. Most existing BO methods exhibit poor performance on search spaces with more than a few dozen parameters. In this work we propose MORBO, a method for multi-objective Bayesian optimization over high-dimensional search spaces. MORBO performs local Bayesian optimization within multiple trust regions simultaneously, allowing it to explore and identify diverse solutions even when the objective functions are difficult to model globally. We show that MORBO significantly advances the state-of-the-art in sample-efficiency for several high-dimensional synthetic and real-world multi-objective problems, including a vehicle design problem with 222 parameters, demonstrating that MORBO is a practical approach for challenging and important problems that were previously out of reach for BO methods.
In this work, we consider the problem of Quality-Diversity (QD) optimization with multiple objectives. QD algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. Thriving for diversity was shown to be useful in many industrial and robotics applications. On the other hand, most real-life problems exhibit several potentially antagonist objectives to be optimized. Hence being able to optimize for multiple objectives with an appropriate technique while thriving for diversity is important to many fields. Here, we propose an extension of the MAP-Elites algorithm in the multi-objective setting: Multi-Objective MAP-Elites (MOME). Namely, it combines the diversity inherited from the MAP-Elites grid algorithm with the strength of multi-objective optimizations by filling each cell with a Pareto Front. As such, it allows to extract diverse solutions in the descriptor space while exploring different compromises between objectives. We evaluate our method on several tasks, from standard optimization problems to robotics simulations. Our experimental evaluation shows the ability of MOME to provide diverse solutions while providing global performances similar to standard multi-objective algorithms.
Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared which focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguishing between metaheuristic-based algorithms, metamodel-based algorithms, and approaches using a mixture of both. We also discuss the quality metrics used to compare multi-objective HPO procedures and present future research directions.
Ozaki, Yoshihiko | Tanigaki, Yuki (National Institute of Advanced Industrial Science and Technology) | Watanabe, Shuhei (University of Freiburg) | Nomura, Masahiro (CyberAgent, Inc.) | Onishi, Masaki (National Institute of Advanced Industrial Science and Technology)
Practitioners often encounter challenging real-world problems that involve a simultaneous optimization of multiple objectives in a complex search space. To address these problems, we propose a practical multiobjective Bayesian optimization algorithm. It is an extension of the widely used Tree-structured Parzen Estimator (TPE) algorithm, called Multiobjective Tree-structured Parzen Estimator (MOTPE). We demonstrate that MOTPE approximates the Pareto fronts of a variety of benchmark problems and a convolutional neural network design problem better than existing methods through the numerical results. We also investigate how the configuration of MOTPE affects the behavior and the performance of the method and the effectiveness of asynchronous parallelization of the method based on the empirical results.