An Entropy Search Portfolio for Bayesian Optimization

Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misleading. To address this issue, we introduce the Entropy Search Portfolio (ESP): a novel approach to portfolio construction which is motivated by information theoretic considerations. We show that ESP outperforms existing portfolio methods on several real and synthetic problems, including geostatistical datasets and simulated control tasks. We not only show that ESP is able to offer performance as good as the best, but unknown, acquisition function, but surprisingly it often gives better performance. Finally, over a wide range of conditions we find that ESP is robust to the inclusion of poor acquisition functions.Comment: 10 pages, 5 figure

Dynamic Control of Explore/Exploit Trade-Off In Bayesian Optimization

Bayesian optimization offers the possibility of optimizing black-box operations not accessible through traditional techniques. The success of Bayesian optimization methods such as Expected Improvement (EI) are significantly affected by the degree of trade-off between exploration and exploitation. Too much exploration can lead to inefficient optimization protocols, whilst too much exploitation leaves the protocol open to strong initial biases, and a high chance of getting stuck in a local minimum. Typically, a constant margin is used to control this trade-off, which results in yet another hyper-parameter to be optimized. We propose contextual improvement as a simple, yet effective heuristic to counter this - achieving a one-shot optimization strategy. Our proposed heuristic can be swiftly calculated and improves both the speed and robustness of discovery of optimal solutions. We demonstrate its effectiveness on both synthetic and real world problems and explore the unaccounted for uncertainty in the pre-determination of search hyperparameters controlling explore-exploit trade-off.Comment: Accepted for publication in the proceedings of 2018 Computing Conferenc

Tuning Word2vec for Large Scale Recommendation Systems

Word2vec is a powerful machine learning tool that emerged from Natural Lan-guage Processing (NLP) and is now applied in multiple domains, including recom-mender systems, forecasting, and network analysis. As Word2vec is often used offthe shelf, we address the question of whether the default hyperparameters are suit-able for recommender systems. The answer is emphatically no. In this paper, wefirst elucidate the importance of hyperparameter optimization and show that un-constrained optimization yields an average 221% improvement in hit rate over thedefault parameters. However, unconstrained optimization leads to hyperparametersettings that are very expensive and not feasible for large scale recommendationtasks. To this end, we demonstrate 138% average improvement in hit rate with aruntime budget-constrained hyperparameter optimization. Furthermore, to makehyperparameter optimization applicable for large scale recommendation problemswhere the target dataset is too large to search over, we investigate generalizinghyperparameters settings from samples. We show that applying constrained hy-perparameter optimization using only a 10% sample of the data still yields a 91%average improvement in hit rate over the default parameters when applied to thefull datasets. Finally, we apply hyperparameters learned using our method of con-strained optimization on a sample to the Who To Follow recommendation serviceat Twitter and are able to increase follow rates by 15%.Comment: 11 pages, 4 figures, Fourteenth ACM Conference on Recommender System

Taking the Human Out of the Loop: A Review of Bayesian Optimization

Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.Engineering and Applied Science

Discovering Representations for Black-box Optimization

The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Variational Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions -- but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinematics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.Comment: Presented at GECCO 2020 -- v2 (Previous title 'Automating Representation Discovery with MAP-Elites'

On Multi-objective Policy Optimization as a Tool for Reinforcement Learning

Many advances that have improved the robustness and efficiency of deep reinforcement learning (RL) algorithms can, in one way or another, be understood as introducing additional objectives, or constraints, in the policy optimization step. This includes ideas as far ranging as exploration bonuses, entropy regularization, and regularization toward teachers or data priors when learning from experts or in offline RL. Often, task reward and auxiliary objectives are in conflict with each other and it is therefore natural to treat these examples as instances of multi-objective (MO) optimization problems. We study the principles underlying MORL and introduce a new algorithm, Distillation of a Mixture of Experts (DiME), that is intuitive and scale-invariant under some conditions. We highlight its strengths on standard MO benchmark problems and consider case studies in which we recast offline RL and learning from experts as MO problems. This leads to a natural algorithmic formulation that sheds light on the connection between existing approaches. For offline RL, we use the MO perspective to derive a simple algorithm, that optimizes for the standard RL objective plus a behavioral cloning term. This outperforms state-of-the-art on two established offline RL benchmarks