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Quality and Computation Time in Optimization Problems

arXiv.org Artificial Intelligence

Optimization problems are crucial in artificial intelligence. Optimization algorithms are generally used to adjust the performance of artificial intelligence models to minimize the error of mapping inputs to outputs. Current evaluation methods on optimization algorithms generally consider the performance in terms of quality. However, not all optimization algorithms for all test cases are evaluated equal from quality, the computation time should be also considered for optimization tasks. In this paper, we investigate the quality and computation time of optimization algorithms in optimization problems, instead of the one-for-all evaluation of quality. We select the well-known optimization algorithms (Bayesian optimization and evolutionary algorithms) and evaluate them on the benchmark test functions in terms of quality and computation time. The results show that BO is suitable to be applied in the optimization tasks that are needed to obtain desired quality in the limited function evaluations, and the EAs are suitable to search the optimal of the tasks that are allowed to find the optimal solution with enough function evaluations. This paper provides the recommendation to select suitable optimization algorithms for optimization problems with different numbers of function evaluations, which contributes to the efficiency that obtains the desired quality with less computation time for optimization problems.


Meta Learning Black-Box Population-Based Optimizers

arXiv.org Artificial Intelligence

The no free lunch theorem states that no model is better suited to every problem. A question that arises from this is how to design methods that propose optimizers tailored to specific problems achieving state-of-the-art performance. This paper addresses this issue by proposing the use of meta-learning to infer population-based black-box optimizers that can automatically adapt to specific classes of problems. We suggest a general modeling of population-based algorithms that result in Learning-to-Optimize POMDP (LTO-POMDP), a meta-learning framework based on a specific partially observable Markov decision process (POMDP). From that framework's formulation, we propose to parameterize the algorithm using deep recurrent neural networks and use a meta-loss function based on stochastic algorithms' performance to train efficient data-driven optimizers over several related optimization tasks. The learned optimizers' performance based on this implementation is assessed on various black-box optimization tasks and hyperparameter tuning of machine learning models. Our results revealed that the meta-loss function encourages a learned algorithm to alter its search behavior so that it can easily fit into a new context. Thus, it allows better generalization and higher sample efficiency than state-of-the-art generic optimization algorithms, such as the Covariance matrix adaptation evolution strategy (CMA-ES).


Time Efficiency in Optimization with a Bayesian-Evolutionary Algorithm

arXiv.org Artificial Intelligence

Not all generate-and-test search algorithms are created equal. Bayesian Optimization (BO) invests a lot of computation time to generate the candidate solution that best balances the predicted value and the uncertainty given all previous data, taking increasingly more time as the number of evaluations performed grows. Evolutionary Algorithms (EA) on the other hand rely on search heuristics that typically do not depend on all previous data and can be done in constant time. Both the BO and EA community typically assess their performance as a function of the number of evaluations. However, this is unfair once we start to compare the efficiency of these classes of algorithms, as the overhead times to generate candidate solutions are significantly different. We suggest to measure the efficiency of generate-and-test search algorithms as the expected gain in the objective value per unit of computation time spent. We observe that the preference of an algorithm to be used can change after a number of function evaluations. We therefore propose a new algorithm, a combination of Bayesian optimization and an Evolutionary Algorithm, BEA for short, that starts with BO, then transfers knowledge to an EA, and subsequently runs the EA. We compare the BEA with BO and the EA. The results show that BEA outperforms both BO and the EA in terms of time efficiency, and ultimately leads to better performance on well-known benchmark objective functions with many local optima. Moreover, we test the three algorithms on nine test cases of robot learning problems and here again we find that BEA outperforms the other algorithms.


Bayesian Optimization for Dynamic Problems

arXiv.org Machine Learning

We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our extensions to Bayesian optimization use the information learnt from this model to guide the tracking of a temporally evolving minimum. By exploiting temporal correlations, the proposed method also determines when to make evaluations, how fast to make those evaluations, and it induces an appropriate budget of steps based on the available information. Lastly, we evaluate our technique on synthetic and real-world problems.


Efficient Hyperparameter Optimization for Deep Learning Algorithms Using Deterministic RBF Surrogates

AAAI Conferences

Automatically searching for optimal hyperparameter configurations is of crucial importance for applying deep learning algorithms in practice. Recently, Bayesian optimization has been proposed for optimizing hyperparameters of various machine learning algorithms. Those methods adopt probabilistic surrogate models like Gaussian processes to approximate and minimize the validation error function of hyperparameter values. However, probabilistic surrogates require accurate estimates of sufficient statistics (e.g., covariance) of the error distribution and thus need many function evaluations with a sizeable number of hyperparameters. This makes them inefficient for optimizing hyperparameters of deep learning algorithms, which are highly expensive to evaluate. In this work, we propose a new deterministic and efficient hyperparameter optimization method that employs radial basis functions as error surrogates. The proposed mixed integer algorithm, called HORD, searches the surrogate for the most promising hyperparameter values through dynamic coordinate search and requires many fewer function evaluations. HORD does well in low dimensions but it is exceptionally better in higher dimensions. Extensive evaluations on MNIST and CIFAR-10 for four deep neural networks demonstrate HORD significantly outperforms the well-established Bayesian optimization methods such as GP, SMAC, and TPE. For instance, on average, HORD is more than 6 times faster than GP-EI in obtaining the best configuration of 19 hyperparameters.