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Register a new useriBOA: The Incremental Bayesian Optimization Algorithm
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Added by
Martin Pelikan
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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This paper proposes the incremental Bayesian optimization algorithm (iBOA), which modifies standard BOA by removing the population of solutions and using incremental updates of the Bayesian network. iBOA is shown to be able to learn and exploit unrestricted Bayesian networks using incremental techniques for updating both the structure as well as the parameters of the probabilistic model. This represents an important step toward the design of competent incremental estimation of distribution algorithms that can solve difficult nearly decomposable problems scalably and reliably.
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This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions, but also for estimating their fitness. The results indicate that fitness inheritance is a promising concept in BOA, because population-sizing requirements for building appropriate models of promising solutions lead to good fitness estimates even if only a small proportion of candidate solutions is evaluated using the actual fitness function. This can lead to a reduction of the number of actual fitness evaluations by a factor of 30 or more.
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.
The surrogate-assisted optimization algorithm is a promising approach for solving expensive multi-objective optimization problems. However, most existing surrogate-assisted multi-objective optimization algorithms have three main drawbacks: 1) cannot scale well for solving problems with high dimensional decision space, 2) cannot incorporate available gradient information, and 3) do not support batch optimization. These drawbacks prevent their use for solving many real-world large scale optimization problems. This paper proposes a batched scalable multi-objective Bayesian optimization algorithm to tackle these issues. The proposed algorithm uses the Bayesian neural network as the scalable surrogate model. Powered with Monte Carlo dropout and Sobolov training, the model can be easily trained and can incorporate available gradient information. We also propose a novel batch hypervolume upper confidence bound acquisition function to support batch optimization. Experimental results on various benchmark problems and a real-world application demonstrate the efficiency of the proposed algorithm.
Estimation of Distribution Algorithms have been proposed as a new paradigm for evolutionary optimization. This paper focuses on the parallelization of Estimation of Distribution Algorithms. More specifically, the paper discusses how to predict performance of parallel Mixed Bayesian Optimization Algorithm (MBOA) that is based on parallel construction of Bayesian networks with decision trees. We determine the time complexity of parallel Mixed Bayesian Optimization Algorithm and compare this complexity with experimental results obtained by solving the spin glass optimization problem. The empirical results fit well the theoretical time complexity, so the scalability and efficiency of parallel Mixed Bayesian Optimization Algorithm for unknown instances of spin glass benchmarks can be predicted. Furthermore, we derive the guidelines that can be used to design effective parallel Estimation of Distribution Algorithms with the speedup proportional to the number of variables in the problem.
Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization is always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and is subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogate construction so that multiple clients collaboratively train a radial-basis-function-network as the global surrogate. Then a new federated acquisition function is proposed for the central server to approximate the objective values using the global surrogate and estimate the uncertainty level of the approximated objective values based on the local models. The performance of the proposed algorithm is verified on a series of multi/many-objective benchmark problems by comparing it with two state-of-the-art surrogate-assisted multi-objective evolutionary algorithms.
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