不确定条件下贝叶斯optimization中约束的耦合与选择
Coupling and selecting constraints in Bayesian optimization under uncertainties
摘要：
我们考虑机会约束优化，它是寻求优化的功能，同时遵守约束，这两者都受到不确定性。现实模拟的高计算成本极大地限制了评估的数量，并使这类问题特别具有挑战性。在这种情况下，通常依赖贝叶斯优化算法。在不失一般性的情况下，假设不确定性来自一些输入，则可以在设计变量和不确定变量的联合空间中构建高斯过程模型。一个两步采集功能，然后使用提供，既有前途的优化变量相关的不确定样本。我们的总体贡献是关联GP模型中的约束，并利用这一点来最佳地决定，在每次迭代中，哪个约束应该被评估，以及在哪个点。约束的耦合高斯模型依赖于输出作为输入的编码。约束选择思想的发展，使每个约束可以评估一个不同的不确定性输入，从而提高求精效率。约束耦合和选择是逐步实现在3个算法的变种相比，参考贝叶斯方法。结果是有前途的收敛速度，精度和稳定性方面观察到的2，4和27维的问题。
英文摘要：
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the number of evaluations and makes this type of problems particularly challenging. In such a context, it is common to rely on Bayesian optimization algorithms. Assuming, without loss of generality, that the uncertainty comes from some of the inputs, it becomes possible to build a Gaussian process model in the joint space of design and uncertain variables. A two-step acquisition function is then used to provide, both, promising optimization variables associated to relevant uncertain samples. Our overall contribution is to correlate the constraints in the GP model and exploit this to optimally decide, at each iteration, which constraint should be evaluated and at which point. The coupled Gaussian model of the constraints relies on an output-as-input encoding. The constraint selection idea is developed by enabling that each constraint can be evaluated for a different uncertain input, thus improving the refinement efficiency. Constraints coupling and selection are gradually implement in 3 algorithm variants which are compared to a reference Bayesian approach. The results are promising in terms of convergence speed, accuracy and stability as observed on a 2, a 4 and a 27-dimensional problems.
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