Nested Expectations with Kernel Quadrature
This addresses a computational bottleneck for practitioners in fields like finance and healthcare who need efficient nested expectation estimation, representing a strong specific gain rather than a broad paradigm shift.
The paper tackles the computational challenge of estimating nested expectations by proposing a novel estimator using nested kernel quadrature, which achieves faster convergence rates than existing methods when integrands are sufficiently smooth. Empirical results demonstrate the method requires fewer samples for applications including Bayesian optimization, option pricing, and health economics.
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then demonstrate empirically that our proposed method does indeed require fewer samples to estimate nested expectations on real-world applications including Bayesian optimisation, option pricing, and health economics.