Sequential Design for Ranking Response Surfaces
This work addresses a stochastic control problem for applications like epidemics management, but it is incremental as it adapts existing uncertainty reduction and bandit methods to a continuous-input setting.
The authors tackled the problem of ranking multiple unknown response surfaces by efficiently identifying the minimal response across a continuous input space, using sequential design methods that achieved improved sampling efficiency in synthetic and epidemics control examples.
We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given $L \ge 2$ response surfaces over a continuous input space $\cal X$, the aim is to efficiently find the index of the minimal response across the entire $\cal X$. The response surfaces are not known and have to be noisily sampled one-at-a-time. This setting is motivated by stochastic control applications and requires joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging surrogates. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.