Indirect Query Bayesian Optimization with Integrated Feedback
This addresses optimization challenges in real-world applications like privacy-sensitive or hardware-limited settings, though it appears incremental as it extends existing Bayesian optimization methods.
The paper tackles the problem of optimizing a function when only indirect, conditional feedback is available due to privacy or computational constraints, by proposing a new Bayesian optimization framework and acquisition function, and demonstrates its effectiveness on simulated tasks with regret bounds.
We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm with multi-resolution feedback to improve computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.