On safe sequential optimization using posterior sampling

We consider the problem of designing posterior sampling based sequential optimization policies for maximizing a blackbox function subject to safety constraints. Posterior sampling algorithms, which are easier to implement, have met with empirical success for blackbox maximization problems without safety constraints. We consider whether posterior sampling algorithms which satisfy safety constraints have good performance with respect to achieving the global maxima while minimizing the number of safety constraint violations. We propose a safe Gaussian process Thompson Sampling algorithm for safe maximization of a blackbox function. The algorithm uses a sample estimate of safe set in order to meet safety constraints and uses a mutual information based acquisition function in order to improve the estimate of the safe set. We evaluate the performance of the proposed policy with respect to prior work using simulations. We observe that the proposed policy achieves similar behaviour compared to prior work for safety violations while achieving the global maximum.