Better safe than sorry: Risky function exploitation through safe optimization

Exploration-exploitation of functions, that is learning and optimizing a mapping between inputs and expected outputs, is ubiquitous to many real world situations. These situations sometimes require us to avoid certain outcomes at all cost, for example because they are poisonous, harmful, or otherwise dangerous. We test participants' behavior in scenarios in which they have to find the optimum of a function while at the same time avoid outputs below a certain threshold. In two experiments, we find that Safe-Optimization, a Gaussian Process-based exploration-exploitation algorithm, describes participants' behavior well and that participants seem to care firstly whether a point is safe and then try to pick the optimal point from all such safe points. This means that their trade-off between exploration and exploitation can be seen as an intelligent, approximate, and homeostasis-driven strategy.Comment: 6 pages, submitted to Cognitive Science Conferenc

Time-Varying Gaussian Process Bandit Optimization

We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. We introduce two natural extensions of the classical Gaussian process upper confidence bound (GP-UCB) algorithm. The first, R-GP-UCB, resets GP-UCB at regular intervals. The second, TV-GP-UCB, instead forgets about old data in a smooth fashion. Our main contribution comprises of novel regret bounds for these algorithms, providing an explicit characterization of the trade-off between the time horizon and the rate at which the function varies. We illustrate the performance of the algorithms on both synthetic and real data, and we find the gradual forgetting of TV-GP-UCB to perform favorably compared to the sharp resetting of R-GP-UCB. Moreover, both algorithms significantly outperform classical GP-UCB, since it treats stale and fresh data equally.Comment: To appear in AISTATS 201