Optimization as Estimation with Gaussian Processes in Bandit Settings
This work addresses optimization challenges in machine learning, particularly for robotics and vision applications, but is incremental as it builds on and adapts existing GP-based methods.
The paper tackles the problem of optimizing unknown functions in Bayesian optimization by proposing a strategy that directly estimates the argmax, eliminating the need for tradeoff parameters and connecting to existing methods like GP-UCB and GP-PI. It demonstrates robustness through regret bounds and empirical evaluations on robotics and vision tasks, showing competitive performance without specifying concrete numbers.
Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an estimate of the argmax of the function. This strategy offers both practical and theoretical advantages: no tradeoff parameter needs to be selected, and, moreover, we establish close connections to the popular GP-UCB and GP-PI strategies. Our approach can be understood as automatically and adaptively trading off exploration and exploitation in GP-UCB and GP-PI. We illustrate the effects of this adaptive tuning via bounds on the regret as well as an extensive empirical evaluation on robotics and vision tasks, demonstrating the robustness of this strategy for a range of performance criteria.