To exploit, UCT often selects the same action on successive trials, which can result in it getting stuck in local optima.

We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.

In stochastic zeroth-order optimization, a problem of practical relevance is understanding how to fully exploit the local geometry of the underlying objective function.

Neural Information Processing Systems http://nips.cc/

Our sequential optimization setting is as follows. Consider an objective functionf defined over a domainX Rd, whered N is the dimension of the input.

Roy, 2014] are not sufficient for optimal regret.

Bandits

We call that σ -algebra history before n . Identification tasks We focus on best arm identification (BAI).

Theimplementation optimizes theacquisition function, andtheposterior mean,bysampling adensegridofpoints,and uses a gradient-based optimizer to further optimize the single best point. Thus, onlyacquisition function setup and acquisition function optimization are considered as part of the runtime. For the synthetic test functions, 100 sampled optimal pairs are used for each acquisition function. GP hyperparameters are marginalized over for these tasks, so an equal number ofoptimal pairs aresampled foreachhyperparameter set. Thehyperparameters are re-sampled onafixedschedule throughout the run.