Hybridization of One- and Two-Point Bandits Convex Optimization in Non-stationary Environments
摘要
Bandit Convex Optimization (BCO) is an imperative analysis framework when dealing with sequential decision-making problems. Considering to balance the computational cost and bounds of regrets, in this paper, we propose a hybridized algorithm of one- and two-point bandit convex models in non-stationary environments and use a more general performance measure dynamic regret, which records the cumulative difference between function loss and a feasible comparator sequence during the time horizon T. The path length of a comparator sequence \(P_T\) reveals the non-stationarity of environments. Our proposed algorithm builds an upper bound of dynamic regret \(\mathcal {O}((1+P_{T})^{1/2}[\beta (\lambda T)^{{1}/{2}} + ((1-\lambda )T)^{{3}/{4}}])\) , where the parameter \(\lambda \) can dynamically adjust the bound guarantee to balance the computational cost in real applications.