It is widely acknowledged that the agile reconfiguration of network slice according to traffic demand is of vital importance in 5G-and-beyond systems. Existing relevant works make reconfiguration decisions based either on point prediction of the uncertain demand, which lacks indications on how accurate it is, or on handcrafted uncertainty set with robust optimization, which may lead to resource over-provisioning due to the lack of prediction mechanism. To overcome these drawbacks, in this paper, we propose a predictor-optimizer framework that intelligently performs inter-slice reconfiguration with the aim of minimizing the energy consumption of serving these slices. Specifically, the predictor produces a prediction interval comprised of lower and upper bounds that bracket the future traffic demands with a prespecified probability. Then by regarding the prediction interval as the uncertainty set, we formulate the network slice reconfiguration problem as a Robust Mixed Integer Programming (RMIP). We solve this RMIP by using linearization technique and robust optimization. Numerical results demonstrate that the proposed framework outperforms traditional methods in terms of robustness and energy consumption. Meanwhile, the tradeoff between robustness and the energy consumption can be automatically adjusted according to the type of slice and traffic demands.