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The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B3) approaches for CV selection using the minimum singular value (MSV) rule and the local worst-case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.