Multi-arm trials are gaining interest in practice given the statistical and logistical advantages they can offer. The standard approach uses a fixed allocation ratio, but there is a call for making it adaptive and skewing the allocation of patients towards better-performing arms. However, it is well-known that these approaches might suffer from lower statistical power. We present a response-adaptive design for continuous endpoints which explicitly allows to control the trade-off between the number of patients allocated to the "optimal" arm and the statistical power. Such a balance is achieved through the calibration of a tuning parameter, and we explore robust procedures to select it. The proposed criterion is based on a context-dependent information measure which gives greater weight to treatment arms with characteristics close to a pre-specified clinical target. We establish conditions under which the procedure consistently selects the target arm and derive the corresponding limiting allocation ratios. We also introduce a simulation-based hypothesis testing procedure which focuses on selecting the target arm and discuss strategies to effectively control the type-I error rate. The practical implementation of the proposed criterion and its potential advantage over currently used alternatives are illustrated in the context of early Phase IIa proof-of-concept oncology trials.