The question of selecting the ‘best’ among different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example, which treatment gives the best response rate. Motivated by recent developments in the theory of context‐dependent information measures, we propose a flexible response‐adaptive experimental design based on a novel criterion governing treatment arm selections which can be used in adaptive experiments with simple (e.g. binary) and complex (e.g. co‐primary, ordinal or nested) end points. It was found that, for specific choices of the context‐dependent measure, the criterion leads to a reliable selection of the correct arm without any parametric or monotonicity assumptions and provides noticeable gains in settings with costly observations. The asymptotic properties of the design are studied for different allocation rules, and the small sample size behaviour is evaluated in simulations in the context of phase II clinical trials with different end points. We compare the proposed design with currently used alternatives and discuss its practical implementation.