Many recommendation systems must optimise for multiple objectives at the same time, such as relevance, popularity, or personal preferences. We formulated the multi-objective optimisation problem as a constrained optimisation problem: the overall objective is to maximise the expected value of a primary metric, subject to constraints in terms of expected values of secondary metrics. During online serving, the objectives may shift according to user’s needs – for example, a user that had previously been interested in housing search apps might have found a new flat, and so is now interested in home decor apps – so we worked toward a dynamic solution.

Rather than solving the problem offline and bringing a fixed model online, we solved this problem on-line, per-request, based on the actual values of the objectives during serving time. We define the constraints to be relative constraints, meaning we would like to improve the secondary objective by a percentage rather than an absolute value. This way, any shifts in the secondary objectives didn’t affect our solver.

The algorithm that we developed can be used to find tradeoffs between a number of metrics. Finding suitable points along the tradeoff curve, our algorithm can significantly raise secondary metrics with only minor effects on the primary metric.