In many recommender systems and search problems, presenting a well balanced set of results can be an important goal in addition to serving highly relevant content. For example, in a movie recommendation system, it may be helpful to achieve a certain balance of different genres, likewise, it may be important to balance between highly popular versus highly personalized shows. Such balances could be thought across many categories and may be required for enhanced user experience, business considerations, fairness objectives etc. In this paper, we consider the problem of calibrating with respect to any given categories over items. We propose a way to balance a trade-off between relevance and calibration via a Linear Programming optimization problem where we learn a doubly stochastic matrix to achieve optimal balance in expectation. We then realize the learned policy using the Birkhoff-von Neumann decomposition of a doubly stochastic matrix. Several optimizations are considered over the proposed basic approach to make it fast. The experiments show that the proposed formulation can achieve a much better trade-off compared to many other baselines. This paper does not prescribe the exact categories to calibrate over (such as genres) universally for applications. This is likely dependent on the particular task or business objective. The main contribution of the paper is that it proposes a framework that can be applied to a variety of problems and demonstrates the efficacy of the proposed method using a few use-cases.

翻译：摘要：在许多推荐系统和搜索问题中，除了提供高相关性内容外，呈现均衡的结果集也是一个重要目标。例如，在电影推荐系统中，实现不同流派的适当平衡可能有所帮助；同样，在热门节目与高度个性化节目之间取得平衡也至关重要。这种平衡可以跨越多个类别，并且可能出于提升用户体验、商业考量、公平性目标等需求。本文考虑了针对任何给定类别对物品进行校准的问题。我们提出了一种通过线性规划优化问题来平衡相关性与校准之间权衡的方法，其中学习一个双随机矩阵以实现期望中的最优平衡。随后，我们利用Birkhoff-von Neumann分解将学习到的策略实现为双随机矩阵。针对所提出的基础方法，我们考虑了多种优化以提升速度。实验表明，与许多其他基线相比，所提出的公式能实现更好的权衡。本文并未规定所有应用通用的校准类别（如流派），这通常取决于特定任务或商业目标。本文的主要贡献在于提出了一个可应用于多种问题的框架，并通过几个用例证明了所提方法的有效性。