A stochastic learning-to-rank algorithm and its application to contextual advertising

This paper is concerned with the problem of learning a model to rank objects (Web pages, ads and etc.). We pro-pose a framework where the ranking model is both opti-mized and evaluated using the same information retrieval measures such as Normalized Discounted Cumulative Gain (NDCG) and Mean Average Precision (MAP). The main difficulty in direct optimization of NDCG and MAP is that these measures depend on the rank of objects and are not differentiable. Most learning-to-rank methods that attempt to optimize NDCG or MAP approximate such measures so that they can be differentiable. In this paper, we propose a simple yet effective stochastic optimization algorithm to directly minimize any loss function, which can be defined on NDCG or MAP for the learning-to-rank problem. The algorithm employs Simulated Annealing along with Simplex method for its parameter search and finds the global optimal parameters. Experiment results using NDCG-Annealing al-gorithm, an instance of the proposed algorithm, on LETOR benchmark data sets show that the proposed algorithm is both effective and stable when compared to the baselines provided in LETOR 3.0. In addition, we applied the algo-rithm for ranking ads in contextual advertising. Our method has shown to significantly improve relevance in offline evalu-ation and business metrics in online tests in a real large-scale advertising serving system. To scale our computations, we parallelize the algorithm in a MapReduce framework run-ning on Hadoop