Models requiring probabilistic outputs are ubiquitous and used in fields such as natural language processing, contrastive learning, and recommendation systems. The standard method of designing such a model is to output unconstrained logits, which are normalized into probabilities with the softmax function. The normalization involves computing a summation across all classes, which becomes prohibitively expensive for problems with a large number of classes. An important strategy to reduce the cost is to sum over a sampled subset of classes in the softmax function, known as the sampled softmax. It was known that the sampled softmax is biased; the expectation taken over the sampled classes is not equal to the softmax function. Many works focused on reducing the bias by using a better way of sampling the subset. However, while sampled softmax is biased, it is unclear whether an unbiased function different from sampled softmax exists. In this paper, we show that all functions that only access a sampled subset of classes must be biased. With this result, we prevent efforts in finding unbiased loss functions and validate that past efforts devoted to reducing bias are the best we can do.

For building recommender systems, a critical task is to learn a policy with collected feedback (e.g., ratings, clicks) to decide which items to be recommended to users. However, it has been shown that the selection bias in the collected feedback leads to biased learning and thus a sub-optimal policy. To deal with this issue, counterfactual learning has received much attention, where existing approaches can be categorized as either value learning or policy learning approaches. This work studies policy learning approaches for top-K recommendations with a large item space and points out several difficulties related to importance weight explosion, observation insufficiency, and training efficiency. A practical framework for policy learning is then proposed to overcome these difficulties. Our experiments confirm the effectiveness and efficiency of the proposed framework.

Click-through rate (CTR) prediction is a core problem of building advertising systems. In many real-world applications, because an ad placed in various positions has different click probabilities, the position information should be considered in both training and prediction. For such position-aware systems, existing approaches learn CTR models from clicks/not-clicks on historically displayed events by leveraging the position information in different ways. In this work, we explain that these approaches may give a heavily biased model. We first point out that in position-aware systems, two different types of selection biases coexist in displayed events. Secondly, we explain that some approaches attempting to eliminate the position effect from clicks/not-clicks may possess an additional bias. Finally, to obtain an unbiased CTR model for position-aware systems, we propose a novel counterfactual learning framework. Experiments confirm both our analysis on selection biases and the effectiveness of our proposed counterfactual learning framework.