We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.

We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm’s update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.

Extreme multi-label classification (XMLC) is the task of selecting a small subset of relevant labels from a very large set of possible labels. As such, it is characterized by long-tail labels, i.e., most labels have very few positive instances. With standard performance measures such as precision@k, a classifier can ignore tail labels and still report good performance. However, it is often argued that correct predictions in the tail are more "interesting" or "rewarding," but the community has not yet settled on a metric capturing this intuitive concept. The existing propensity-scored metrics fall short on this goal by confounding the problems of long-tail and missing labels. In this paper, we analyze generalized metrics budgeted "at k" as an alternative solution. To tackle the challenging problem of optimizing these metrics, we formulate it in the expected test utility (ETU) framework, which aims to optimize the expected performance on a given test set. We derive optimal prediction rules and construct their computationally efficient approximations with provable regret guarantees and being robust against model misspecification. Our algorithm, based on block coordinate descent, scales effortlessly to XMLC problems and obtains promising results in terms of long-tail performance.

The propensity model introduced by Jain et al has become a standard approach for dealing with missing and long-tail labels in extreme multi-label classification (XMLC). In this paper, we critically revise this approach showing that despite its theoretical soundness, its application in contemporary XMLC works is debatable. We exhaustively discuss the flaws of the propensity-based approach, and present several recipes, some of them related to solutions used in search engines and recommender systems, that we believe constitute promising alternatives to be followed in XMLC.

Extreme multi-label classification (XMLC) refers to the task of tagging instances with small subsets of relevant labels coming from an extremely large set of all possible labels. Recently, XMLC has been widely applied to diverse web applications such as automatic content labeling, online advertising, or recommendation systems. In such environments, label distribution is often highly imbalanced, consisting mostly of very rare tail labels, and relevant labels can be missing. As a remedy to these problems, the propensity model has been introduced and applied within several XMLC algorithms. In this work, we focus on the problem of optimal predictions under this model for probabilistic label trees, a popular approach for XMLC problems. We introduce an inference procedure, based on the A*-search algorithm, that efficiently finds the optimal solution, assuming that all probabilities and propensities are known. We demonstrate the attractiveness of this approach in a wide empirical study on popular XMLC benchmark datasets.

This paper presents the first two editions of Visual Doom AI Competition, held in 2016 and 2017. The challenge was to create bots that compete in a multiplayer deathmatch in a first-person shooter game Doom. The bots had to make their decisions solely based on visual information, i.e., a raw screen buffer. To play well, the bots needed to understand their surroundings, navigate, explore, and handle the opponents at the same time. These aspects, together with the competitive multiagent aspect of the game, make the competition a unique platform for evaluating the state-of-the-art reinforcement learning algorithms. This paper discusses the rules, solutions, results, and statistics that give insight into the agents' behaviors. Best performing agents are described in more detail. The results of the competition lead to the conclusion that, although reinforcement learning can produce capable Doom bots, they still are not yet able to successfully compete against humans in this game. This paper also revisits the ViZDoom environment, which is a flexible, easy to use, and efficient three-dimensional platform for research for vision-based reinforcement learning, based on a well-recognized first-person perspective game Doom.

Extreme multi-label classification (XMLC) is a problem of tagging an instance with a small subset of relevant labels chosen from an extremely large pool of possible labels. Large label spaces can be efficiently handled by organizing labels as a tree, like in the hierarchical softmax (HSM) approach commonly used for multi-class problems. In this paper, we investigate probabilistic label trees (PLTs) that have been recently devised for tackling XMLC problems. We show that PLTs are a no-regret multi-label generalization of HSM when precision@$k$ is used as a model evaluation metric. Critically, we prove that pick-one-label heuristic---a reduction technique from multi-label to multi-class that is routinely used along with HSM---is not consistent in general. We also show that our implementation of PLTs, referred to as extremeText (XT), obtains significantly better results than HSM with the pick-one-label heuristic and XML-CNN, a deep network specifically designed for XMLC problems. Moreover, XT is competitive to many state-of-the-art approaches in terms of statistical performance, model size and prediction time which makes it amenable to deploy in an online system.