Cost-sensitive loss functions are crucial in many real-world prediction problems, where different types of errors are penalized differently; for example, in medical diagnosis, a false negative prediction can lead to worse consequences than a false positive prediction. However, traditional PAC learning theory has mostly focused on the symmetric 0-1 loss, leaving cost-sensitive losses largely unaddressed. In this work, we extend the celebrated theory of boosting to incorporate both cost-sensitive and multi-objective losses. Cost-sensitive losses assign costs to the entries of a confusion matrix, and are used to control the sum of prediction errors accounting for the cost of each error type. Multi-objective losses, on the other hand, simultaneously track multiple cost-sensitive losses, and are useful when the goal is to satisfy several criteria at once (e.g., minimizing false positives while keeping false negatives below a critical threshold). We develop a comprehensive theory of cost-sensitive and multi-objective boosting, providing a taxonomy of weak learning guarantees that distinguishes which guarantees are trivial (i.e., can always be achieved), which ones are boostable (i.e., imply strong learning), and which ones are intermediate, implying non-trivial yet not arbitrarily accurate learning. For binary classification, we establish a dichotomy: a weak learning guarantee is either trivial or boostable. In the multiclass setting, we describe a more intricate landscape of intermediate weak learning guarantees. Our characterization relies on a geometric interpretation of boosting, revealing a surprising equivalence between cost-sensitive and multi-objective losses.

We study a generalization of boosting to the multiclass setting. We introduce a weak learning condition for multiclass classification that captures the original notion of weak learnability as being "slightly better than random guessing". We give a simple and efficient boosting algorithm, that does not require realizability assumptions and its sample and oracle complexity bounds are independent of the number of classes. In addition, we utilize our new boosting technique in several theoretical applications within the context of List PAC Learning. First, we establish an equivalence to weak PAC learning. Furthermore, we present a new result on boosting for list learners, as well as provide a novel proof for the characterization of multiclass PAC learning and List PAC learning. Notably, our technique gives rise to a simplified analysis, and also implies an improved error bound for large list sizes, compared to previous results.

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.

Reducing reinforcement learning to supervised learning is a well-studied and effective approach that leverages the benefits of compact function approximation to deal with large-scale Markov decision processes. Independently, the boosting methodology (e.g. AdaBoost) has proven to be indispensable in designing efficient and accurate classification algorithms by combining inaccurate rules-of-thumb. In this paper, we take a further step: we reduce reinforcement learning to a sequence of weak learning problems. Since weak learners perform only marginally better than random guesses, such subroutines constitute a weaker assumption than the availability of an accurate supervised learning oracle. We prove that the sample complexity and running time bounds of the proposed method do not explicitly depend on the number of states. While existing results on boosting operate on convex losses, the value function over policies is non-convex. We show how to use a non-convex variant of the Frank-Wolfe method for boosting, that additionally improves upon the known sample complexity and running time even for reductions to supervised learning.

In the framework of online convex optimization, most iterative algorithms require the computation of projections onto convex sets, which can be computationally expensive. To tackle this problem HK12 proposed the study of projection-free methods that replace projections with less expensive computations. The most common approach is based on the Frank-Wolfe method, that uses linear optimization computation in lieu of projections. Recent work by GK22 gave sublinear adaptive regret guarantees with projection free algorithms based on the Frank Wolfe approach. In this work we give projection-free algorithms that are based on a different technique, inspired by Mhammedi22, that replaces projections by set-membership computations. We propose a simple lazy gradient-based algorithm with a Minkowski regularization that attains near-optimal adaptive regret bounds. For general convex loss functions we improve previous adaptive regret bounds from $O(T^{3/4})$ to $O(\sqrt{T})$, and further to tight interval dependent bound $\tilde{O}(\sqrt{I})$ where $I$ denotes the interval length. For strongly convex functions we obtain the first poly-logarithmic adaptive regret bounds using a projection-free algorithm.

We consider the problem of online boosting for regression tasks, when only limited information is available to the learner. We give an efficient regret minimization method that has two implications: an online boosting algorithm with noisy multi-point bandit feedback, and a new projection-free online convex optimization algorithm with stochastic gradient, that improves state-of-the-art guarantees in terms of efficiency.

We introduce a method for following high-level navigation instructions by mapping directly from images, instructions and pose estimates to continuous low-level velocity commands for real-time control. The Grounded Semantic Mapping Network (GSMN) is a fully-differentiable neural network architecture that builds an explicit semantic map in the world reference frame by incorporating a pinhole camera projection model within the network. The information stored in the map is learned from experience, while the local-to-world transformation is computed explicitly. We train the model using DAggerFM, a modified variant of DAgger that trades tabular convergence guarantees for improved training speed and memory use. We test GSMN in virtual environments on a realistic quadcopter simulator and show that incorporating an explicit mapping and grounding modules allows GSMN to outperform strong neural baselines and almost reach an expert policy performance. Finally, we analyze the learned map representations and show that using an explicit map leads to an interpretable instruction-following model.