Related papers: On aggregation for heavy-tailed classes
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Advantage Learning (AL) seeks to increase the action gap between the optimal action and its competitors, so as to improve the robustness to estimation errors. However, the method becomes problematic when the optimal action induced by the…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…
Value aggregation is a general framework for solving imitation learning problems. Based on the idea of data aggregation, it generates a policy sequence by iteratively interleaving policy optimization and evaluation in an online learning…
Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020).…
In statistical decision theory, a model is said to be Pareto optimal (or admissible) if no other model carries less risk for at least one state of nature while presenting no more risk for others. How can you rationally aggregate/combine a…
This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on…
We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…
$Q$-learning is one of the most fundamental reinforcement learning algorithms. It is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence until the recent work…
Federated Learning enables collaborative model training without centralising data, but its effectiveness varies with the selection of the aggregation strategy. This choice is non-trivial, as performance varies widely across datasets,…
We consider the problem of learning a non-negative linear classifier with a $1$-norm of at most $k$, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a $k$-monotone disjunction. We prove that we…
Multi-Task Learning is a learning paradigm that uses correlated tasks to improve performance generalization. A common way to learn multiple tasks is through the hard parameter sharing approach, in which a single architecture is used to…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
Stochastic-approximation gradient methods are attractive for large-scale convex optimization because they offer inexpensive iterations. They are especially popular in data-fitting and machine-learning applications where the data arrives in…
We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign,…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may…