A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…
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 can learn efficiently in this setting, at a rate which is linear in both k and…
Unified framework for robust linear predictions without distributional assumptions.
problem Robust linear predictions in the presence of outliers and model misspecification.
method Unified robust framework for linear prediction problems on Hilbert spaces, using Median of Means (MoM) approach.
result Achieves an error rate of \(O(\max\left\{|\mathcal{O}|^{1/2}n^{-1/2}, |\mathcal{I}|^{1/2}n^{-1}
ight\}+ε)\) for misspecification level \(ε\), matching best-known rates.
Study on L2-boosting behavior as learning rate approaches zero.
problem Understanding the asymptotic behavior of L2-boosting algorithms with vanishing learning rates.
method Analyzes L2-boosting for regression with linear base learners, proving a deterministic limit and characterizing it as a solution to a linear differential equation.
result Proves the existence of a unique solution to the limit problem and analyzes the training and test error.
Study examines how data augmentation impacts optimization in linear regression.
problem Understanding how data augmentation schedules affect optimization in linear regression.
method Analyzed the effect of augmentation on optimization in linear regression with MSE loss, using classical convex optimization and recent work on implicit bias.
result Proved that under certain joint schedules for learning rate and augmentation scheme, augmented gradient descent converges and characterized the resulting minimum.
Linear Q-learning converges to a bounded set without divergence.
problem Proving linear Q-learning does not diverge and converges to a bounded set.
method No modifications to the original linear Q-learning algorithm, no Bellman completeness or near-optimality assumptions, only an ε-softmax behavior policy with adaptive temperature.
result First L2 convergence rate of linear Q-learning iterates to a bounded set.
We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all convex surrogate losses, the hinge loss gives essentially the best possible bound, o…
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov fun…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for minimizing a smooth convex function over a linear space spanned by a set of atoms…
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…