A Regularized Online Newton Method for Stochastic Convex Bandits with Linear Vanishing Noise
We study a stochastic convex bandit problem where the subgaussian noise parameter is assumed to decrease linearly as the learner selects actions closer and closer to the minimizer of the convex loss function. Accordingly, we propose a Regularized Online Newton Method (RONM) for solving the problem, based on the Online Newton Method (ONM) of arXiv:2406.06506. Our RONM reaches a polylogarithmic regret in the time horizon $n$ when the loss function grows quadratically in the constraint set, which recovers the results of arXiv:2402.12042 in linear bandits. Our analyses rely on the growth rate of the precision matrix $\Sigma_t^{-1}$ in ONM and we find that linear growth solves the question exactly. These analyses also help us obtain better convergence rates when the loss function grows faster. We also study and analyze two new bandit models: stochastic convex bandits with noise scaled to a subgaussian parameter function and convex bandits with stochastic multiplicative noise.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Improving Stochastic Cubic Newton with Momentum
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method.…
Second-order methodsStochastic Variance-Reduced Cubic Regularized Newton Method
We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are speci…
A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only …
Binary ClassificationStochastic OptimizationStochastic Subspace Cubic Newton Method
In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stoc…
Second-order methodsCombining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization
We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global conve…
BIG-bench Machine Learning