Improving Adaptive Online Learning Using Refined Discretization

• URL: http://arxiv.org/abs/2309.16044v2
• Date: Thu, 22 Feb 2024 05:09:56 GMT
• Title: Improving Adaptive Online Learning Using Refined Discretization
• Authors: Zhiyu Zhang, Heng Yang, Ashok Cutkosky, Ioannis Ch. Paschalidis
• Abstract summary: We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm. Central to these results is a continuous time approach to online learning.
• Score: 44.646191058243645
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and ($ii$) the comparator norm adaptivity also known as "parameter freeness" in the literature. In particular, - our algorithm does not employ the impractical doubling trick, and does not require an a priori estimate of the time-uniform Lipschitz constant; - the associated regret bound has the optimal $O(\sqrt{V_T})$ dependence on the gradient variance $V_T$, without the typical logarithmic multiplicative factor; - the leading constant in the regret bound is "almost" optimal. Central to these results is a continuous time approach to online learning. We first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.

Related papers

• Gradient-Variation Online Learning under Generalized Smoothness [56.38427425920781]
  gradient-variation online learning aims to achieve regret guarantees that scale with variations in gradients of online functions. Recent efforts in neural network optimization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. We provide the applications for fast-rate convergence in games and extended adversarial optimization.
  arXiv  Detail & Related papers  (2024-08-17T02:22:08Z)
• Efficient Methods for Non-stationary Online Learning [67.3300478545554]
  We present efficient methods for optimizing dynamic regret and adaptive regret, which reduce the number of projections per round from $mathcalO(log T)$ to $1$. Our technique hinges on the reduction mechanism developed in parameter-free online learning and requires non-trivial twists on non-stationary online methods.
  arXiv  Detail & Related papers  (2023-09-16T07:30:12Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Efficient and Near-Optimal Smoothed Online Learning for Generalized Linear Functions [28.30744223973527]
  We give a computationally efficient algorithm that is the first to enjoy the statistically optimal log(T/sigma) regret for realizable K-wise linear classification. We develop a novel characterization of the geometry of the disagreement region induced by generalized linear classifiers.
  arXiv  Detail & Related papers  (2022-05-25T21:31:36Z)
• Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization [70.4342220499858]
  We introduce novel online algorithms that can exploit smoothness and replace the dependence on $T$ in dynamic regret with problem-dependent quantities. Our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and safeguard the same rate in the worst case.
  arXiv  Detail & Related papers  (2021-12-29T02:42:59Z)
• Optimal Rates for Random Order Online Optimization [60.011653053877126]
  We study the citetgarber 2020online, where the loss functions may be chosen by an adversary, but are then presented online in a uniformly random order. We show that citetgarber 2020online algorithms achieve the optimal bounds and significantly improve their stability.
  arXiv  Detail & Related papers  (2021-06-29T09:48:46Z)
• Accelerated Learning with Robustness to Adversarial Regressors [1.0499611180329802]
  We propose a new discrete time algorithm which provides stability and convergence guarantees in the presence of adversarial regressors. In particular, our algorithm reaches an $epsilon$ sub-optimal point in at most $tildemathcalO (1/sqrtepsilon)$ when regressors are constant.
  arXiv  Detail & Related papers  (2020-05-04T14:42:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.