Efficient Methods for Non-stationary Online Learning

• URL: http://arxiv.org/abs/2309.08911v2
• Date: Thu, 30 Jan 2025 09:02:00 GMT
• Title: Efficient Methods for Non-stationary Online Learning
• Authors: Peng Zhao, Yan-Feng Xie, Lijun Zhang, Zhi-Hua Zhou,
• Abstract summary: We present efficient methods for optimizing dynamic regret and adaptive regret, which reduce the number of projections per round from $mathcalO(log T)$ to $1$. We also study an even strengthened measure, namely the interval dynamic regret'', and reduce the number of projections per round from $mathcalO(log2 T)$ to $1$.
• Score: 61.63338724659592
• License:
• Abstract: Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To optimize them, a two-layer online ensemble is usually deployed due to the inherent uncertainty of the non-stationarity, in which a group of base-learners are maintained and a meta-algorithm is employed to track the best one on the fly. However, the two-layer structure raises the concern about the computational complexity -- those methods typically maintain $\mathcal{O}(\log T)$ base-learners simultaneously for a $T$-round online game and thus perform multiple projections onto the feasible domain per round, which becomes the computational bottleneck when the domain is complicated. In this paper, we first present efficient methods for optimizing dynamic regret and adaptive regret, which reduce the number of projections per round from $\mathcal{O}(\log T)$ to $1$. The obtained algorithms require only one gradient query and one function evaluation at each round. Our technique hinges on the reduction mechanism developed in parameter-free online learning and requires non-trivial twists on non-stationary online methods. Furthermore, we study an even strengthened measure, namely the ``interval dynamic regret'', and reduce the number of projections per round from $\mathcal{O}(\log^2 T)$ to $1$ to minimize it. Our reduction demonstrates great generalizability and can be applied to two important applications: online stochastic control and online principal component analysis, resulting in methods that are both efficient and optimal. Finally, empirical studies verify our theoretical findings.

Related papers

• Variance Reduced Online Gradient Descent for Kernelized Pairwise Learning with Limited Memory [19.822215548822882]
  Online gradient descent (OGD) algorithms have been proposed to handle online pairwise learning, where data arrives sequentially. Recent advancements in OGD algorithms have aimed to reduce the complexity of calculating online gradients, achieving complexities less than $O(T)$ and even as low as $O(1)$. In this study, we propose a limited memory OGD algorithm that extends to kernel online pairwise learning while improving the sublinear regret.
  arXiv  Detail & Related papers  (2023-10-10T09:50:54Z)
• Improving Adaptive Online Learning Using Refined Discretization [44.646191058243645]
  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.
  arXiv  Detail & Related papers  (2023-09-27T21:54:52Z)
• Universal Online Learning with Gradient Variations: A Multi-layer Online Ensemble Approach [57.92727189589498]
  We propose an online convex optimization approach with two different levels of adaptivity. We obtain $mathcalO(log V_T)$, $mathcalO(d log V_T)$ and $hatmathcalO(sqrtV_T)$ regret bounds for strongly convex, exp-concave and convex loss functions.
  arXiv  Detail & Related papers  (2023-07-17T09:55:35Z)
• Improved Algorithms for Neural Active Learning [74.89097665112621]
  We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. We introduce two regret metrics by minimizing the population loss that are more suitable in active learning than the one used in state-of-the-art (SOTA) related work.
  arXiv  Detail & Related papers  (2022-10-02T05:03:38Z)
• Proximal Point Imitation Learning [48.50107891696562]
  We develop new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning. We leverage classical tools from optimization, in particular, the proximal-point method (PPM) and dual smoothing. We achieve convincing empirical performance for both linear and neural network function approximation.
  arXiv  Detail & Related papers  (2022-09-22T12:40:21Z)
• 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)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Adaptive Approximate Policy Iteration [22.915651391812187]
  We present a learning scheme which enjoys a $tildeO(T2/3)$ regret bound for undiscounted, continuing learning in uniformly ergodic MDPs. This is an improvement over the best existing bound of $tildeO(T3/4)$ for the average-reward case with function approximation.
  arXiv  Detail & Related papers  (2020-02-08T02:27:03Z)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)

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.