On Adaptivity in Non-stationary Stochastic Optimization With Bandit Feedback

• URL: http://arxiv.org/abs/2210.05584v1
• Date: Tue, 11 Oct 2022 16:16:34 GMT
• Title: On Adaptivity in Non-stationary Stochastic Optimization With Bandit Feedback
• Authors: Yining Wang
• Abstract summary: We show that, when aggregated function changes is known a priori, a simple re-starting algorithm attains the optimal dynamic regret. We also establish an additional result showing that any algorithm achieving good regret against stationary benchmarks with high probability could be automatically converted to an algorithm that achieves good regret against dynamic benchmarks.
• Score: 11.208914594208654
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we study the non-stationary stochastic optimization question with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes is known a priori, a simple re-starting algorithm attains the optimal dynamic regret. In this work, we designed a stochastic optimization algorithm with fixed step sizes, which combined together with the multi-scale sampling framework of Wei and Luo (2021) achieves the optimal dynamic regret in non-stationary stochastic optimization without requiring prior knowledge of function change budget, thereby closes a question that has been open for a while. We also establish an additional result showing that any algorithm achieving good regret against stationary benchmarks with high probability could be automatically converted to an algorithm that achieves good regret against dynamic benchmarks, which is applicable to a wide class of bandit convex optimization algorithms.

Related papers

• Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity [59.75300530380427]
  We consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.
  arXiv  Detail & Related papers  (2024-06-28T02:56:22Z)
• 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)
• Adaptive Stochastic Optimisation of Nonconvex Composite Objectives [2.1700203922407493]
  We propose and analyse a family of generalised composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. We exploit the low-dimensional structure of the decision sets for high-dimensional problems.
  arXiv  Detail & Related papers  (2022-11-21T18:31:43Z)
• Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stability [107.65337427333064]
  optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. In this work, we present the first trial in the single-dependent generalization of AUPRC optimization. Experiments on three image retrieval datasets on speak to the effectiveness and soundness of our framework.
  arXiv  Detail & Related papers  (2022-09-27T09:06:37Z)
• Optimistic Optimisation of Composite Objective with Exponentiated Update [2.1700203922407493]
  The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. They achieve a sequence-dependent regret upper bound, matching the best-known bounds for sparse target decision variables.
  arXiv  Detail & Related papers  (2022-08-08T11:29:55Z)
• Latency considerations for stochastic optimizers in variational quantum algorithms [0.02294014185517203]
  Variational quantum algorithms, which have risen to prominence in the noisy intermediate noisy quantum-scale setting, require the implementation of hardware. To date, most research has employed algorithms based on the gradient iteration as the classical iteration. In this work we propose instead using optimization algorithms that yield processes emulating the dynamics of classical deterministic algorithms.
  arXiv  Detail & Related papers  (2022-01-31T18:51:24Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• Adaptive Importance Sampling for Finite-Sum Optimization and Sampling with Decreasing Step-Sizes [4.355567556995855]
  We propose Avare, a simple and efficient algorithm for adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Under standard technical conditions, we show that Avare achieves $mathcalO(T2/3)$ and $mathcalO(T5/6)$ dynamic regret for SGD and SGLD respectively when run with $mathcalO(T5/6)$ step sizes.
  arXiv  Detail & Related papers  (2021-03-23T00:28:15Z)
• Optimizing Optimizers: Regret-optimal gradient descent algorithms [9.89901717499058]
  We study the existence, uniqueness and consistency of regret-optimal algorithms. By providing first-order optimality conditions for the control problem, we show that regret-optimal algorithms must satisfy a specific structure in their dynamics. We present fast numerical methods for approximating them, generating optimization algorithms which directly optimize their long-term regret.
  arXiv  Detail & Related papers  (2020-12-31T19:13:53Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Stochastic batch size for adaptive regularization in deep network optimization [63.68104397173262]
  We propose a first-order optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets.
  arXiv  Detail & Related papers  (2020-04-14T07:54:53Z)

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.