Simultaneously Achieving Sublinear Regret and Constraint Violations for Online Convex Optimization with Time-varying Constraints

• URL: http://arxiv.org/abs/2111.07707v1
• Date: Mon, 15 Nov 2021 12:23:31 GMT
• Title: Simultaneously Achieving Sublinear Regret and Constraint Violations for Online Convex Optimization with Time-varying Constraints
• Authors: Qingsong Liu, Wenfei Wu, Longbo Huang, Zhixuan Fang
• Abstract summary: We develop a novel virtual-queue-based online algorithm for online convex optimization (OCO) problems with long-term and time-varying constraints. Our algorithm is the first parameter-free algorithm to simultaneously achieve sublinear dynamic regret and constraint violations.
• Score: 26.473560927031176
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In this paper, we develop a novel virtual-queue-based online algorithm for online convex optimization (OCO) problems with long-term and time-varying constraints and conduct a performance analysis with respect to the dynamic regret and constraint violations. We design a new update rule of dual variables and a new way of incorporating time-varying constraint functions into the dual variables. To the best of our knowledge, our algorithm is the first parameter-free algorithm to simultaneously achieve sublinear dynamic regret and constraint violations. Our proposed algorithm also outperforms the state-of-the-art results in many aspects, e.g., our algorithm does not require the Slater condition. Meanwhile, for a group of practical and widely-studied constrained OCO problems in which the variation of consecutive constraints is smooth enough across time, our algorithm achieves $O(1)$ constraint violations. Furthermore, we extend our algorithm and analysis to the case when the time horizon $T$ is unknown. Finally, numerical experiments are conducted to validate the theoretical guarantees of our algorithm, and some applications of our proposed framework will be outlined.

Related papers

• A Penalty-Based Guardrail Algorithm for Non-Decreasing Optimization with Inequality Constraints [1.5498250598583487]
  Traditional mathematical programming solvers require long computational times to solve constrained minimization problems. We propose a penalty-based guardrail algorithm (PGA) to efficiently solve them.
  arXiv  Detail & Related papers  (2024-05-03T10:37:34Z)
• Online Non-convex Optimization with Long-term Non-convex Constraints [2.033434950296318]
  A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in online manner. The proposed algorithm is applied to tackle a long-term (extreme value) constrained river pollutant source identification problem.
  arXiv  Detail & Related papers  (2023-11-04T15:08:36Z)
• Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints [21.38692458445459]
  This paper studies the problem of online performance optimization of constrained closed-loop control systems. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution.
  arXiv  Detail & Related papers  (2023-04-12T18:37:52Z)
• 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)
• A Constrained Optimization Approach to Bilevel Optimization with Multiple Inner Minima [49.320758794766185]
  We propose a new approach, which convert the bilevel problem to an equivalent constrained optimization, and then the primal-dual algorithm can be used to solve the problem. Such an approach enjoys a few advantages including (a) addresses the multiple inner minima challenge; (b) fully first-order efficiency without Jacobian computations.
  arXiv  Detail & Related papers  (2022-03-01T18:20:01Z)
• 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)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits [129.1029690825929]
  We introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits.
  arXiv  Detail & Related papers  (2020-10-23T09:12:47Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)

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.