Optimal Regularized Online Allocation by Adaptive Re-Solving

• URL: http://arxiv.org/abs/2209.00399v2
• Date: Sun, 16 Jul 2023 02:26:55 GMT
• Title: Optimal Regularized Online Allocation by Adaptive Re-Solving
• Authors: Wanteng Ma and Ying Cao and Danny H.K. Tsang and Dong Xia
• Abstract summary: This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems. Under a strategy of adaptively updating the resource constraints, the proposed framework only requests approximate solutions to the empirical dual problems up to a certain accuracy. Surprisingly, a delicate analysis of the dual objective function enables us to eliminate the notorious log-log factor in regret bound.
• Score: 16.873430173722994
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under a strategy of adaptively updating the resource constraints, the proposed framework only requests approximate solutions to the empirical dual problems up to a certain accuracy and yet delivers an optimal logarithmic regret under a locally second-order growth condition. Surprisingly, a delicate analysis of the dual objective function enables us to eliminate the notorious log-log factor in regret bound. The flexible framework renders renowned and computationally fast algorithms immediately applicable, e.g., dual stochastic gradient descent. Additionally, an infrequent re-solving scheme is proposed, which significantly reduces computational demands without compromising the optimal regret performance. A worst-case square-root regret lower bound is established if the resource constraints are not adaptively updated during dual optimization, which underscores the critical role of adaptive dual variable update. Comprehensive numerical experiments demonstrate the merits of the proposed algorithm framework.

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)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Distributed Online Non-convex Optimization with Composite Regret [31.53784277195043]
  We propose a novel composite regret with a new network regret for distributed online general bounds losses. To our knowledge, is the first regret bound for distributed online nonlinear learning.
  arXiv  Detail & Related papers  (2022-09-21T04:16:33Z)
• Algorithm for Constrained Markov Decision Process with Linear Convergence [55.41644538483948]
  An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs. A new dual approach is proposed with the integration of two ingredients: entropy regularized policy and Vaidya's dual. The proposed approach is shown to converge (with linear rate) to the global optimum.
  arXiv  Detail & Related papers  (2022-06-03T16:26:38Z)
• 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)
• Online Allocation with Two-sided Resource Constraints [44.5635910908944]
  We consider an online allocation problem subject to lower and upper resource constraints, where the requests arrive sequentially. We propose a new algorithm that obtains $1-O(fracepsilonalpha-epsilon)$ -competitive ratio for the offline problems that know the entire requests ahead of time.
  arXiv  Detail & Related papers  (2021-12-28T02:21:06Z)
• 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)
• Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems [1.6709415233613623]
  This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set. We also introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.
  arXiv  Detail & Related papers  (2021-02-18T01:49:06Z)
• Resource Allocation via Model-Free Deep Learning in Free Space Optical Communications [119.81868223344173]
  The paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. Under this framework, we propose two algorithms that solve FSO resource allocation problems.
  arXiv  Detail & Related papers  (2020-07-27T17:38:51Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Simplified Swarm Optimization for Bi-Objection Active Reliability Redundancy Allocation Problems [1.5990720051907859]
  The reliability redundancy allocation problem (RRAP) is a well-known problem in system design, development, and management. In this study, a bi-objective RRAP is formulated by changing the cost constraint as a new goal. To solve the proposed problem, a new simplified swarm optimization (SSO) with a penalty function, a real one-type solution structure, a number-based self-adaptive new update mechanism, a constrained non-dominated solution selection, and a new pBest replacement policy is developed.
  arXiv  Detail & Related papers  (2020-06-17T13:15:44Z)

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.