Online Convex Optimization with Memory and Limited Predictions

• URL: http://arxiv.org/abs/2410.23574v1
• Date: Thu, 31 Oct 2024 02:33:47 GMT
• Title: Online Convex Optimization with Memory and Limited Predictions
• Authors: Lintao Ye, Zhengmiao Wang, Zhi-Wei Liu, Ming Chi, Xiaoling Wang, Housheng Su,
• Abstract summary: We study the problem of online convex optimization with memory and predictions over a horizon $T$. We propose an algorithm to solve this problem and show that the dynamic regret of the algorithm decays exponentially with the prediction window length.
• Score: 19.7248150754102
• License:
• Abstract: We study the problem of online convex optimization with memory and predictions over a horizon $T$. At each time step, a decision maker is given some limited predictions of the cost functions from a finite window of future time steps, i.e., values of the cost function at certain decision points in the future. The decision maker then chooses an action and incurs a cost given by a convex function that depends on the actions chosen in the past. We propose an algorithm to solve this problem and show that the dynamic regret of the algorithm decays exponentially with the prediction window length. Our algorithm contains two general subroutines that work for wider classes of problems. The first subroutine can solve general online convex optimization with memory and bandit feedback with $\sqrt{T}$-dynamic regret with respect to $T$. The second subroutine is a zeroth-order method that can be used to solve general convex optimization problems with a linear convergence rate that matches the best achievable rate of first-order methods for convex optimization. The key to our algorithm design and analysis is the use of truncated Gaussian smoothing when querying the decision points for obtaining the predictions. We complement our theoretical results using numerical experiments.

Related papers

• Second Order Methods for Bandit Optimization and Control [34.51425758864638]
  We show that our algorithm achieves optimal (in terms of terms of convex functions that we call $kappa$-2020) regret bounds for a large class of convex functions. We also investigate the adaptation of our second-order bandit algorithm to online convex optimization with memory.
  arXiv  Detail & Related papers  (2024-02-14T04:03:38Z)
• First-Order Dynamic Optimization for Streaming Convex Costs [0.0]
  We develop an approach to track the optimal solution with a bounded error. Our algorithm is executed only by using the first-order derivatives of the cost function.
  arXiv  Detail & Related papers  (2023-10-11T22:41:00Z)
• An Algorithm with Optimal Dimension-Dependence for Zero-Order Nonsmooth Nonconvex Stochastic Optimization [37.300102993926046]
  We study the complexity of producing neither smooth nor convex points of Lipschitz objectives which are possibly using only zero-order evaluations. Our analysis is based on a simple yet powerful. Goldstein-subdifferential set, which allows recent advancements in. nonsmooth non optimization.
  arXiv  Detail & Related papers  (2023-07-10T11:56:04Z)
• Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability [59.81339109121384]
  We study the $K$ contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes emphpreference-based feedback suggesting that one decision was better than the other. We provide a new algorithm that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works.
  arXiv  Detail & Related papers  (2021-11-24T07:14:57Z)
• Recent Theoretical Advances in Non-Convex Optimization [56.88981258425256]
  Motivated by recent increased interest in analysis of optimization algorithms for non- optimization in deep networks and other problems in data, we give an overview of recent results of theoretical optimization algorithms for non- optimization.
  arXiv  Detail & Related papers  (2020-12-11T08:28:51Z)
• Divide and Learn: A Divide and Conquer Approach for Predict+Optimize [50.03608569227359]
  The predict+optimize problem combines machine learning ofproblem coefficients with a optimization prob-lem that uses the predicted coefficients. We show how to directlyexpress the loss of the optimization problem in terms of thepredicted coefficients as a piece-wise linear function. We propose a novel divide and algorithm to tackle optimization problems without this restriction and predict itscoefficients using the optimization loss.
  arXiv  Detail & Related papers  (2020-12-04T00:26:56Z)
• Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits [99.70167985955352]
  We study the problem of zero-order optimization of a strongly convex function. We consider a randomized approximation of the projected gradient descent algorithm. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters.
  arXiv  Detail & Related papers  (2020-06-14T10:42:23Z)
• 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)
• Private Stochastic Convex Optimization: Optimal Rates in Linear Time [74.47681868973598]
  We study the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. has established the optimal bound on the excess population loss achievable given $n$ samples. We describe two new techniques for deriving convex optimization algorithms both achieving the optimal bound on excess loss and using $O(minn, n2/d)$ gradient computations.
  arXiv  Detail & Related papers  (2020-05-10T19:52:03Z)
• A New Randomized Primal-Dual Algorithm for Convex Optimization with Optimal Last Iterate Rates [16.54912614895861]
  We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems. We prove that our algorithm achieves optimal convergence rates in two cases: general convexity and strong convexity. Our results show that the proposed method has encouraging performance on different experiments.
  arXiv  Detail & Related papers  (2020-03-03T03:59:26Z)

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.