Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation

• URL: http://arxiv.org/abs/2507.04133v1
• Date: Sat, 05 Jul 2025 19:08:11 GMT
• Title: Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation
• Authors: Harsh Shah, Purna Chandrasekhar, Rahul Vaze,
• Abstract summary: When the switching cost is linear, online algorithms with optimal order-wise competitive ratios are derived for the frugal setting.<n>When the gradient information is noisy, an online algorithm whose competitive ratio grows quadratically with the noise magnitude is derived.
• Score: 9.174655018861504
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Online convex optimization with switching cost is considered under the frugal information setting where at time $t$, before action $x_t$ is taken, only a single function evaluation and a single gradient is available at the previously chosen action $x_{t-1}$ for either the current cost function $f_t$ or the most recent cost function $f_{t-1}$. When the switching cost is linear, online algorithms with optimal order-wise competitive ratios are derived for the frugal setting. When the gradient information is noisy, an online algorithm whose competitive ratio grows quadratically with the noise magnitude is derived.

Related papers

• Projection-free Algorithms for Online Convex Optimization with Adversarial Constraints [10.047668792033033]
  We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints.<n>In this problem, after selecting a feasible action from the convex decision set $X,$ a convex constraint function is revealed alongside the cost function in each round.<n>We propose a *projection-free* online policy which makes a single call to a Linear Program (LP) solver per round.
  arXiv  Detail & Related papers  (2025-01-28T13:04:32Z)
• Optimal Decentralized Smoothed Online Convex Optimization [9.449153668916098]
  We study the multi-agent Smoothed Online Convex Optimization (SOCO) problem, where $N$ agents interact through a communication graph.<n>We propose the first truly decentralized algorithm ACORD for multi-agent SOCO that provably exhibits optimality.<n>Our results hold even when the communication graph changes arbitrarily and adaptively over time.
  arXiv  Detail & Related papers  (2024-11-13T05:59:04Z)
• Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity [50.25258834153574]
  We focus on the class of (strongly) convex $(L0)$-smooth functions and derive new convergence guarantees for several existing methods.<n>In particular, we derive improved convergence rates for Gradient Descent with smoothnessed Gradient Clipping and for Gradient Descent with Polyak Stepsizes.
  arXiv  Detail & Related papers  (2024-09-23T13:11:37Z)
• Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path [80.60592344361073]
  We study the Shortest Path (SSP) problem with a linear mixture transition kernel. An agent repeatedly interacts with a environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the iteration cost function or an upper bound of the expected length for the optimal policy.
  arXiv  Detail & Related papers  (2024-02-14T07:52:00Z)
• Online Convex Optimization with Switching Cost and Delayed Gradients [7.903539618132858]
  An online algorithm can choose its action using only gradient information about the previous objective function. We show that the competitive ratio for the OCO problem with quadratic switching cost is at most $4(L + 5) + frac16(L + 5)mu$. We conclude that the optimal competitive ratio for the quadratic and linear switching costs are fundamentally different in the limited information setting.
  arXiv  Detail & Related papers  (2023-10-18T11:06:06Z)
• 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)
• 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)
• Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion [56.92236659731376]
  We present new algorithms for optimizing non-known, non-smooth objectives based on a novel analysis technique. For deterministic second-order smooth objectives, applying advanced optimistic online learning techniques enables a new $O(delta0.5) all$ to recover optimal or best-known results.
  arXiv  Detail & Related papers  (2023-02-07T22:09:20Z)
• Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor [68.17855675511602]
  We investigate an online prediction strategy named as Discounted-Normal-Predictor (Kapralov and Panigrahy, 2010) for smoothed online convex optimization (SOCO) We show that the proposed algorithm can minimize the adaptive regret with switching cost in every interval.
  arXiv  Detail & Related papers  (2022-05-02T08:48:22Z)
• 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)
• Revisiting Smoothed Online Learning [70.09792747315323]
  We investigate the problem of smoothed online learning, in which the online learner suffers both a hitting cost and a switching cost. To bound the competitive ratio, we assume the hitting cost is known to the learner in each round, and investigate the greedy algorithm which simply minimizes the weighted sum of the hitting cost and the switching cost.
  arXiv  Detail & Related papers  (2021-02-13T14:15:55Z)
• Gradient Free Minimax Optimization: Variance Reduction and Faster Convergence [120.9336529957224]
  In this paper, we denote the non-strongly setting on the magnitude of a gradient-free minimax optimization problem. We show that a novel zeroth-order variance reduced descent algorithm achieves the best known query complexity.
  arXiv  Detail & Related papers  (2020-06-16T17:55:46Z)

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.