Online Learning for Approximately-Convex Functions with Long-term Adversarial Constraints

• URL: http://arxiv.org/abs/2508.16992v1
• Date: Sat, 23 Aug 2025 11:21:24 GMT
• Title: Online Learning for Approximately-Convex Functions with Long-term Adversarial Constraints
• Authors: Dhruv Sarkar, Samrat Mukhopadhyay, Abhishek Sinha,
• Abstract summary: We study an online learning problem with long-term budget constraints in the adversarial setting.<n>In this problem, at each round $t$, a learner selects an action from a convex set, after which an adversary reveals a cost function.<n>Our approach yields an efficient solution for the $textttAdversas$ problem with improved guarantees.
• Score: 8.314956969778692
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study an online learning problem with long-term budget constraints in the adversarial setting. In this problem, at each round $t$, the learner selects an action from a convex decision set, after which the adversary reveals a cost function $f_t$ and a resource consumption function $g_t$. The cost and consumption functions are assumed to be $\alpha$-approximately convex - a broad class that generalizes convexity and encompasses many common non-convex optimization problems, including DR-submodular maximization, Online Vertex Cover, and Regularized Phase Retrieval. The goal is to design an online algorithm that minimizes cumulative cost over a horizon of length $T$ while approximately satisfying a long-term budget constraint of $B_T$. We propose an efficient first-order online algorithm that guarantees $O(\sqrt{T})$ $\alpha$-regret against the optimal fixed feasible benchmark while consuming at most $O(B_T \log T)+ \tilde{O}(\sqrt{T})$ resources in both full-information and bandit feedback settings. In the bandit feedback setting, our approach yields an efficient solution for the $\texttt{Adversarial Bandits with Knapsacks}$ problem with improved guarantees. We also prove matching lower bounds, demonstrating the tightness of our results. Finally, we characterize the class of $\alpha$-approximately convex functions and show that our results apply to a broad family of problems.

Related papers

• Beyond $\tilde{O}(\sqrt{T})$ Constraint Violation for Online Convex Optimization with Adversarial Constraints [16.99491218081617]
  We revisit the Online Convex Optimization problem with adversarial constraints.<n>We propose an online policy that achieves $tildeO(sqrtdT+ Tbeta)$ regret and $tildeO(dT1-beta)$ CCV.
  arXiv  Detail & Related papers  (2025-05-10T17:23:10Z)
• 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)
• An Optimistic Algorithm for Online Convex Optimization with Adversarial Constraints [55.2480439325792]
  We study Online Convex Optimization (OCO) with adversarial constraints.<n>We focus on a setting where the algorithm has access to predictions of the loss and constraint functions.<n>Our results show that we can improve the current best bounds of $ O(sqrtT) $ regret and $ tildeO(sqrtT) $ cumulative constraint violations.
  arXiv  Detail & Related papers  (2024-12-11T03:06:42Z)
• 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)
• Optimal Algorithms for Online Convex Optimization with Adversarial Constraints [16.99491218081617]
  In COCO, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. We show that an online policy can simultaneously achieve $O(sqrtT)$ regret and $tildeO(sqrtT)$ CCV without any restrictive assumptions.
  arXiv  Detail & Related papers  (2023-10-29T09:55:41Z)
• 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)
• Efficient Online-Bandit Strategies for Minimax Learning Problems [21.300877551771197]
  Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning or minimization with non-standard aggregated losses. More specifically, these problems are convex-linear problems where the learning is carried out over the model parameters $winmathcalW$ and over the empirical distribution $pinmathcalK$ of the training set. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm.
  arXiv  Detail & Related papers  (2021-05-28T16:01:42Z)
• Nearly Optimal Regret for Learning Adversarial MDPs with Linear Function Approximation [92.3161051419884]
  We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback. We show that it can achieve $tildeO(dHsqrtT)$ regret, where $H$ is the length of the episode. We also prove a matching lower bound of $tildeOmega(dHsqrtT)$ up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-02-17T18:54:08Z)
• Lazy OCO: Online Convex Optimization on a Switching Budget [34.936641201844054]
  We study a variant of online convex optimization where the player is permitted to switch decisions at most $S$ times in expectation throughout $T$ rounds. Similar problems have been addressed in prior work for the discrete decision set setting, and more recently in the continuous setting but only with an adaptive adversary.
  arXiv  Detail & Related papers  (2021-02-07T14:47:19Z)
• Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions [53.77572276969548]
  We show that the C$2$UCB algorithm has the optimal regret bound $tildeO(dsqrtkT + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C$2$UCB algorithm.
  arXiv  Detail & Related papers  (2021-01-20T04:29:18Z)
• Maximizing Determinants under Matroid Constraints [69.25768526213689]
  We study the problem of finding a basis $S$ of $M$ such that $det(sum_i in Sv_i v_i v_itop)$ is maximized. This problem appears in a diverse set of areas such as experimental design, fair allocation of goods, network design, and machine learning.
  arXiv  Detail & Related papers  (2020-04-16T19:16:38Z)

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.