Tracking Most Severe Arm Changes in Bandits

• URL: http://arxiv.org/abs/2112.13838v1
• Date: Mon, 27 Dec 2021 18:59:05 GMT
• Title: Tracking Most Severe Arm Changes in Bandits
• Abstract summary: We derive an adaptive procedure that guarantees a dynamic regret of order $tildeO(sqrtT)ll tildeO(sqrtLT)ll tildeO(sqrtT)ll tildeO(sqrtT)ll tildeO(sqrtT)ll tildeO(sqrtT)ll tildeO
• Score: 12.29762518277676
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In bandits with distribution shifts, one aims to automatically detect an unknown number $L$ of changes in reward distribution, and restart exploration when necessary. While this problem remained open for many years, a recent breakthrough of Auer et al. (2018, 2019) provide the first adaptive procedure to guarantee an optimal (dynamic) regret $\sqrt{LT}$, for $T$ rounds, with no knowledge of $L$. However, not all distributional shifts are equally severe, e.g., suppose no best arm switches occur, then we cannot rule out that a regret $O(\sqrt{T})$ may remain possible; in other words, is it possible to achieve dynamic regret that optimally scales only with an unknown number of severe shifts? This unfortunately has remained elusive, despite various attempts (Auer et al., 2019, Foster et al., 2020). We resolve this problem in the case of two-armed bandits: we derive an adaptive procedure that guarantees a dynamic regret of order $\tilde{O}(\sqrt{\tilde{L} T})$, where $\tilde L \ll L$ captures an unknown number of severe best arm changes, i.e., with significant switches in rewards, and which last sufficiently long to actually require a restart. As a consequence, for any number $L$ of distributional shifts outside of these severe shifts, our procedure achieves regret just $\tilde{O}(\sqrt{T})\ll \tilde{O}(\sqrt{LT})$. Finally, we note that our notion of severe shift applies in both classical settings of stochastic switching bandits and of adversarial bandits.

Related papers

• Breaking the Total Variance Barrier: Sharp Sample Complexity for Linear Heteroscedastic Bandits with Fixed Action Set [93.03556214432615]
  In this paper, we revisit the linear bandit problem with heteroscedastic noise, where the action set is prefixed throughout the learning process.<n>We propose a novel variance-adaptive algorithm textttVAEE for large action set, which actively explores actions that maximize the information gain.<n>We establish a nearly matching lower bound for the fixed action set setting indicating that emphharmonic-mean dependent rate is unavoidable.
  arXiv  Detail & Related papers  (2026-07-26T14:24:34Z)
• Near-Optimal Regret for KL-Regularized Multi-Armed Bandits [54.77408659142336]
  We study the statistical efficiency of online learning with respect to KL-regularized objectives.<n>We show that the KL-regularized regret for MABs is $$-independent and scales as $tilde(sqrtKT)$.
  arXiv  Detail & Related papers  (2026-03-02T18:17:33Z)
• Adaptive Smooth Non-Stationary Bandits [0.8158530638728501]
  We study a $K$-armed non-stationary bandit model where rewards change smoothly. We establish the minimax dynamic regret rate generally for all $K,beta,lambda$. We also study the problem of attaining faster gap-dependent regret rates in non-stationary bandits.
  arXiv  Detail & Related papers  (2024-07-11T16:37:15Z)
• Variance-Dependent Regret Bounds for Non-stationary Linear Bandits [52.872628573907434]
  We propose algorithms that utilize the variance of the reward distribution as well as the $B_K$, and show that they can achieve tighter regret upper bounds. We introduce two novel algorithms: Restarted Weighted$textOFUL+$ and Restarted $textSAVE+$. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary linear bandits under different settings.
  arXiv  Detail & Related papers  (2024-03-15T23:36:55Z)
• Discounted Thompson Sampling for Non-Stationary Bandit Problems [13.656518163592349]
  Non-stationary multi-armed bandit (NS-MAB) problems have recently received significant attention. We propose Discounted Thompson Sampling (DS-TS) with Gaussian priors to address both non-stationary settings. Our algorithm passively adapts to changes by incorporating a discounted factor into Thompson Sampling.
  arXiv  Detail & Related papers  (2023-05-18T05:29:52Z)
• Smooth Non-Stationary Bandits [49.19728527803684]
  We study a non-stationary bandits problem where each arm's mean reward sequence can be embedded into a $beta$-H"older function. We show the first separation between the smooth (i.e., $betage 2$) and non-smooth (i.e., $beta=1$) regimes by presenting a policy with $tilde O(k4/5 T3/5)$ regret on any $k$-armed, $2$-H"older instance.
  arXiv  Detail & Related papers  (2023-01-29T06:03:20Z)
• Variance-Aware Sparse Linear Bandits [64.70681598741417]
  Worst-case minimax regret for sparse linear bandits is $widetildeThetaleft(sqrtdTright)$. In the benign setting where there is no noise and the action set is the unit sphere, one can use divide-and-conquer to achieve an $widetildemathcal O(1)$ regret. We develop a general framework that converts any variance-aware linear bandit algorithm to a variance-aware algorithm for sparse linear bandits.
  arXiv  Detail & Related papers  (2022-05-26T15:55:44Z)
• Corralling a Larger Band of Bandits: A Case Study on Switching Regret for Linear Bandits [99.86860277006318]
  We consider the problem of combining and learning over a set of adversarial algorithms with the goal of adaptively tracking the best one on the fly. The CORRAL of Agarwal et al. achieves this goal with a regret overhead of order $widetildeO(sqrtd S T)$ where $M$ is the number of base algorithms and $T$ is the time horizon. Motivated by this issue, we propose a new recipe to corral a larger band of bandit algorithms whose regret overhead has only emphlogarithmic dependence on $M$ as long
  arXiv  Detail & Related papers  (2022-02-12T21:55:44Z)
• A New Look at Dynamic Regret for Non-Stationary Stochastic Bandits [11.918230810566945]
  We study the non-stationary multi-armed bandit problem, where the reward statistics of each arm may change several times during the course of learning. We propose a method that achieves, in $K$-armed bandit problems, a near-optimal $widetilde O(sqrtK N(S+1))$ dynamic regret.
  arXiv  Detail & Related papers  (2022-01-17T17:23:56Z)
• The best of both worlds: stochastic and adversarial episodic MDPs with unknown transition [49.78053380710322]
  We consider the best-of-both-worlds problem for learning an episodic Markov Decision Process through $T$ episodes. Recent work by [Jin and Luo, 2020] achieves this goal when the fixed transition is known. In this work, we resolve this open problem by using the same Follow-the-Regularized-Leader ($textFTRL$) framework together with a set of new techniques.
  arXiv  Detail & Related papers  (2021-06-08T05:46:35Z)
• Online Convex Optimization with Continuous Switching Constraint [78.25064451417082]
  We introduce the problem of online convex optimization with continuous switching constraint. We show that, for strongly convex functions, the regret bound can be improved to $O(log T)$ for $S=Omega(log T)$, and $O(minT/exp(S)+S,T)$ for $S=O(log T)$.
  arXiv  Detail & Related papers  (2021-03-21T11:43:35Z)
• Finding the Stochastic Shortest Path with Low Regret: The Adversarial Cost and Unknown Transition Case [29.99619764839178]
  We make significant progress toward the shortest path problem with adversarial costs and unknown transition. Specifically, we develop algorithms that achieve $widetildeO(sqrtS3A2DT_star K)$ regret for the full-information setting. We are also the first to consider the most challenging combination: bandit feedback with adversarial costs and unknown transition.
  arXiv  Detail & Related papers  (2021-02-10T06:33:04Z)
• Stochastic Bandits with Linear Constraints [69.757694218456]
  We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
  arXiv  Detail & Related papers  (2020-06-17T22:32:19Z)
• Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transition [38.28925339231888]
  We develop the first algorithm with a best-of-both-worlds'' guarantee. It achieves $mathcalO(log T)$ regret when the losses are adversarial. More generally, it achieves $tildemathcalO(sqrtC)$ regret in an intermediate setting.
  arXiv  Detail & Related papers  (2020-06-10T01:59:34Z)

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.