Improved Regret for Bandit Convex Optimization with Delayed Feedback

• URL: http://arxiv.org/abs/2402.09152v2
• Date: Sun, 23 Jun 2024 15:12:02 GMT
• Title: Improved Regret for Bandit Convex Optimization with Delayed Feedback
• Authors: Yuanyu Wan, Chang Yao, Mingli Song, Lijun Zhang,
• Abstract summary: bandit convex optimization (BCO) with delayed feedback, where only the loss value of the action is revealed under a delay. We develop a novel algorithm, and prove that it enjoys a regret bound of $O(sqrtnT3/4+sqrtdT)$ in general. We show that the proposed algorithm can improve the regret bound to $O((nT)2/3log/3T+dlog T)$ for strongly convex functions.
• Score: 50.46856739179311
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate bandit convex optimization (BCO) with delayed feedback, where only the loss value of the action is revealed under an arbitrary delay. Let $n,T,\bar{d}$ denote the dimensionality, time horizon, and average delay, respectively. Previous studies have achieved an $O(\sqrt{n}T^{3/4}+(n\bar{d})^{1/3}T^{2/3})$ regret bound for this problem, whose delay-independent part matches the regret of the classical non-delayed bandit gradient descent algorithm. However, there is a large gap between its delay-dependent part, i.e., $O((n\bar{d})^{1/3}T^{2/3})$, and an existing $\Omega(\sqrt{\bar{d}T})$ lower bound. In this paper, we illustrate that this gap can be filled in the worst case, where $\bar{d}$ is very close to the maximum delay $d$. Specifically, we first develop a novel algorithm, and prove that it enjoys a regret bound of $O(\sqrt{n}T^{3/4}+\sqrt{dT})$ in general. Compared with the previous result, our regret bound is better for $d=O((n\bar{d})^{2/3}T^{1/3})$, and the delay-dependent part is tight in the worst case. The primary idea is to decouple the joint effect of the delays and the bandit feedback on the regret by carefully incorporating the delayed bandit feedback with a blocking update mechanism. Furthermore, we show that the proposed algorithm can improve the regret bound to $O((nT)^{2/3}\log^{1/3}T+d\log T)$ for strongly convex functions. Finally, if the action sets are unconstrained, we demonstrate that it can be simply extended to achieve an $O(n\sqrt{T\log T}+d\log T)$ regret bound for strongly convex and smooth functions.

Related papers

• Adversarial Combinatorial Bandits with Switching Costs [55.2480439325792]
  We study the problem of adversarial bandit with a switching cost $lambda$ for a switch of each selected arm in each round. We derive lower bounds for the minimax regret and design algorithms to approach them.
  arXiv  Detail & Related papers  (2024-04-02T12:15:37Z)
• Non-stationary Online Convex Optimization with Arbitrary Delays [50.46856739179311]
  This paper investigates the delayed online convex optimization (OCO) in non-stationary environments. We first propose a simple algorithm, namely DOGD, which performs a gradient descent step for each delayed gradient according to their arrival order. We develop an improved algorithm, which reduces those dynamic regret bounds achieved by DOGD to $O(sqrtbardT(P_T+1))$.
  arXiv  Detail & Related papers  (2023-05-20T07:54:07Z)
• Improved High-Probability Regret for Adversarial Bandits with Time-Varying Feedback Graphs [62.52390282012508]
  We study high-probability regret bounds for adversarial $K$-armed bandits with time-varying feedback graphs over $T$ rounds. We develop an algorithm that achieves the optimal regret $widetildemathcalO((sum_t=1Talpha_t)1/2+max_tin[T]alpha_t]$ with high probability. We also develop the first algorithm that achieves the optimal high-probability regret bound for weakly observable graphs.
  arXiv  Detail & Related papers  (2022-10-04T04:36:15Z)
• A Best-of-Both-Worlds Algorithm for Bandits with Delayed Feedback [25.68113242132723]
  We present a modified tuning of the algorithm of Zimmert and Seldin [2020] for adversarial multiarmed bandits with delayed feedback. We simultaneously achieves a near-optimal adversarial regret guarantee in the setting with fixed delays. We also present an extension of the algorithm to the case of arbitrary delays.
  arXiv  Detail & Related papers  (2022-06-29T20:49:45Z)
• Better Best of Both Worlds Bounds for Bandits with Switching Costs [37.71741656687868]
  We study best-of-both-worlds algorithms for bandits with switching cost, recently addressed by Rouyer, Seldin and Cesa-Bianchi, 2021. We introduce a surprisingly simple and effective that simultaneously achieves minimax optimal regret bound of $mathcalO(T2/3)$ in the oblivious adversarial setting.
  arXiv  Detail & Related papers  (2022-06-07T08:22:56Z)
• Scale-Free Adversarial Multi-Armed Bandit with Arbitrary Feedback Delays [21.94728545221709]
  We consider the Scale-Free Adversarial Multi Armed Bandit (MAB) problem with unrestricted feedback delays. textttSFBanker achieves $mathcal O(sqrtK(D+T)L)cdot rm polylog(T, L)$ total regret, where $T$ is the total number of steps and $D$ is the total feedback delay.
  arXiv  Detail & Related papers  (2021-10-26T04:06:51Z)
• 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)
• No Discounted-Regret Learning in Adversarial Bandits with Delays [40.670563413892154]
  We show that the expected discounted ergodic distribution of play converges to the set of coarse correlated equilibrium (CCE) if the algorithms have "no discounted-regret" For a zero-sum game, we show that no discounted-regret is sufficient for the discounted ergodic average of play to converge to the set of Nash equilibria.
  arXiv  Detail & Related papers  (2021-03-08T05:15:31Z)
• Adversarial Dueling Bandits [85.14061196945599]
  We introduce the problem of regret in Adversarial Dueling Bandits. The learner has to repeatedly choose a pair of items and observe only a relative binary win-loss' feedback for this pair. Our main result is an algorithm whose $T$-round regret compared to the emphBorda-winner from a set of $K$ items.
  arXiv  Detail & Related papers  (2020-10-27T19:09:08Z)
• Adapting to Delays and Data in Adversarial Multi-Armed Bandits [7.310043452300736]
  We analyze variants of the Exp3 algorithm that tune their step-size using only information available at the time of the decisions. We obtain regret guarantees that adapt to the observed (rather than the worst-case) sequences of delays and/or losses.
  arXiv  Detail & Related papers  (2020-10-12T20:53:52Z)

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.