Batched Stochastic Bandit for Nondegenerate Functions

• URL: http://arxiv.org/abs/2405.05733v2
• Date: Thu, 29 Aug 2024 17:58:35 GMT
• Title: Batched Stochastic Bandit for Nondegenerate Functions
• Authors: Yu Liu, Yunlu Shu, Tianyu Wang,
• Abstract summary: This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally.
• Score: 8.015503209312786
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm, called Geometric Narrowing (GN), whose regret bound is of order $\widetilde{{\mathcal{O}}} ( A_{+}^d \sqrt{T} )$. In addition, GN only needs $\mathcal{O} (\log \log T)$ batches to achieve this regret. We also provide lower bound analysis for this problem. More specifically, we prove that over some (compact) doubling metric space of doubling dimension $d$: 1. For any policy $\pi$, there exists a problem instance on which $\pi$ admits a regret of order ${\Omega} ( A_-^d \sqrt{T})$; 2. No policy can achieve a regret of order $ A_-^d \sqrt{T} $ over all problem instances, using less than $ \Omega ( \log \log T ) $ rounds of communications. Our lower bound analysis shows that the GN algorithm achieves near optimal regret with minimal number of batches.

Related papers

• Logarithmic Regret from Sublinear Hints [76.87432703516942]
  We show that an algorithm can obtain $O(log T)$ regret with just $O(sqrtT)$ hints under a natural query model. We also show that $o(sqrtT)$ hints cannot guarantee better than $Omega(sqrtT)$ regret.
  arXiv  Detail & Related papers  (2021-11-09T16:50:18Z)
• Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization [51.23789922123412]
  We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions admit a "pseudo-1d" structure. We show a lower bound of $min(sqrtdT, T3/4)$ for the regret of any algorithm, where $T$ is the number of rounds. We propose a new algorithm sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively.
  arXiv  Detail & Related papers  (2021-02-15T08:16:51Z)
• Thresholded Lasso Bandit [70.17389393497125]
  Thresholded Lasso bandit is an algorithm that estimates the vector defining the reward function as well as its sparse support. We establish non-asymptotic regret upper bounds scaling as $mathcalO( log d + sqrtT )$ in general, and as $mathcalO( log d + sqrtT )$ under the so-called margin condition.
  arXiv  Detail & Related papers  (2020-10-22T19:14:37Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• $Q$-learning with Logarithmic Regret [60.24952657636464]
  We prove that an optimistic $Q$-learning enjoys a $mathcalOleft(fracSAcdot mathrmpolyleft(Hright)Delta_minlogleft(SATright)right)$ cumulative regret bound, where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, $T$ is the total number of steps, and $Delta_min$ is the minimum sub-optimality gap.
  arXiv  Detail & Related papers  (2020-06-16T13:01:33Z)
• Optimal Contextual Pricing and Extensions [32.152826900874075]
  We give a poly-time algorithm for contextual pricing with $O(d log log T)$ regret which matches the $Omega(d log T)$ lower bound up to the $d log d$ additive factor. These algorithms are based on a novel technique of bounding the value of the Steiner intrinsic of a convex region at various scales.
  arXiv  Detail & Related papers  (2020-03-03T18:46:29Z)
• Logistic Regression Regret: What's the Catch? [3.7311680121118345]
  We derive lower bounds with logarithmic regret under $L_infty$ constraints on the parameters. For $L$ constraints, it is shown that for large enough $d$, the regret remains linear in $d$ but no longer logarithmic in $T$.
  arXiv  Detail & Related papers  (2020-02-07T18:36:39Z)
• Tight Regret Bounds for Noisy Optimization of a Brownian Motion [118.65407541895851]
  We consider the problem of Bayesian optimization of a one-dimensional Brownian motion in which the $T$ adaptively chosen observations are corrupted by Gaussian noise. We show that as the smallest possible expected cumulative regret and the smallest possible expected simple regret scale as $Omega(sigmasqrtT cdot log T)$.
  arXiv  Detail & Related papers  (2020-01-25T14:44:53Z)

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.