Model Predictive Control is Almost Optimal for Restless Bandit

• URL: http://arxiv.org/abs/2410.06307v1
• Date: Tue, 8 Oct 2024 19:34:23 GMT
• Title: Model Predictive Control is Almost Optimal for Restless Bandit
• Authors: Nicolas Gast, Dheeraj Narasimha,
• Abstract summary: We consider the discrete time infinite horizon average reward restless markovian bandit (RMAB) problem. We propose a emphmodel predictive control based non-stationary policy with a rolling computational horizon $tau$. We show that its sub-optimality gap is $O(1/sqrtN)$ in general, and $exp(-Omega(N))$ under a local-stability condition.
• Score: 2.295863158976069
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We consider the discrete time infinite horizon average reward restless markovian bandit (RMAB) problem. We propose a \emph{model predictive control} based non-stationary policy with a rolling computational horizon $\tau$. At each time-slot, this policy solves a $\tau$ horizon linear program whose first control value is kept as a control for the RMAB. Our solution requires minimal assumptions and quantifies the loss in optimality in terms of $\tau$ and the number of arms, $N$. We show that its sub-optimality gap is $O(1/\sqrt{N})$ in general, and $\exp(-\Omega(N))$ under a local-stability condition. Our proof is based on a framework from dynamic control known as \emph{dissipativity}. Our solution easy to implement and performs very well in practice when compared to the state of the art. Further, both our solution and our proof methodology can easily be generalized to more general constrained MDP settings and should thus, be of great interest to the burgeoning RMAB community.

Related papers

• Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems [61.85150061213987]
  We study the generalized low-rank matrix bandit problem, proposed in citelu2021low under the Generalized Linear Model (GLM) framework. To overcome the computational infeasibility and theoretical restrain of existing algorithms, we first propose the G-ESTT framework. We show that G-ESTT can achieve the $tildeO(sqrt(d_1+d_2)3/2Mr3/2T)$ bound of regret while G-ESTS can achineve the $tildeO
  arXiv  Detail & Related papers  (2024-01-14T14:14:19Z)
• Corruption-Robust Offline Reinforcement Learning with General Function Approximation [60.91257031278004]
  We investigate the problem of corruption in offline reinforcement learning (RL) with general function approximation. Our goal is to find a policy that is robust to such corruption and minimizes the suboptimality gap with respect to the optimal policy for the uncorrupted Markov decision processes (MDPs)
  arXiv  Detail & Related papers  (2023-10-23T04:07:26Z)
• Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption [12.471848976031904]
  A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. We propose a general, simulation-based framework, that converts any single-armed policy into a policy for the original $N$-armed problem.
  arXiv  Detail & Related papers  (2023-05-31T21:26:43Z)
• Estimating Optimal Policy Value in General Linear Contextual Bandits [50.008542459050155]
  In many bandit problems, the maximal reward achievable by a policy is often unknown in advance. We consider the problem of estimating the optimal policy value in the sublinear data regime before the optimal policy is even learnable. We present a more practical, computationally efficient algorithm that estimates a problem-dependent upper bound on $V*$.
  arXiv  Detail & Related papers  (2023-02-19T01:09:24Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• Towards Painless Policy Optimization for Constrained MDPs [46.12526917024248]
  We study policy optimization in an infinite horizon, $gamma$-discounted constrained Markov decision process (CMDP) Our objective is to return a policy that achieves large expected reward with a small constraint violation. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms.
  arXiv  Detail & Related papers  (2022-04-11T15:08:09Z)
• Towards Instance-Optimal Offline Reinforcement Learning with Pessimism [34.54294677335518]
  We study the offline reinforcement learning (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown Markov Decision Process (MDP) In this work, we analyze the Adaptive Pessimistic Value Iteration (APVI) algorithm and derive the suboptimality upper bound that nearly matches [ Oleft(sum_h=1Hsum_s_h,a_hdpistar_h(s_h,a_h)sqrtfracmathrmmathrmVar_
  arXiv  Detail & Related papers  (2021-10-17T01:21:52Z)
• 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)
• Naive Exploration is Optimal for Online LQR [49.681825576239355]
  We show that the optimal regret scales as $widetildeTheta(sqrtd_mathbfu2 d_mathbfx T)$, where $T$ is the number of time steps, $d_mathbfu$ is the dimension of the input space, and $d_mathbfx$ is the dimension of the system state. Our lower bounds rule out the possibility of a $mathrmpoly(logT)$-regret algorithm, which had been
  arXiv  Detail & Related papers  (2020-01-27T03:44:54Z)

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.