A Sample-Efficient Algorithm for Episodic Finite-Horizon MDP with Constraints

• URL: http://arxiv.org/abs/2009.11348v1
• Date: Wed, 23 Sep 2020 19:30:46 GMT
• Title: A Sample-Efficient Algorithm for Episodic Finite-Horizon MDP with Constraints
• Authors: Krishna C. Kalagarla, Rahul Jain, Pierluigi Nuzzo
• Abstract summary: Constrained Markov Decision Processes (CMDPs) formalize sequential decision-making problems. We propose an online algorithm which leverages the linear programming formulation of finite-horizon CMDP for repeated optimistic planning.
• Score: 8.849815837266977
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Constrained Markov Decision Processes (CMDPs) formalize sequential decision-making problems whose objective is to minimize a cost function while satisfying constraints on various cost functions. In this paper, we consider the setting of episodic fixed-horizon CMDPs. We propose an online algorithm which leverages the linear programming formulation of finite-horizon CMDP for repeated optimistic planning to provide a probably approximately correct (PAC) guarantee on the number of episodes needed to ensure an $\epsilon$-optimal policy, i.e., with resulting objective value within $\epsilon$ of the optimal value and satisfying the constraints within $\epsilon$-tolerance, with probability at least $1-\delta$. The number of episodes needed is shown to be of the order $\tilde{\mathcal{O}}\big(\frac{|S||A|C^{2}H^{2}}{\epsilon^{2}}\log\frac{1}{\delta}\big)$, where $C$ is the upper bound on the number of possible successor states for a state-action pair. Therefore, if $C \ll |S|$, the number of episodes needed have a linear dependence on the state and action space sizes $|S|$ and $|A|$, respectively, and quadratic dependence on the time horizon $H$.

Related papers

• Near Sample-Optimal Reduction-based Policy Learning for Average Reward MDP [58.13930707612128]
  This work considers the sample complexity of obtaining an $varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP) We prove an upper bound of $widetilde O(H varepsilon-3 ln frac1delta)$ samples per state-action pair, where $H := sp(h*)$ is the span of bias of any optimal policy, $varepsilon$ is the accuracy and $delta$ is the failure probability.
  arXiv  Detail & Related papers  (2022-12-01T15:57:58Z)
• Near-Optimal Regret Bounds for Multi-batch Reinforcement Learning [54.806166861456035]
  We study the episodic reinforcement learning (RL) problem modeled by finite-horizon Markov Decision Processes (MDPs) with constraint on the number of batches. We design a computational efficient algorithm to achieve near-optimal regret of $tildeO(sqrtSAH3Kln (1/delta))$tildeO(cdot) hides logarithmic terms of $(S,A,H,K)$ in $K$ episodes. Our technical contribution are two-fold: 1) a near-optimal design scheme to explore
  arXiv  Detail & Related papers  (2022-10-15T09:22:22Z)
• Reward-Mixing MDPs with a Few Latent Contexts are Learnable [75.17357040707347]
  We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs) Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model.
  arXiv  Detail & Related papers  (2022-10-05T22:52:00Z)
• 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)
• Horizon-Free Reinforcement Learning in Polynomial Time: the Power of Stationary Policies [88.75843804630772]
  We design an algorithm that achieves an $Oleft(mathrmpoly(S,A,log K)sqrtKright)$ regret in contrast to existing bounds. Our result relies on a sequence of new structural lemmas establishing the approximation power, stability, and concentration property of stationary policies.
  arXiv  Detail & Related papers  (2022-03-24T08:14:12Z)
• Nearly Minimax Optimal Reward-free Reinforcement Learning [88.75843804630772]
  We study the reward-free reinforcement learning framework, which is particularly suitable for batch reinforcement learning and scenarios where one needs policies for multiple reward functions. We give a new efficient algorithm, textbfStaged textbfSampling + textbfTruncated textbfPlanning (algoname), which interacts with the environment at most $Oleft( fracS2Aepsilon2textpolylogleft(fracSAHepsilon2
  arXiv  Detail & Related papers  (2020-10-12T17:51:19Z)
• Provably Efficient Model-Free Algorithm for MDPs with Peak Constraints [38.2783003051101]
  This paper considers the peak Constrained Markov Decision Process (PCMDP), where the agent chooses the policy to maximize total reward in the finite horizon as well as satisfy constraints at each epoch with probability 1. We propose a model-free algorithm that converts PCMDP problem to an unconstrained problem and a Q-learning based approach is applied.
  arXiv  Detail & Related papers  (2020-03-11T23:23:29Z)

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.