# Bounds on Sample Size for Policy Evaluation in Markov Environments

@article{Peshkin2001BoundsOS, title={Bounds on Sample Size for Policy Evaluation in Markov Environments}, author={Leonid Peshkin and Sayan Mukherjee}, journal={ArXiv}, year={2001}, volume={cs.LG/0105027} }

Reinforcement learning means finding the optimal course of action in Markovian environments without knowledge of the environment's dynamics. Stochastic optimization algorithms used in the field rely on estimates of the value of a policy. Typically, the value of a policy is estimated from results of simulating that very policy in the environment. This approach requires a large amount of simulation as different points in the policy space are considered. In this paper, we develop value estimators…

## 23 Citations

### Learning from Scarce Experience

- Computer ScienceICML
- 2002

A family of algorithms based on likelihood ratio estimation that use data gathered when executing one policy (or collection of policies) to estimate the value of a different policy and show positive empirical results and provide the sample complexity bound.

### PAC bounds for simulation-based optimization of Markov decision processes

- Mathematics, Computer Science2007 46th IEEE Conference on Decision and Control
- 2007

An estimate is obtained for the value function of a Markov decision process, which assigns to each policy its expected discounted reward, and a framework to obtain an e-optimal policy from simulation is proposed.

### Simulation-based optimization of Markov decision processes: An empirical process theory approach

- MathematicsAutom.
- 2010

### Simulation-based Uniform Value Function Estimates of Markov Decision Processes

- MathematicsSIAM J. Control. Optim.
- 2006

Borders on the number of runs needed for the uniform convergence of the empirical average to the expected reward for a class of policies are derived, in terms of the Vapnik-Chervonenkis or P-dimension of the policy class.

### Policy Improvement for POMDPs Using Normalized Importance Sampling

- MathematicsUAI
- 2001

A new method for estimating the expected return of a POMDP from experience that is motivated from function-approximation and importance sampling points-of-view, which has low variance and the bias is often irrelevant when the estimator is used for pair-wise comparisons.

### Balanced Importance Sampling Estimation

- Mathematics, Computer Science
- 2006

This paper introduces the family of balanced importance sampling estimators, which prove their consistency and demonstrate empirically their superiority over the classical counterparts.

### Balanced Importance Sampling Estimation

- Mathematics, Computer Science
- 2006

This paper introduces the family of balanced importance sampling estimators, which prove their consistency and demonstrate empirically their superiority over the classical counterparts.

### Importance sampling for reinforcement learning with multiple objectives

- Computer Science
- 2001

This thesis considers three complications that arise from applying reinforcement learning to a real-world application, and employs importance sampling (likelihood ratios) to achieve good performance in partially observable Markov decision processes with few data.

### Representation of a State Value Function No Yes Representation No Simple DP Value Function of a Policy Yes Policy Search Hybrid

- Computer Science
- 2004

A survey of policy search algorithms in reinforcement learning is presented, examining practical applications, future trends and other issues that pertain to current day policy search techniques.

### Integrated Common Sense Learning and Planning in POMDPs

- Computer ScienceJ. Mach. Learn. Res.
- 2016

The results essentially establish that the possession of a suitable exploration policy for collecting the necessary examples is the fundamental obstacle to learning to act in such environments.

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