Sample-Optimal Parametric Q-Learning Using Linearly Additive Features

Lin Yang, Mengdi Wang
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6995-7004, 2019.

Abstract

Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process’s probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension $K$ and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is $\epsilon$-optimal from any initial state with high probability using $\widetilde{O}(K/\epsilon^2(1-\gamma)^3)$ sample transitions for arbitrarily large-scale MDP with a discount factor $\gamma\in(0,1)$. A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-yang19b, title = {Sample-Optimal Parametric Q-Learning Using Linearly Additive Features}, author = {Yang, Lin and Wang, Mengdi}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6995--7004}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/yang19b/yang19b.pdf}, url = {https://proceedings.mlr.press/v97/yang19b.html}, abstract = {Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process’s probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension $K$ and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is $\epsilon$-optimal from any initial state with high probability using $\widetilde{O}(K/\epsilon^2(1-\gamma)^3)$ sample transitions for arbitrarily large-scale MDP with a discount factor $\gamma\in(0,1)$. A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).} }
Endnote
%0 Conference Paper %T Sample-Optimal Parametric Q-Learning Using Linearly Additive Features %A Lin Yang %A Mengdi Wang %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-yang19b %I PMLR %P 6995--7004 %U https://proceedings.mlr.press/v97/yang19b.html %V 97 %X Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process’s probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension $K$ and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is $\epsilon$-optimal from any initial state with high probability using $\widetilde{O}(K/\epsilon^2(1-\gamma)^3)$ sample transitions for arbitrarily large-scale MDP with a discount factor $\gamma\in(0,1)$. A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).
APA
Yang, L. & Wang, M.. (2019). Sample-Optimal Parametric Q-Learning Using Linearly Additive Features. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6995-7004 Available from https://proceedings.mlr.press/v97/yang19b.html.

Related Material