Towards painless policy optimization for constrained MDPs

Arushi Jain, Sharan Vaswani, Reza Babanezhad, Csaba Szepesvári, Doina Precup
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:895-905, 2022.

Abstract

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 consider the online setting with linear function approximation and assume global access to the corresponding features. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms in terms of their primal and dual regret on online linear optimization problems. We instantiate this framework to use coin-betting algorithms and propose the \textbf{Coin Betting Politex (CBP)} algorithm. Assuming that the action-value functions are $\epsilon_{\text{\tiny{b}}}$-close to the span of the $d$-dimensional state-action features and no sampling errors, we prove that $T$ iterations of CBP result in an $O\left(\frac{1}{(1 - \gamma)^3 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{(1 - \gamma)^2} \right)$ reward sub-optimality and an $O\left(\frac{1}{(1 - \gamma)^2 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{1 - \gamma} \right)$ constraint violation. Importantly, unlike gradient descent-ascent and other recent methods, CBP does not require extensive hyperparameter tuning. Via experiments on synthetic and Cartpole environments, we demonstrate the effectiveness and robustness of CBP.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-jain22a, title = {Towards painless policy optimization for constrained {MDP}s}, author = {Jain, Arushi and Vaswani, Sharan and Babanezhad, Reza and Szepesv\'ari, Csaba and Precup, Doina}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {895--905}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/jain22a/jain22a.pdf}, url = {https://proceedings.mlr.press/v180/jain22a.html}, abstract = {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 consider the online setting with linear function approximation and assume global access to the corresponding features. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms in terms of their primal and dual regret on online linear optimization problems. We instantiate this framework to use coin-betting algorithms and propose the \textbf{Coin Betting Politex (CBP)} algorithm. Assuming that the action-value functions are $\epsilon_{\text{\tiny{b}}}$-close to the span of the $d$-dimensional state-action features and no sampling errors, we prove that $T$ iterations of CBP result in an $O\left(\frac{1}{(1 - \gamma)^3 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{(1 - \gamma)^2} \right)$ reward sub-optimality and an $O\left(\frac{1}{(1 - \gamma)^2 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{1 - \gamma} \right)$ constraint violation. Importantly, unlike gradient descent-ascent and other recent methods, CBP does not require extensive hyperparameter tuning. Via experiments on synthetic and Cartpole environments, we demonstrate the effectiveness and robustness of CBP.} }
Endnote
%0 Conference Paper %T Towards painless policy optimization for constrained MDPs %A Arushi Jain %A Sharan Vaswani %A Reza Babanezhad %A Csaba Szepesvári %A Doina Precup %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-jain22a %I PMLR %P 895--905 %U https://proceedings.mlr.press/v180/jain22a.html %V 180 %X 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 consider the online setting with linear function approximation and assume global access to the corresponding features. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms in terms of their primal and dual regret on online linear optimization problems. We instantiate this framework to use coin-betting algorithms and propose the \textbf{Coin Betting Politex (CBP)} algorithm. Assuming that the action-value functions are $\epsilon_{\text{\tiny{b}}}$-close to the span of the $d$-dimensional state-action features and no sampling errors, we prove that $T$ iterations of CBP result in an $O\left(\frac{1}{(1 - \gamma)^3 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{(1 - \gamma)^2} \right)$ reward sub-optimality and an $O\left(\frac{1}{(1 - \gamma)^2 \sqrt{T}} + \frac{\epsilon_{\text{\tiny{b}}} \sqrt{d}}{1 - \gamma} \right)$ constraint violation. Importantly, unlike gradient descent-ascent and other recent methods, CBP does not require extensive hyperparameter tuning. Via experiments on synthetic and Cartpole environments, we demonstrate the effectiveness and robustness of CBP.
APA
Jain, A., Vaswani, S., Babanezhad, R., Szepesvári, C. & Precup, D.. (2022). Towards painless policy optimization for constrained MDPs. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:895-905 Available from https://proceedings.mlr.press/v180/jain22a.html.

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