Model-Based Reinforcement Learning with Value-Targeted Regression

Alex Ayoub, Zeyu Jia, Csaba Szepesvari, Mengdi Wang, Lin Yang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:463-474, 2020.

Abstract

This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $\mathcal{P}$, a special case of which is when models in $\mathcal{P}$ take the form of linear mixtures: $P_{\theta} = \sum_{i=1}^{d} \theta_{i}P_{i}$. We propose a model based RL algorithm that is based on the optimism principle: In each episode, the set of models that are ‘consistent’ with the data collected is constructed. The criterion of consistency is based on the total squared error that the model incurs on the task of predicting \emph{state values} as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, takes the form $\tilde{\mathcal{O}}(d\sqrt{H^{3}T})$, where $H$, $T$ and $d$ are the horizon, the total number of steps and the dimension of $\theta$, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound $\Omega(\sqrt{HdT})$. For a general model family $\mathcal{P}$, the regret bound is derived based on the Eluder dimension.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-ayoub20a, title = {Model-Based Reinforcement Learning with Value-Targeted Regression}, author = {Ayoub, Alex and Jia, Zeyu and Szepesvari, Csaba and Wang, Mengdi and Yang, Lin}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {463--474}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/ayoub20a/ayoub20a.pdf}, url = { http://proceedings.mlr.press/v119/ayoub20a.html }, abstract = {This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $\mathcal{P}$, a special case of which is when models in $\mathcal{P}$ take the form of linear mixtures: $P_{\theta} = \sum_{i=1}^{d} \theta_{i}P_{i}$. We propose a model based RL algorithm that is based on the optimism principle: In each episode, the set of models that are ‘consistent’ with the data collected is constructed. The criterion of consistency is based on the total squared error that the model incurs on the task of predicting \emph{state values} as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, takes the form $\tilde{\mathcal{O}}(d\sqrt{H^{3}T})$, where $H$, $T$ and $d$ are the horizon, the total number of steps and the dimension of $\theta$, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound $\Omega(\sqrt{HdT})$. For a general model family $\mathcal{P}$, the regret bound is derived based on the Eluder dimension.} }
Endnote
%0 Conference Paper %T Model-Based Reinforcement Learning with Value-Targeted Regression %A Alex Ayoub %A Zeyu Jia %A Csaba Szepesvari %A Mengdi Wang %A Lin Yang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-ayoub20a %I PMLR %P 463--474 %U http://proceedings.mlr.press/v119/ayoub20a.html %V 119 %X This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $\mathcal{P}$, a special case of which is when models in $\mathcal{P}$ take the form of linear mixtures: $P_{\theta} = \sum_{i=1}^{d} \theta_{i}P_{i}$. We propose a model based RL algorithm that is based on the optimism principle: In each episode, the set of models that are ‘consistent’ with the data collected is constructed. The criterion of consistency is based on the total squared error that the model incurs on the task of predicting \emph{state values} as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, takes the form $\tilde{\mathcal{O}}(d\sqrt{H^{3}T})$, where $H$, $T$ and $d$ are the horizon, the total number of steps and the dimension of $\theta$, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound $\Omega(\sqrt{HdT})$. For a general model family $\mathcal{P}$, the regret bound is derived based on the Eluder dimension.
APA
Ayoub, A., Jia, Z., Szepesvari, C., Wang, M. & Yang, L.. (2020). Model-Based Reinforcement Learning with Value-Targeted Regression. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:463-474 Available from http://proceedings.mlr.press/v119/ayoub20a.html .

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