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Poster
Learning Near Optimal Policies with Low Inherent Bellman Error
Andrea Zanette · Alessandro Lazaric · Mykel Kochenderfer · Emma Brunskill

Wed Jul 15 11:00 AM -- 11:45 AM & Wed Jul 15 10:00 PM -- 10:45 PM (PDT) @
in Poster Session 25 »
We study the exploration problem with approximate linear action-value functions in episodic reinforcement learning under the notion of low inherent Bellman error, a condition normally employed to show convergence of approximate value iteration. First we relate this condition to other common frameworks and show that it is strictly more general than the low rank (or linear) MDP assumption of prior work. Second we provide an algorithm with a high probability regret bound $\widetilde O(\sum_{t=1}^H d_t \sqrt{K} + \sum_{t=1}^H \sqrt{d_t} \IBE K)$ where $H$ is the horizon, $K$ is the number of episodes, $\IBE$ is the value if the inherent Bellman error and $d_t$ is the feature dimension at timestep $t$. In addition, we show that the result is unimprovable beyond constants and logs by showing a matching lower bound. This has two important consequences: 1) it shows that exploration is possible using only \emph{batch assumptions} with an algorithm that achieves the optimal statistical rate for the setting we consider, which is more general than prior work on low-rank MDPs 2) the lack of closedness (measured by the inherent Bellman error) is only amplified by $\sqrt{d_t}$ despite working in the online setting. Finally, the algorithm reduces to the celebrated \textsc{LinUCB} when $H=1$ but with a different choice of the exploration parameter that allows handling misspecified contextual linear bandits. While computational tractability questions remain open for the MDP setting, this enriches the class of MDPs with a linear representation for the action-value function where statistically efficient reinforcement learning is possible.
Keywords: Reinforcement Learning · Reinforcement Learning Theory · Reinforcement Learning - Theory

Author Information

Andrea Zanette (Stanford University)
Alessandro Lazaric (Facebook AI Research)
Mykel Kochenderfer (Stanford University)
Emma Brunskill (Stanford University)
Emma Brunskill

Emma Brunskill is an associate tenured professor in the Computer Science Department at Stanford University. Brunskill’s lab aims to create AI systems that learn from few samples to robustly make good decisions and is part of the Stanford AI Lab, the Stanford Statistical ML group, and AI Safety @Stanford. Brunskill has received a NSF CAREER award, Office of Naval Research Young Investigator Award, a Microsoft Faculty Fellow award and an alumni impact award from the computer science and engineering department at the University of Washington. Brunskill and her lab have received multiple best paper nominations and awards both for their AI and machine learning work (UAI best paper, Reinforcement Learning and Decision Making Symposium best paper twice) and for their work in Ai of education (Intelligent Tutoring Systems Conference, Educational Data Mining conference x3, CHI).

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