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Fast Rates for Maximum Entropy Exploration
Daniil Tiapkin · Denis Belomestny · Daniele Calandriello · Eric Moulines · Remi Munos · Alexey Naumov · Pierre Perrault · Yunhao Tang · Michal Valko · Pierre Menard

Wed Jul 26 02:00 PM -- 03:30 PM (PDT) @ Exhibit Hall 1 #400
We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Author Information

Daniil Tiapkin (HSE University)
Denis Belomestny (Universitaet Duisburg-Essen)
Daniele Calandriello (DeepMind)
Eric Moulines (Ecole Polytechnique)
Remi Munos (DeepMind)
Alexey Naumov (National Research University Higher School of Economics)
Pierre Perrault (ENS Paris Saclay & Inria)
Yunhao Tang (Google DeepMind)
Michal Valko (Google DeepMind / Inria / MVA)
Pierre Menard (ENS Lyon)

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