Timezone: »

Oral
From Dirichlet to Rubin: Optimistic Exploration in RL without Bonuses
Daniil Tiapkin · Denis Belomestny · Eric Moulines · Alexey Naumov · Sergey Samsonov · Yunhao Tang · Michal Valko · Pierre Menard

Thu Jul 21 12:30 PM -- 12:50 PM (PDT) @ Room 309
We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. 2012 for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order $\widetilde{\mathcal{O}}(\sqrt{H^3SAT})$ where $H$ is the length of one episode, $S$ is the number of states, $A$ the number of actions, $T$ the number of episodes, that matches the lower-bound of $\Omega(\sqrt{H^3SAT})$ up to poly-$\log$ terms in $H,S,A,T$ for a large enough $T$. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon $H$ (and $S$) \textit{without the need of an involved Bernstein-like bonus or noise.} Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin,1981).

#### Author Information

##### Michal Valko (DeepMind / Inria / ENS Paris-Saclay)

Michal is a machine learning scientist in DeepMind Paris, tenured researcher at Inria, and the lecturer of the master course Graphs in Machine Learning at l'ENS Paris-Saclay. Michal is primarily interested in designing algorithms that would require as little human supervision as possible. This means 1) reducing the “intelligence” that humans need to input into the system and 2) minimizing the data that humans need to spend inspecting, classifying, or “tuning” the algorithms. That is why he is working on methods and settings that are able to deal with minimal feedback, such as deep reinforcement learning, bandit algorithms, or self-supervised learning. Michal is actively working on represenation learning and building worlds models. He is also working on deep (reinforcement) learning algorithm that have some theoretical underpinning. He has also worked on sequential algorithms with structured decisions where exploiting the structure leads to provably faster learning. He received his Ph.D. in 2011 from the University of Pittsburgh under the supervision of Miloš Hauskrecht and after was a postdoc of Rémi Munos before taking a permanent position at Inria in 2012.