Reinforcement learning (RL) [1] studies the problem of learning in sequential decision-making problems where the dynamics of the environment is unknown, but can be learnt by performing actions andobserving their outcome inanonline fashion. Asample-efficient RLagent must trade off the explorationneeded to collect information about the environment, and theexploitation of the experience gathered so far to gain as much reward as possible.

This is an excellent theoretical contribution. The analysis is quite heavy and has many subtleties. I do not have enough time to read the appended proofs; also, the subject of the paper is not in my area of research. The comments below are based on the impression I got after reading carefully the first 8 pages of the paper and glancing through the rest in the supplementary file. Summary: This paper is about reinforcement learning in weakly-communicating MDP under the average-reward criterion.

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). In this paper, we introduce TUCRL, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S c$ communicating states, $A$ actions and $\Gamma c \leq S c$ possible communicating next states, we derive a $O(D c \sqrt{\Gamma c S c A T}) regret bound, where $D c$ is the diameter (i.e., the length of the longest shortest path between any two states) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP.

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This results in weakly-communicating or multi-chain MDPs. In this paper, we introduce TUCRL, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^c$ communicating states, $A$ actions and $\Gamma^c \leq S^c$ possible communicating next states, we derive a $O(D^c \sqrt{\Gamma^c S^c A T}) regret bound, where $D^c$ is the diameter (i.e., the length of the longest shortest path between any two states) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art.

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This results in weakly-communicating or multi-chain MDPs. In this paper, we introduce TUCRL, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^c$ communicating states, $A$ actions and $\Gamma^c \leq S^c$ possible communicating next states, we derive a $O(D^c \sqrt{\Gamma^c S^c A T}) regret bound, where $D^c$ is the diameter (i.e., the length of the longest shortest path between any two states) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art.

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this paper, we introduce \tucrl, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^{\texttt{C}}$ communicating states, $A$ actions and $\Gamma^{\texttt{C}} \leq S^{\texttt{C}}$ possible communicating next states, we derive a $\widetilde{O}(D^{\texttt{C}} \sqrt{\Gamma^{\texttt{C}} S^{\texttt{C}} AT})$ regret bound, where $D^{\texttt{C}}$ is the diameter (i.e., the longest shortest path) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art.