DeepAI AI Chat
Log In Sign Up

Reinforcement Learning in Linear MDPs: Constant Regret and Representation Selection

10/27/2021
by   Matteo Papini, et al.
12

We study the role of the representation of state-action value functions in regret minimization in finite-horizon Markov Decision Processes (MDPs) with linear structure. We first derive a necessary condition on the representation, called universally spanning optimal features (UNISOFT), to achieve constant regret in any MDP with linear reward function. This result encompasses the well-known settings of low-rank MDPs and, more generally, zero inherent Bellman error (also known as the Bellman closure assumption). We then demonstrate that this condition is also sufficient for these classes of problems by deriving a constant regret bound for two optimistic algorithms (LSVI-UCB and ELEANOR). Finally, we propose an algorithm for representation selection and we prove that it achieves constant regret when one of the given representations, or a suitable combination of them, satisfies the UNISOFT condition.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/31/2022

Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints

We study regret minimization for infinite-horizon average-reward Markov ...
02/29/2020

Learning Near Optimal Policies with Low Inherent Bellman Error

We study the exploration problem with approximate linear action-value fu...
10/15/2019

Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes

Model-free reinforcement learning is known to be memory and computation ...
02/15/2021

Causal Markov Decision Processes: Learning Good Interventions Efficiently

We introduce causal Markov Decision Processes (C-MDPs), a new formalism ...
02/09/2021

RL for Latent MDPs: Regret Guarantees and a Lower Bound

In this work, we consider the regret minimization problem for reinforcem...
09/09/2020

Improved Exploration in Factored Average-Reward MDPs

We consider a regret minimization task under the average-reward criterio...
07/22/2022

Optimism in Face of a Context: Regret Guarantees for Stochastic Contextual MDP

We present regret minimization algorithms for stochastic contextual MDPs...