Research Post

Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes


We study reinforcement learning (RL) with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model (Jia et al., 2020; Ayoub et al., 2020; Zhou et al., 2020) and the learning agent has access to either an integration or a sampling oracle of the individual basis kernels. We propose a new Bernstein-type concentration inequality for self-normalized martingales for linear bandit problems with bounded noise. Based on the new inequality, we propose a new, computationally efficient algorithm with linear function approximation named UCRL-VTR+ for the aforementioned linear mixture MDPs in the episodic undiscounted setting. We show that UCRL-VTR+ attains an Õ (dHT‾‾√) regret where d is the dimension of feature mapping, H is the length of the episode and T is the number of interactions with the MDP. We also prove a matching lower bound Ω(dHT‾‾√) for this setting, which shows that UCRL-VTR+ is minimax optimal up to logarithmic factors. In addition, we propose the UCLK+ algorithm for the same family of MDPs under discounting and show that it attains an Õ (dT‾‾√/(1−γ)1.5) regret, where γ∈[0,1) is the discount factor. Our upper bound matches the lower bound Ω(dT‾‾√/(1−γ)1.5) proved by Zhou et al. (2020) up to logarithmic factors, suggesting that UCLK+ is nearly minimax optimal. To the best of our knowledge, these are the first computationally efficient, nearly minimax optimal algorithms for RL with linear function approximation.

Latest Research Papers

Connect with the community

Get involved in Alberta's growing AI ecosystem! Speaker, sponsorship, and letter of support requests welcome.

Explore training and advanced education

Curious about study options under one of our researchers? Want more information on training opportunities?

Harness the potential of artificial intelligence

Let us know about your goals and challenges for AI adoption in your business. Our Investments & Partnerships team will be in touch shortly!