Safe Reinforcement Learning in Tensor Reproducing Kernel Hilbert Space
Xiaoyuan Cheng Boli Chen Liz Varga Yukun Hu
This paper delves into the problem of safe reinforcement learning (RL) in a
partially observable environment with the aim of achieving safe-reachability
objectives. In traditional partially observable Markov decision processes
(POMDP), ensuring safety typically involves estimating the belief in latent
states. However, accurately estimating an optimal Bayesian filter in POMDP to
infer latent states from observations in a continuous state space poses a
significant challenge, largely due to the intractable likelihood. To tackle
this issue, we propose a stochastic model-based approach that guarantees RL
safety almost surely in the face of unknown system dynamics and partial
observation environments. We leveraged the Predictive State Representation
(PSR) and Reproducing Kernel Hilbert Space (RKHS) to represent future
multi-step observations analytically, and the results in this context are
provable. Furthermore, we derived essential operators from the kernel Bayes'
rule, enabling the recursive estimation of future observations using various
operators. Under the assumption of \textit{undercompleness}, a polynomial
sample complexity is established for the RL algorithm for the infinite size of
observation and action spaces, ensuring an $\epsilon-$suboptimal safe policy
guarantee.