  This paper addresses the problem of maintaining safety during training in
Reinforcement Learning (RL), such that the safety constraint violations are
bounded at any point during learning. In a variety of RL applications the
safety of the agent is particularly important, e.g. autonomous platforms or
robots that work in proximity of humans. As enforcing safety during training
might severely limit the agent's exploration, we propose here a new
architecture that handles the trade-off between efficient progress and safety
during exploration. As the exploration progresses, we update via Bayesian
inference Dirichlet-Categorical models of the transition probabilities of the
Markov decision process that describes the environment dynamics. This paper
proposes a way to approximate moments of belief about the risk associated to
the action selection policy. We construct those approximations, and prove the
convergence results. We propose a novel method for leveraging the expectation
approximations to derive an approximate bound on the confidence that the risk
is below a certain level. This approach can be easily interleaved with RL and
we present experimental results to showcase the performance of the overall
architecture.
