  Thermal convection is ubiquitous in nature as well as in many industrial
applications. The identification of effective control strategies to, e.g.,
suppress or enhance the convective heat exchange under fixed external thermal
gradients is an outstanding fundamental and technological issue. In this work,
we explore a novel approach, based on a state-of-the-art Reinforcement Learning
(RL) algorithm, which is capable of significantly reducing the heat transport
in a two-dimensional Rayleigh-B\'enard system by applying small temperature
fluctuations to the lower boundary of the system. By using numerical
simulations, we show that our RL-based control is able to stabilize the
conductive regime and bring the onset of convection up to a Rayleigh number
$Ra_c \approx 3 \cdot 10^4$, whereas in the uncontrolled case it holds
$Ra_{c}=1708$. Additionally, for $Ra > 3 \cdot 10^4$, our approach outperforms
other state-of-the-art control algorithms reducing the heat flux by a factor of
about $2.5$. In the last part of the manuscript, we address theoretical limits
connected to controlling an unstable and chaotic dynamics as the one considered
here. We show that controllability is hindered by observability and/or
capabilities of actuating actions, which can be quantified in terms of
characteristic time delays. When these delays become comparable with the
Lyapunov time of the system, control becomes impossible.
