  High Power Laser's (HPL) optimal performance is essential for the success of
a wide variety of experimental tasks related to light-matter interactions.
Traditionally, HPL parameters are optimised in an automated fashion relying on
black-box numerical methods. However, these can be demanding in terms of
computational resources and usually disregard transient and complex dynamics.
Model-free Deep Reinforcement Learning (DRL) offers a promising alternative
framework for optimising HPL performance since it allows to tune the control
parameters as a function of system states subject to nonlinear temporal
dynamics without requiring an explicit dynamics model of those. Furthermore,
DRL aims to find an optimal control policy rather than a static parameter
configuration, particularly suitable for dynamic processes involving sequential
decision-making. This is particularly relevant as laser systems are typically
characterised by dynamic rather than static traits. Hence the need for a
strategy to choose the control applied based on the current context instead of
one single optimal control configuration. This paper investigates the potential
of DRL in improving the efficiency and safety of HPL control systems. We apply
this technique to optimise the temporal profile of laser pulses in the L1 pump
laser hosted at the ELI Beamlines facility. We show how to adapt DRL to the
setting of spectral phase control by solely tuning dispersion coefficients of
the spectral phase and reaching pulses similar to transform limited with
full-width at half-maximum (FWHM) of ca1.6 ps.
