  We consider the problem of optimal unsignalized intersection management,
wherein we seek to obtain safe and optimal trajectories, for a set of robots
that arrive randomly and continually. This problem involves repeatedly solving
a mixed integer program (with robot acceleration trajectories as decision
variables) with different parameters, for which the computation time using a
naive optimization algorithm scales exponentially with the number of robots and
lanes. Hence, such an approach is not suitable for real-time implementation. In
this paper, we propose a solution framework that combines learning and
sequential optimization. In particular, we propose an algorithm for learning a
shared policy that given the traffic state information, determines the crossing
order of the robots. Then, we optimize the trajectories of the robots
sequentially according to that crossing order. This approach inherently
guarantees safety at all times. We validate the performance of this approach
using extensive simulations and compare our approach against $5$ different
heuristics from the literature in $9$ different simulation settings. Our
approach, on average, significantly outperforms the heuristics from the
literature in various metrics like objective function, weighted average of
crossing times and computation time. For example, in some scenarios, we have
observed that our approach offers up to $150\%$ improvement in objective value
over the first come first serve heuristic. Even on untrained scenarios, our
approach shows a consistent improvement (in objective value) of more than
$30\%$ over all heuristics under consideration. We also show through
simulations that the computation time for our approach scales linearly with the
number of robots (assuming all other factors are constant). Learnt policies are
implemented on physical robots with slightly modified framework to address
real-world challenges.
