HEPGAME and the Simplification of Expressions
  Advances in high energy physics have created the need to increase
computational capacity. Project HEPGAME was composed to address this challenge.
One of the issues is that numerical integration of expressions of current
interest have millions of terms and takes weeks to compute. We have
investigated ways to simplify these expressions, using Horner schemes and
common subexpression elimination. Our approach applies MCTS, a search procedure
that has been successful in AI. We use it to find near-optimal Horner schemes.
Although MCTS finds better solutions, this approach gives rise to two further
challenges. (1) MCTS (with UCT) introduces a constant, $C_p$ that governs the
balance between exploration and exploitation. This constant has to be tuned
manually. (2) There should be more guided exploration at the bottom of the
tree, since the current approach reduces the quality of the solution towards
the end of the expression. We investigate NMCS (Nested Monte Carlo Search) to
address both issues, but find that NMCS is computationally unfeasible for our
problem. Then, we modify the MCTS formula by introducing a dynamic
exploration-exploitation parameter $T$ that decreases linearly with the
iteration number. Consequently, we provide a performance analysis. We observe
that a variable $C_p$ solves our domain: it yields more exploration at the
bottom and as a result the tuning problem has been simplified. The region in
$C_p$ for which good values are found is increased by more than a tenfold. This
result encourages us to continue our research to solve other prominent problems
in High Energy Physics.
