smr_alignment.MetricAlignmentOptimizer: Make entropy penalty convex (#19)

Previously, `MetricAlignmentOptimizer.optimize_weights()` used the
`cvxpy` built-in `cvxpy.entr(x)` entropy penalty. What I didn't
realise until I ran the optimizer on real data, is that this
function is actually concave. Therefore, it is possible, that the
overall optimization problem is not convex anymore, messing up our
convex solver.

This adapts the entropy penalty to be a basic L2 penalty,
which is convex.

Fixes #16

Author: s-heppner

smr_alignment/src/smr_alignment/metric_alignment.py

@@ -147,8 +147,10 @@ def optimize_weights(
         loss = cp.sum(cp.pos(margins))  # piecewise-linear convex
 
         if entropy_lambda > 0:
-            # cp.entr(x) = x*log(x); we add small offset to keep it defined near zero
-            loss += entropy_lambda * cp.sum(cp.entr(w + 1e-16))
+            # we add small offset to keep it defined near zero
+            n = len(metrics)
+            u = np.full(n, 1.0 / n)
+            loss += entropy_lambda * cp.sum_squares(w - u)
 
         constraints = [cp.sum(w) == 1.0]  # cp.sum(w) == 1.0 in CVXPY doesn’t return a plain bool at runtime,
         # it returns a Constraint object, confusing type checkers. Therefore, the "type: ignore" below.