direct: add soo.py

direct/soo.py

@@ -0,0 +1,144 @@
+#!/usr/bin/env python3
+from collections import namedtuple
+from queue import PriorityQueue
+import numpy as np
+
+Result = namedtuple("Result", ["h", "p", "value"])
+
+
+def checked_fma(x, m, a):
+    # assumes x, m, and a are integers.
+    # assumes m >= 1 and a >= 0.
+    y = x * m
+    assert y >= x, "integer overflow"
+    z = y + a
+    assert z >= y, "integer overflow"
+    return z
+
+
+# Simultaneous Optimistic Optimization
+def soo(obj, origin, sigma, evals, K=3, h_max=None, iters=None):
+    assert K > 1, "K must be at least 2"
+
+    origin = np.array(origin, float)
+    dims = len(origin)
+    h_max = int(31 * np.log(2) / np.log(K) - 1e-8) if h_max is None else h_max
+
+    # Tree (coordinates)
+    Ts = [PriorityQueue() for _ in range(h_max + 1)]
+
+    def coords(h, p):
+        return (np.array(p, int) + 0.5) * (sigma * 2) / K ** np.array(h, int) - sigma
+
+    samples = 0
+
+    def query(h, p):
+        nonlocal samples
+        depth = np.max(h)
+        value = obj(coords(h, p) + origin)
+        Ts[depth].put((float(value), samples, list(h), list(p)))
+        samples += 1
+        return Result(h, p, value)
+
+    # kickstart with middle point at the root node.
+    best_ever = query([0] * dims, [0] * dims)
+
+    history, stopping = [], False
+    for t in range(1_000_000 if iters is None else iters):
+        best = np.inf
+        for depth in range(h_max):
+            if Ts[depth].empty():
+                continue
+
+            # select a node at this depth.
+            tup = Ts[depth].get(block=False)
+            value, _, h, p = tup
+            if value > best:
+                Ts[depth].put(tup, block=False)
+                continue
+            best = value
+
+            # split this node, potentially increasing its overall depth.
+            inc = 0
+            for j in reversed(range(1, dims)):
+                if h[j] < h[j - 1]:
+                    inc = j
+
+            if K & 1 == 1:  # when odd,
+                # maintain center point but split it differently next time.
+                h[inc] += 1
+                p[inc] = checked_fma(p[inc], K, K // 2)
+
+                new_depth = np.max(h)
+                Ts[new_depth].put(tup, block=False)
+
+                for i in range(K):
+                    if i == K // 2:
+                        continue
+                    p_new = p.copy()
+                    p_new[inc] += i - K // 2
+                    candidate = query(h.copy(), p_new)
+                    if candidate.value < best_ever.value:
+                        best_ever = candidate
+                    if samples >= evals:
+                        stopping = True
+                        break
+
+            else:  # when even,
+                # discard center point and only use its subdivisions.
+                for i in range(K):
+                    h_new, p_new = h.copy(), p.copy()
+                    h_new[inc] += 1
+                    p_new[inc] = checked_fma(p_new[inc], K, i)
+                    candidate = query(h_new, p_new)
+                    if candidate.value < best_ever.value:
+                        best_ever = candidate
+                    if samples >= evals:
+                        stopping = True
+                        break
+
+            if stopping:
+                break
+
+        history.append(best_ever.value)
+        if stopping:
+            break
+
+    h, p, _ = best_ever
+
+    return coords(h, p) + origin, history
+
+
+if __name__ == "__main__":
+    # get this here: https://github.com/imh/hipsterplot/blob/master/hipsterplot.py
+    from hipsterplot import plot
+    import numpy as np
+
+    def objective2210(x):
+        # another linear transformation of the rosenbrock banana function.
+        assert len(x) > 1, len(x)
+        a, b = x[:-1], x[1:]
+
+        a = a / 4.0 * 2 - 12 / 15
+        b = b / 1.5 * 2 - 43 / 15
+        # solution: 3.60      1.40
+
+        return (
+            np.sum(100 * np.square(np.square(a) + b) + np.square(a - 1))
+            / 499.0444444444444
+        )
+
+    optimized, history = soo(
+        objective2210,
+        origin=np.array([2.5, 2.5]),
+        sigma=np.array([2.5, 2.5]),
+        evals=2_000,
+        # K=3,
+        # h_max=19,  # should be equivalent-ish to min_diag=1e-8 in birect.py
+        K=2,
+        h_max=27,  # should be equivalent-ish to min_diag=1e-8 in birect.py
+    )
+    print(" " * 11 + "plot of log10-losses over time")
+    plot(np.log10(history), num_y_chars=23)
+    print("", "soo result:", list(optimized), history[-1], sep="\n")
+    print("", "double checked:", objective2210(optimized), sep="\n")