InfoRSI/tests/rules-forward.test.ts

import assert from "node:assert/strict";
import { createHash } from "node:crypto";
import { test } from "node:test";
import {
  adopt,
  adoptionLine,
  batchValue,
  runBatchRule,
  selectBestExpected,
  selectUniformRandom,
  type BatchInput,
  personKnots,
  type Mixture,
} from "../src/rules/index.ts";

// 预期值来源写在每条测试旁边。数取二进制能精确表示的数（0.25、0.5 等），避免浮点末位干扰"正好相等"的边界。

function close(actual: number, expected: number, tol = 1e-12): void {
  assert.ok(Math.abs(actual - expected) <= tol, `实际 ${actual}，预期 ${expected}`);
}

/** 很窄的范围 (y − 0.01, y, y + 0.01)，连尾巴 [y − 0.02, y + 0.02]。 */
const narrow = (y: number) => ({ q1: y - 0.01, q5: y, q9: y + 0.01 });
/** 一个人交的一份范围（研究者 r1）。 */
const one = (range: { q1: number; q5: number; q9: number }) => [{ researcher: "r1", range }];

test("6.4 示例：X 一半涨 0、一半涨 0.02，Y 一定涨 0.01；Y 单跑 0.010，一起跑 0.015", () => {
  // 来源：方法.md 6.4 示例，把"一定涨"换成很窄的范围（三个数严格递增）。改进量上直接给：
  // X = 一半 (−0.001, 0, 0.001)、一半 (0.019, 0.02, 0.021)；Y = (0.009, 0.01, 0.011)。
  // 预期值由 tests/fixtures/rules/rules_ref.py 的 V（有理数精确）算出：V(X) = 407/40000 = 0.010175（窄范围在 0 以下的
  // 一点被截成 0，比 0.010 多 0.5 × 0.00035）；V(Y) = 0.01；V(X, Y) = 3/200 = 0.015。
  const tri = (y: number, h: number) => personKnots({ q1: y - h, q5: y, q9: y + h });
  const X: Mixture = [
    { weight: 0.5, knots: tri(0, 0.001) },
    { weight: 0.5, knots: tri(0.02, 0.001) },
  ];
  const Y: Mixture = [{ weight: 1, knots: tri(0.01, 0.001) }];
  close(batchValue([X]), 407 / 40000);
  close(batchValue([Y]), 0.01);
  close(batchValue([X, Y]), 0.015);
  assert.equal(batchValue([]), 0);
});

function input(over: Partial<BatchInput>): BatchInput {
  return {
    candidates: [],
    baseline: 0,
    direction: "maximize",
    epsilon: 0.25,
    lambda: 0,
    batchCap: 2,
    balance: 10,
    seed: "seed-1",
    ...over,
  };
}

test("6.4 入池：P(Y < −ε) 正好一半不入池，小于一半入池", () => {
  // 手算：b = 1，ε = 0.25，λ = 0。甲交 (0.5, 0.75, 1)：P(分数 < 0.75) = 0.5，不入池。
  // 乙交 (0.5, 0.8125, 1)：P(分数 < 0.75) = 0.1 + 0.4 × 0.25/0.3125 = 0.42，入池。
  const d = selectBestExpected(
    input({
      baseline: 1,
      candidates: [
        { id: "a", ranges: one({ q1: 0.5, q5: 0.75, q9: 1 }) },
        { id: "b", ranges: one({ q1: 0.5, q5: 0.8125, q9: 1 }) },
      ],
    }),
  );
  assert.equal(d.candidates[0]!.lossProbability, 0.5);
  assert.equal(d.candidates[0]!.inPool, false);
  close(d.candidates[1]!.lossProbability, 0.42);
  assert.deepEqual(d.pool, ["b"]);
});

test("6.4 入池（越小越好）：交 (1, 1.25, 1.5)、b = 1、ε = 0.25 时 P(Y < −ε) = 0.5，不入池", () => {
  // 手算：越小越好时 Y = b − 分数，Y < −0.25 即分数 > 1.25，把握 0.5。
  const d = selectBestExpected(
    input({ baseline: 1, direction: "minimize", candidates: [{ id: "a", ranges: one({ q1: 1, q5: 1.25, q9: 1.5 }) }] }),
  );
  close(d.candidates[0]!.lossProbability, 0.5);
  assert.equal(d.candidates[0]!.lossProbability >= 0.5, true);
  assert.deepEqual(d.pool, []);
  assert.deepEqual(d.chosen, []);
  assert.equal(d.chosenValue, 0);
  assert.equal(d.scaleReading, 0);
});

test("6.4 选批：列出全部组合；V 完全相等时按编号定；池外候选不进组合", () => {
  // b = 0，λ = 0，k = 1。四个窄范围：a 在 0.25，b、c 都在 0.75（输入完全相同，V 逐位相等），
  // d 在 −0.5（P(Y < −ε) = 1，不入池）。手算：V(a) = 0.25，V(b) = V(c) = 0.75（对称窄范围的期望，都在 0 以上）。
  // b、c 相等，取编号小的 b。V(池) = E[max(a, b, c)] = 11323/15000，分数尺读数 = 11323/15000 − 0.75 = 73/15000
  // （rules_ref.py 的 V，有理数精确）。
  const d = selectBestExpected(
    input({
      batchCap: 1,
      candidates: [
        { id: "d", ranges: one(narrow(-0.5)) },
        { id: "c", ranges: one(narrow(0.75)) },
        { id: "b", ranges: one(narrow(0.75)) },
        { id: "a", ranges: one(narrow(0.25)) },
      ],
    }),
  );
  assert.equal(d.k, 1);
  assert.deepEqual(d.pool, ["a", "b", "c"]);
  assert.deepEqual(
    d.combos.map((c) => c.ids.join("")),
    ["a", "b", "c"],
  );
  close(d.combos[0]!.value, 0.25);
  close(d.combos[1]!.value, 0.75);
  assert.equal(d.combos[1]!.value, d.combos[2]!.value);
  assert.deepEqual(d.chosen, ["b"]);
  close(d.poolValue, 11323 / 15000);
  close(d.scaleReading, 73 / 15000);
  assert.deepEqual(d.candidates.map((c) => c.id), ["a", "b", "c", "d"]);
  const m = d.candidates[1]!.merged;
  close(m.q1, 0.74);
  close(m.q5, 0.75);
  close(m.q9, 0.76);
});

test("6.4 分数尺读数 = V(候选池) − V(S*)", () => {
  // 手算：b = 0，λ = 0，k = 1。a 交 (0, 0.5, 1)：E[max(0, Y)] = ∫₀^1.5 (1 − F)
  //   = 0.5 × (1 − 0.3) + 0.5 × (1 − 0.7) + 0.5 × (1 − 0.95) = 0.35 + 0.15 + 0.025 = 0.525。
  // b 交 (0.49, 0.5, 0.51)：V = 0.5。选 a。V(池) = E[max(a, b)] = 31642/46875，读数 31642/46875 − 0.525
  // （rules_ref.py 的 V，有理数精确；b 换成 0.5 处的定值时是 0.675 和 0.15）。
  const d = selectBestExpected(
    input({
      batchCap: 1,
      candidates: [
        { id: "a", ranges: one({ q1: 0, q5: 0.5, q9: 1 }) },
        { id: "b", ranges: one(narrow(0.5)) },
      ],
    }),
  );
  assert.deepEqual(d.chosen, ["a"]);
  close(d.chosenValue, 0.525);
  close(d.poolValue, 31642 / 46875);
  close(d.scaleReading, 31642 / 46875 - 0.525);
});

test("6.4 批量 k = min(每批上限, 余额)；池里不足 k 个时全选", () => {
  // 手算：余额 1 时 k = 1；余额 5、上限 2 时 k = 2，但池里只有 1 个，全选。
  const cands = [
    { id: "a", ranges: one(narrow(0.25)) },
    { id: "b", ranges: one(narrow(0.5)) },
  ];
  assert.equal(selectBestExpected(input({ balance: 1, candidates: cands })).k, 1);
  assert.deepEqual(selectBestExpected(input({ balance: 1, candidates: cands })).chosen, ["b"]);
  const single = selectBestExpected(input({ balance: 5, candidates: [{ id: "a", ranges: one(narrow(0.25)) }] }));
  assert.equal(single.k, 2);
  assert.deepEqual(single.chosen, ["a"]);
});

// 约定表第 40 条的独立写法：sha256(`${seed}:${counter}`) 前 6 字节，拒绝采样，部分 Fisher–Yates。
function referenceSample(ids: string[], size: number, seed: string): string[] {
  const xs = [...ids].sort();
  let counter = 0;
  const draw = (n: number): number => {
    const limit = 2 ** 48 - (2 ** 48 % n);
    for (;;) {
      const hex = createHash("sha256").update(`${seed}:${counter}`).digest("hex").slice(0, 12);
      counter += 1;
      const v = parseInt(hex, 16);
      if (v < limit) return v % n;
    }
  };
  for (let i = 0; i < size; i++) {
    const j = i + draw(xs.length - i);
    const t = xs[i]!;
    xs[i] = xs[j]!;
    xs[j] = t;
  }
  return xs.slice(0, size).sort();
}

test("均匀随机选批：不看入池门槛；同一个种子得到同一组；与约定表第 40 条的独立写法一致", () => {
  const cands = ["e", "a", "d", "b", "c"].map((id, i) => ({ id, ranges: one(narrow(i === 0 ? -1 : 0.25 * i)) }));
  for (const seed of ["s1", "s2", "s3", "s4"]) {
    const d = selectUniformRandom(input({ seed, candidates: cands }));
    assert.deepEqual(d.chosen, referenceSample(["a", "b", "c", "d", "e"], 2, seed));
    assert.deepEqual(selectUniformRandom(input({ seed, candidates: [...cands].reverse() })).chosen, d.chosen);
    assert.deepEqual(d.combos, []);
  }
  // 批量不小于候选数时全部抽中，包括池外的 e（窄范围在 −1）。
  const all = selectUniformRandom(input({ batchCap: 9, candidates: cands }));
  assert.deepEqual(all.chosen, ["a", "b", "c", "d", "e"]);
  assert.equal(all.candidates.find((c) => c.id === "e")!.inPool, false);
});

test("登记表：两条选批规则按名字跑，结果带规则名和版本", () => {
  const cands = [
    { id: "a", ranges: one(narrow(0.25)) },
    { id: "b", ranges: one(narrow(0.5)) },
  ];
  const best = runBatchRule("bestExpected", input({ batchCap: 1, candidates: cands }));
  assert.deepEqual(best.rule, { name: "bestExpected", version: 1 });
  assert.deepEqual(best.chosen, ["b"]);
  const rnd = runBatchRule("uniformRandom", input({ batchCap: 1, candidates: cands, seed: "x" }));
  assert.deepEqual(rnd.rule, { name: "uniformRandom", version: 1 });
  assert.deepEqual(rnd.chosen, referenceSample(["a", "b"], 1, "x"));
  assert.equal(rnd.seed, "x");
});

test("同样的输入算两次，选批结果逐位相同", () => {
  const two = (r1: { q1: number; q5: number; q9: number }, r2: { q1: number; q5: number; q9: number }) => [
    { researcher: "r1", range: r1 },
    { researcher: "r2", range: r2 },
  ];
  const i = input({
    lambda: 0.1,
    candidates: [
      { id: "a", ranges: two({ q1: 0.1, q5: 0.3, q9: 0.7 }, { q1: -0.2, q5: 0.1, q9: 0.2 }) },
      { id: "b", ranges: two({ q1: 0, q5: 0.2, q9: 0.9 }, { q1: 0.05, q5: 0.15, q9: 0.25 }) },
      { id: "c", ranges: two({ q1: -0.3, q5: 0.25, q9: 0.6 }, narrow(0.1)) },
    ],
  });
  assert.deepEqual(selectBestExpected(i), selectBestExpected(i));
});

test("6.5 采纳线：没有已知最好是 ε；有时 min(ε, (K* − B)/4)，下限 ε/100，B 超过 K* 也取 ε/100", () => {
  // 手算：ε = 0.01，K* = 2.635983。
  assert.deepEqual(adoptionLine({ baseline: 2.5, knownBest: null, epsilon: 0.01, direction: "maximize" }), {
    line: 0.01,
    quarter: null,
  });
  // B = 2.5：(0.135983)/4 = 0.03399575 > ε，取 ε。
  assert.equal(adoptionLine({ baseline: 2.5, knownBest: 2.635983, epsilon: 0.01, direction: "maximize" }).line, 0.01);
  // B = 2.6：0.035983/4 = 0.00899575。
  close(adoptionLine({ baseline: 2.6, knownBest: 2.635983, epsilon: 0.01, direction: "maximize" }).line, 0.00899575);
  // B = 2.6359：0.000083/4 = 0.00002075 < 0.0001，取 ε/100 = 0.0001。
  assert.equal(adoptionLine({ baseline: 2.6359, knownBest: 2.635983, epsilon: 0.01, direction: "maximize" }).line, 0.01 / 100);
  // B = 2.64 超过 K*：取 0.0001。
  assert.equal(adoptionLine({ baseline: 2.64, knownBest: 2.635983, epsilon: 0.01, direction: "maximize" }).line, 0.01 / 100);
  // ε 换成 1 时下限是 0.01，跟随 ε。
  assert.equal(adoptionLine({ baseline: 3, knownBest: 2, epsilon: 1, direction: "maximize" }).line, 0.01);
  // 越小越好：K* = 1，B = 1.02：(1.02 − 1)/4 = 0.005。
  close(adoptionLine({ baseline: 1.02, knownBest: 1, epsilon: 0.01, direction: "minimize" }).line, 0.005);
});

test("4.3 ⑫ 采纳：最好的有效候选严格高出采纳线才采纳；正好等于不采纳；同分取编号小的", () => {
  // 手算：B = 1，ε = 0.25，没有已知最好，采纳线 0.25。
  const base = { baseline: 1, knownBest: null, epsilon: 0.25, direction: "maximize" as const };
  assert.equal(adopt({ ...base, candidates: [{ id: "a", score: 1.25 }] }).adopted, null);
  assert.equal(adopt({ ...base, candidates: [{ id: "a", score: 1.5 }] }).adopted, "a");
  const tie = adopt({
    ...base,
    candidates: [
      { id: "b", score: 1.5 },
      { id: "a", score: 1.5 },
      { id: "c", score: 1.25 },
    ],
  });
  assert.deepEqual(tie.best, { id: "a", score: 1.5, improvement: 0.5 });
  assert.equal(tie.adopted, "a");
  assert.equal(adopt({ ...base, candidates: [] }).adopted, null);
  // 越小越好：分数 0.5 比 B = 1 改进 0.5。
  assert.equal(adopt({ ...base, direction: "minimize", candidates: [{ id: "a", score: 0.5 }] }).adopted, "a");
});