"""业务价值兑换关系(Exchange Rate)与统一价值空间。 对应正文第 8 章 §8.5「序列价值评估体系」中的核心机制: 不同业务的价值定义/统计口径/数值分布完全不同,因此业务分天然不可比; 工业界的做法不是简单 Min-Max / Z-Score 缩放,而是通过长期实验建立 **不同业务价值之间的兑换关系**,把一切折算到同一个价值单位(正文选「用户消费时长」)。 本实现做了什么: 1. 逐行复刻正文表「不同业务价值的兑换关系示例」,并由「平台收益 / 单位时长价值」 自动推导兑换系数,验证正文给出的 20 / 10 / 2 三个系数; 2. 复刻正文表「统一价值计算示例」,把 Video-A/Ad-B/Live-C/Ecom-D 的原始价值 折算为统一价值分 {3, 4, 5, 3}; 3. 复刻正文的序列对比:Seq1=[Live-C, Ad-B, Video-A] 得 10.0, Seq2=[Ad-B, Live-C, Video-A] 得 9.8,因此混排选 Seq1; 4. 对照实验:Min-Max 归一化 / Z-Score 标准化 / 兑换关系三种口径, 在合成请求上统计「选出的序列真实平台收益」,说明只有兑换关系口径 优化的是平台整体价值(Platform Value)。 关键公式(全部取自正文): 1 分钟时长价值 = 0.05 元 => 1 元平台收益 = 20 分钟时长价值 Value_ad = 20 x Revenue Value_live = 10 x Gift Value_ec = 2 x GMV Score_seq = sum_{i=1..L} gamma_i * Value(item_i) """ import itertools import random import statistics # ------------------------------------------------------------ 正文给定常量 MINUTE_VALUE_YUAN = 0.05 # 用户消费 1 分钟短视频 = 0.05 元平台收益 # 正文表「不同业务价值的兑换关系示例」:业务 -> (单位原始量描述, 平台收益/单位) # 「平台收益」列的单位是元,除以 MINUTE_VALUE_YUAN 即得折算时长价值(分钟) EXCHANGE_TABLE = [ ("短视频 video", "用户消费 1 分钟", 0.05), ("广告 ad", "广告收入 1 元", 1.00), ("直播 live", "直播打赏 1 元", 0.50), ("电商 ec", "电商 GMV 1 元", 0.10), ] # 正文表「位置衰减权重示例」 POS_WEIGHT = [1.0, 0.8, 0.6, 0.4] def exchange_rate(platform_revenue_per_unit, minute_value=MINUTE_VALUE_YUAN): """兑换系数 = 该业务单位原始量带来的平台收益 / 单位时长价值。""" return platform_revenue_per_unit / minute_value def gamma(i): """位置衰减权重 gamma_i(i 从 1 开始);超出正文给定表则线性外推到 0。""" if i <= len(POS_WEIGHT): return POS_WEIGHT[i - 1] return max(0.0, POS_WEIGHT[-1] - 0.2 * (i - len(POS_WEIGHT))) def score_seq(seq): """Score_seq = sum_i gamma_i * Value(item_i)。""" return sum(gamma(i + 1) * it["value"] for i, it in enumerate(seq)) # ------------------------------------------------------------ 演示 1:兑换关系表 def demo_exchange_table(): print("=" * 78) print("【1】兑换关系推导(正文表「不同业务价值的兑换关系示例」)") print("=" * 78) print(f"统一价值单位:用户消费时长(分钟),1 分钟 = {MINUTE_VALUE_YUAN} 元平台收益") print(f"=> 1 元平台收益 = {1 / MINUTE_VALUE_YUAN:.0f} 分钟时长价值") print() print(f"{'业务':<14}{'用户行为':<18}{'平台收益(元)':>13}{'折算时长(分钟)':>15}" f"{'兑换系数':>10}") print("-" * 78) for biz, behavior, revenue in EXCHANGE_TABLE: r = exchange_rate(revenue) print(f"{biz:<14}{behavior:<18}{revenue:>13.2f}{r:>15.1f}{r:>10.1f}") print("-" * 78) print("与正文结论一致:Value_ad = 20 x Revenue,Value_live = 10 x Gift," "Value_ec = 2 x GMV。") # ------------------------------------------------------------ 演示 2:统一价值分 def textbook_items(): """正文表「统一价值计算示例」的四个 Item(原始价值 -> 统一价值分)。""" return [ {"id": "Video-A", "biz": "video", "raw_desc": "预计观看 3 分钟", "raw": 3.00, "value": 3.00 * exchange_rate(0.05)}, {"id": "Ad-B", "biz": "ad", "raw_desc": "eCPM=0.20 元", "raw": 0.20, "value": 0.20 * exchange_rate(1.00)}, {"id": "Live-C", "biz": "live", "raw_desc": "预计打赏 0.50 元", "raw": 0.50, "value": 0.50 * exchange_rate(0.50)}, {"id": "Ecom-D", "biz": "ec", "raw_desc": "GMV=1.50 元", "raw": 1.50, "value": 1.50 * exchange_rate(0.10)}, ] def demo_unified_value(): items = textbook_items() print() print("=" * 78) print("【2】统一价值映射(正文表「统一价值计算示例」)") print("=" * 78) print(f"{'Item':<10}{'业务':<8}{'原始价值':<18}{'兑换系数':>10}{'统一价值分':>12}") print("-" * 78) for it in items: rate = {"video": 1.0, "ad": 20.0, "live": 10.0, "ec": 2.0}[it["biz"]] print(f"{it['id']:<10}{it['biz']:<8}{it['raw_desc']:<18}" f"{rate:>10.1f}{it['value']:>12.2f}") print("-" * 78) vals = [round(it["value"], 2) for it in items] print(f"Value(item) = {{{', '.join(f'{v:.0f}' for v in vals)}}} " "-> 与正文一致,四个异质业务终于可直接比较。") return items # ------------------------------------------------------------ 演示 3:序列对比 def demo_sequence_choice(items): by_id = {it["id"]: it for it in items} seq1 = [by_id["Live-C"], by_id["Ad-B"], by_id["Video-A"]] seq2 = [by_id["Ad-B"], by_id["Live-C"], by_id["Video-A"]] print() print("=" * 78) print("【3】序列价值对比(正文 Seq1 vs Seq2)") print("=" * 78) print(f"{'位置':<6}{'gamma_i':>9} {'Seq1':<22}{'Seq2':<22}") print("-" * 78) for i in range(3): a, b = seq1[i], seq2[i] ca = f"{a['id']}(v={a['value']:.0f})" cb = f"{b['id']}(v={b['value']:.0f})" print(f"{i + 1:<6}{gamma(i + 1):>9.1f} {ca:<22}{cb:<22}") print("-" * 78) s1, s2 = score_seq(seq1), score_seq(seq2) print(f"Score(Seq1) = 1.0x5 + 0.8x4 + 0.6x3 = {s1:.1f}") print(f"Score(Seq2) = 1.0x4 + 0.8x5 + 0.6x3 = {s2:.1f}") print(f"Score(Seq1) - Score(Seq2) = {s1 - s2:.1f} > 0 -> 混排选择 Seq1,与正文一致。") print("直觉:高价值 Item 放前排能吃到更大的 gamma_i,位置分配本身就是价值分配。") # ------------------------------------------------------------ 演示 4:口径对照实验 def make_request(n_per_biz=2): """[MOCK] 合成一次混排请求的候选池,各业务的原始分尺度刻意差异巨大。 video: 预计观看分钟数 ~ 1-6 分钟 ad: eCPM(元/次) ~ 0.05-0.45 live: 预计打赏(元) ~ 0.0-1.2 ec: GMV(元) ~ 0.0-8.0 """ pool = [] for _ in range(n_per_biz): pool.append({"biz": "video", "raw": random.uniform(1.0, 6.0)}) pool.append({"biz": "ad", "raw": random.uniform(0.05, 0.45)}) pool.append({"biz": "live", "raw": random.uniform(0.0, 1.2)}) pool.append({"biz": "ec", "raw": random.uniform(0.0, 8.0)}) rate = {"video": 1.0, "ad": 20.0, "live": 10.0, "ec": 2.0} for it in pool: it["true_value"] = it["raw"] * rate[it["biz"]] # 真实统一价值(评估用) return pool def minmax_scores(pool): """Min-Max 归一化:只做尺度对齐,不解决口径问题。""" out = [] for biz in ("video", "ad", "live", "ec"): xs = [it["raw"] for it in pool if it["biz"] == biz] lo, hi = min(xs), max(xs) span = hi - lo if hi > lo else 1.0 for it in pool: if it["biz"] == biz: out.append((it, (it["raw"] - lo) / span)) return dict((id(it), s) for it, s in out) def zscore_scores(pool): """Z-Score 标准化:同样只是缩放。""" out = [] for biz in ("video", "ad", "live", "ec"): xs = [it["raw"] for it in pool if it["biz"] == biz] mu = statistics.fmean(xs) sd = statistics.pstdev(xs) or 1.0 for it in pool: if it["biz"] == biz: out.append((it, (it["raw"] - mu) / sd)) return dict((id(it), s) for it, s in out) def exchange_scores(pool): """兑换关系口径:折算到统一时长价值。""" rate = {"video": 1.0, "ad": 20.0, "live": 10.0, "ec": 2.0} return dict((id(it), it["raw"] * rate[it["biz"]]) for it in pool) def best_seq_by(pool, table, length=4): """在候选池里枚举长度为 length 的序列,按给定打分口径取最优。""" best, best_s = None, float("-inf") for comb in itertools.permutations(pool, length): s = sum(gamma(i + 1) * table[id(it)] for i, it in enumerate(comb)) if s > best_s: best, best_s = comb, s return best def demo_caliber_comparison(n_trial=60): print() print("=" * 78) print("【4】对照实验:三种价值口径选出的序列,真实平台收益谁更高") print("=" * 78) gains = {"minmax": [], "zscore": [], "exchange": []} mix = {"minmax": [], "zscore": [], "exchange": []} for _ in range(n_trial): pool = make_request() truth = dict((id(it), it["true_value"]) for it in pool) for key, fn in (("minmax", minmax_scores), ("zscore", zscore_scores), ("exchange", exchange_scores)): seq = best_seq_by(pool, fn(pool)) gains[key].append(sum(gamma(i + 1) * truth[id(it)] for i, it in enumerate(seq))) mix[key].append(tuple(it["biz"] for it in seq)) base = statistics.fmean(gains["exchange"]) print(f"{'价值口径':<26}{'真实序列价值均值':>18}{'相对兑换关系':>14}") print("-" * 78) for key, name in (("minmax", "Min-Max 归一化"), ("zscore", "Z-Score 标准化"), ("exchange", "兑换关系(正文方案)")): m = statistics.fmean(gains[key]) print(f"{name:<26}{m:>18.3f}{m / base:>14.4f}") print("-" * 78) print("首位业务分布(选出的 Top-1 坑位给了谁):") for key, name in (("minmax", "Min-Max"), ("zscore", "Z-Score"), ("exchange", "兑换关系")): cnt = {} for seq in mix[key]: cnt[seq[0]] = cnt.get(seq[0], 0) + 1 dist = " ".join(f"{b}:{cnt.get(b, 0) / n_trial:.0%}" for b in ("video", "ad", "live", "ec")) print(f" {name:<12}{dist}") print("-" * 78) print("归一化口径把「各业务内部的相对名次」当成跨业务价值,等于默认四个业务同等重要,") print("于是常把低价值 Item 放到首位;兑换关系口径优化的是平台整体价值,因此最优。") print("这正是正文强调的:归一化只是缩放,没有解决价值口径不一致的问题。") if __name__ == "__main__": random.seed(42) demo_exchange_table() items = demo_unified_value() demo_sequence_choice(items) demo_caliber_comparison()