algo-ad-budget

asgard-ai-platform ｜ 行銷與 SEO ｜ 原文 ｜ MIT

用邊際報酬分析，在各廣告活動間分配預算

---
name: "algo-ad-budget"
description: "用邊際報酬分析，最佳化各廣告活動之間的預算分配。當使用者需要把預算分給多個廣告活動、最佳化花費節奏，或在預算限制下讓整體 ROAS 最大時使用，即使他們說的是『how to split my ad budget』『campaign budget optimization』或『diminishing returns on ad spend』。"
metadata:
  category: "WP-37 廣告演算法"
  tags: ["advertising", "budget-optimization", "allocation", "marginal-returns"]
---

# 廣告預算分配最佳化

## 概述

預算分配是把一筆廣告總預算分給各個廣告活動，讓整體報酬最大。用的是邊際報酬相等原則：一路分配到所有廣告活動的邊際 CPA（或邊際 ROAS）都相等為止。同時處理報酬遞減和預算限制。

## 何時使用

**觸發條件：**
- 把固定預算分給多個廣告活動或管道
- 找出報酬遞減點，以及每個廣告活動的最佳花費水準
- 成效變動後重新平衡預算

**不該使用的情況：**
- 最佳化單一廣告活動內的出價時（用出價策略）
- 只有一個廣告活動時（沒有東西可以分配）

## 演算法

```
IRON LAW: Equal Marginal Returns Principle
Optimal allocation makes the MARGINAL return of the last dollar
equal across ALL campaigns. If Campaign A's marginal CPA is $5
and Campaign B's is $15, shift budget from B to A until they equalize.
Total budget constraint: Σ budget_i = total_budget.
```

### 階段 1：輸入驗證
每個廣告活動要收集：歷史花費、轉換數、多個花費水準下的營收。每個廣告活動至少要有 3 個資料點，才能擬合反應曲線。
**關卡：** 歷史資料足以估計反應曲線。

### 階段 2：核心演算法
1. 為每個廣告活動擬合反應曲線：conversions = f(spend)。常見模型：對數曲線、冪函數曲線、S 曲線
2. 計算邊際報酬曲線：每個廣告活動的 f'(spend)
3. 分配：用 Lagrangian 最佳化或迭代式貪婪法，把下一塊錢分給邊際報酬最高的廣告活動
4. 套用限制：最低花費下限、最高上限、各管道的專屬規則

### 階段 3：驗證
檢查：分配總額 = 總預算、沒有廣告活動低於下限或超過上限、邊界處的邊際報酬大致相等。
**關卡：** 分配加總等於預算，限制條件全部滿足。

### 階段 4：輸出
回傳分配表，附上預期成效推估。

## 輸出格式

```json
{
  "allocation": [{"campaign": "Search-Brand", "budget": 50000, "expected_conversions": 200, "expected_cpa": 250}],
  "total": {"budget": 200000, "expected_conversions": 650, "blended_cpa": 308},
  "metadata": {"optimization_method": "lagrangian", "response_model": "log_curve"}
}
```

## 範例

### 輸入輸出範例
**輸入：** 預算：$100K，廣告活動：Search（$50K，100 次轉換）、Social（$30K，60 次轉換）、Display（$20K，20 次轉換）
**預期：** 把預算從 Display（邊際 CPA 高）挪到 Search（邊際 CPA 低）。例如 Search $60K、Social $30K、Display $10K。

### 邊界情況
| 輸入 | 預期 | 原因 |
|-------|----------|-----|
| 有一個廣告活動遠遠勝出 | 大部分預算給贏家 | 但其他活動還是要保留最低下限 |
| 所有廣告活動都飽和了 | 降低總花費 | 多花也沒用 |
| 新廣告活動，沒有資料 | 用最低測試預算 | 要先有資料才能最佳化 |

## 注意事項

- **反應曲線外推**：不要在觀察過的花費範圍之外做最佳化。花費更高時，曲線形狀可能會變。
- **歸因重疊**：使用者可能在不同廣告活動都看到廣告。Last-click 歸因會重複計算，把上層漏斗廣告活動的 CPA 墊高。要用多點觸擊歸因（multi-touch attribution）。
- **報酬遞減的假設**：不是每個廣告活動都符合平滑的報酬遞減。有些是階梯函數（例如花費超過某個門檻才觸及到新的受眾區隔）。
- **時間動態**：反應曲線會隨季節和競爭狀況位移。每月重新擬合曲線，或用滾動視窗。
- **最低可行花費**：每個廣告活動都需要足夠的預算才能走出學習階段。分得太薄，就是沒有任何一個活動拿到足夠的資料。

## 參考資料

- 反應曲線的擬合方法，見 `references/response-curves.md`
- 多點觸擊歸因整合，見 `references/attribution-integration.md`

---
name: "algo-ad-budget"
description: "Optimize advertising budget allocation across campaigns using marginal returns analysis. Use this skill when the user needs to distribute budget across multiple campaigns, optimize spend pacing, or maximize overall ROAS under budget constraints — even if they say 'how to split my ad budget', 'campaign budget optimization', or 'diminishing returns on ad spend'."
metadata:
  category: "WP-37 廣告演算法"
  tags: ["advertising", "budget-optimization", "allocation", "marginal-returns"]
---

# Ad Budget Allocation Optimization

## Overview

Budget allocation distributes a total advertising budget across campaigns to maximize overall returns. Uses the equal marginal returns principle: allocate until the marginal CPA (or marginal ROAS) is equalized across all campaigns. Handles diminishing returns and budget constraints.

## When to Use

**Trigger conditions:**
- Distributing a fixed budget across multiple campaigns or channels
- Identifying diminishing returns and optimal spend levels per campaign
- Rebalancing budget after performance changes

**When NOT to use:**
- When optimizing bids within a single campaign (use bidding strategy)
- When there's only one campaign (nothing to allocate across)

## Algorithm

```
IRON LAW: Equal Marginal Returns Principle
Optimal allocation makes the MARGINAL return of the last dollar
equal across ALL campaigns. If Campaign A's marginal CPA is $5
and Campaign B's is $15, shift budget from B to A until they equalize.
Total budget constraint: Σ budget_i = total_budget.
```

### Phase 1: Input Validation
Collect per-campaign: historical spend, conversions, revenue at multiple spend levels. Need at least 3 data points per campaign to fit response curve.
**Gate:** Sufficient historical data to estimate response curves.

### Phase 2: Core Algorithm
1. Fit response curve per campaign: conversions = f(spend). Common models: log curve, power curve, or S-curve
2. Compute marginal return curve: f'(spend) for each campaign
3. Allocate: use Lagrangian optimization or iterative greedy — assign next marginal dollar to campaign with highest marginal return
4. Apply constraints: minimum spend floors, maximum caps, channel-specific rules

### Phase 3: Verification
Check: total allocation = total budget, no campaign below floor or above cap, marginal returns approximately equal at boundaries.
**Gate:** Allocation sums to budget, constraints satisfied.

### Phase 4: Output
Return allocation table with expected performance projections.

## Output Format

```json
{
  "allocation": [{"campaign": "Search-Brand", "budget": 50000, "expected_conversions": 200, "expected_cpa": 250}],
  "total": {"budget": 200000, "expected_conversions": 650, "blended_cpa": 308},
  "metadata": {"optimization_method": "lagrangian", "response_model": "log_curve"}
}
```

## Examples

### Sample I/O
**Input:** Budget: $100K, Campaigns: Search ($50K, 100 conv), Social ($30K, 60 conv), Display ($20K, 20 conv)
**Expected:** Shift budget from Display (high marginal CPA) to Search (low marginal CPA). e.g., Search $60K, Social $30K, Display $10K.

### Edge Cases
| Input | Expected | Why |
|-------|----------|-----|
| One campaign dominates | Most budget to winner | But maintain minimum floor for others |
| All campaigns saturated | Reduce total spend | Spending more won't help |
| New campaign, no data | Use minimum test budget | Need data before optimizing |

## Gotchas

- **Response curve extrapolation**: Don't optimize beyond observed spend ranges. The curve may change shape at higher spend levels.
- **Attribution overlap**: Users may see ads across campaigns. Last-click attribution double-counts, inflating high-funnel campaign CPA. Use multi-touch attribution.
- **Diminishing returns assumption**: Not all campaigns follow smooth diminishing returns. Some have step functions (e.g., reaching a new audience segment at a spend threshold).
- **Time dynamics**: Response curves shift seasonally and competitively. Refit curves monthly or use rolling windows.
- **Minimum viable spend**: Each campaign needs enough budget to exit the learning phase. Spreading too thin means no campaign gets sufficient data.

## References

- For response curve fitting methods, see `references/response-curves.md`
- For multi-touch attribution integration, see `references/attribution-integration.md`