Project 23 · Assembly Line Intelligence

REINFORCE Policy Gradient for Production Decision Optimization

"Q-Learning remembered. REINFORCE decided."

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Overview

Item	Value
Problem	Select the best intervention on a 6-station assembly line at each step
Algorithm	REINFORCE — Monte Carlo Policy Gradient
State space	11 continuous features (6 cycle times + 5 process variables)
Action space	6 discrete interventions
Training	400 episodes · γ = 0.99 · α = 0.002
Baseline (random)	94.86 reward/step · 93.6 UPH
Trained agent	128.74 reward/step · 116.0 UPH
Improvement	+32.1% reward · +20.6% throughput
Statistical validation	P(REINFORCE > Random) = 100% · 95% CI: [+2,851, +4,679] per episode

The improvement is not the result of a fixed rule set. It emerges from 400 episodes of gradient ascent on the policy parameters — the agent learned which intervention to prioritize given the current state of the line, without being told the rules explicitly.

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The Baseline — What Random Management Looks Like

The Data_people.csv file contains 23,832 decision steps from a random manager operating the same 6-station line across 300 episodes. Every action is chosen uniformly at random. This is the performance floor.

State features observed:

Feature	Range	Meaning
ct_norm_s1 – ct_norm_s6	[0, 1]	Normalized cycle time per station — 0 = fast, 1 = slow
wip_norm	[0, 0.45]	Work-in-progress accumulation — 0 = empty, 1 = saturated
speed_norm	[0.42, 1.0]	Line speed — 0 = stopped, 1 = maximum
failure_prob	[0.00, 0.20]	Estimated failure probability
micro_stops_norm	[0.00, 1.0]	Micro-stop accumulation
operator_efficiency	[0.75, 1.0]	Operator performance index

Random policy statistics:

Metric	Value
Mean step reward	94.86
Mean throughput	93.58 UPH
Reward std dev	22.97
Reward range	−109.25 to +203.35
Action distribution	Approximately uniform — 16.7% per action

The reward std dev of 22.97 is high relative to the mean of 94.86: random management produces wide outcome variance with no learning trend across 300 episodes. This flatness is the signal that policy gradient is designed to break.

Reward function (composite):

$$r_t = 1.2 \cdot \text{throughput} - 4.0 \cdot \text{micro_stops} - 1.5 \cdot \text{WIP} - 10.0 \cdot \text{failure_prob}$$

Terminal penalty: −200 if WIP ≥ 40 or failure_prob > 0.20.

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The Algorithm — Technical Specification

Policy architecture: linear softmax over 11-dimensional state vector.

$$\pi_\theta(a \mid s) = \frac{\exp(W_a \cdot s + b_a)}{\sum_{a'} \exp(W_{a'} \cdot s + b_{a'})} \qquad \theta = {W \in \mathbb{R}^{6 \times 11},\ b \in \mathbb{R}^6}$$

At initialization: $\theta = 0$, all actions equally likely (16.7% each). At convergence: the distribution is non-uniform — the policy has learned to prioritize.

Update rule (REINFORCE): after each episode, compute discounted returns $G_t = \sum_{k} \gamma^k r_{t+k}$, normalize them, then:

$$\theta \leftarrow \theta + \alpha \cdot G_t \cdot \nabla_\theta \log \pi_\theta(a_t \mid s_t)$$

The gradient signal: $\nabla_{W_a} \log \pi = (\mathbf{1}[a=a_t] - \pi_\theta(a \mid s)) \cdot s^\top$. High $G_t$ increases the probability of $a_t$ in state $s_t$. Low $G_t$ decreases it.

Why REINFORCE over Q-Learning here:

Criterion	Q-Learning	REINFORCE
State representation	Discrete table	Continuous function
Scales to new states	No — unseen states have no entry	Yes — parameters generalize
Output	Value estimate per action	Probability distribution over actions
Training signal	TD error (step-by-step)	Monte Carlo return (end of episode)
Exploration	ε-greedy schedule	Stochastic policy (always explores)

The 11-dimensional continuous state space makes tabular Q-Learning impractical. REINFORCE operates directly in the parameter space of the policy function.

Hyperparameters:

Parameter	Value	Rationale
gamma	0.99	Near-full future discounting — decisions early in an episode matter
lr	0.002	Small step size — policy gradient estimates are high variance
episodes	400	Sufficient for stable convergence in this environment
max_steps	100	Episode cap — matches realistic production shift window

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Results — What Changed

Training progression:

Phase	Episodes	Mean Episode Reward	Δ vs Ep 1–50
Random-like	1 – 50	9,873	baseline
Rapid improvement	50 – 150	11,144	+12.9%
Consolidation	150 – 250	11,996	+21.5%
Exploitation	250 – 350	12,700	+28.6%
Convergence	350 – 400	12,727	+28.9%

Step-level evaluation (50 episodes, seed 99):

Metric	Random Policy	REINFORCE	Improvement
Mean step reward	97.43	128.74	+32.1%
Mean throughput (UPH)	96.2	116.0	+20.6%

Statistical validation (bootstrap, n=2,000 resamples):

• Mean improvement per episode: +3,766 reward units
• 95% CI: [+2,851, +4,679]
• P(REINFORCE > Random): 100.0%

The confidence interval lower bound is positive: the improvement is not random variation. Every single bootstrap resample showed REINFORCE outperforming the random baseline.

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Policy Logic — What the Agent Learned to Do

Learned action probability distribution (mean across 500 sampled states):

Action	Random (baseline)	Trained	Δ	Signal
Redirect Flow	16.7%	30.1%	+13.4pp	▲ Strongly over-weighted
Reassign Operator	16.7%	24.3%	+7.6pp	▲ Over-weighted
Quick Maintenance	16.7%	18.8%	+2.1pp	≈ Slightly over-weighted
No Action	16.7%	12.8%	−3.9pp	▼ Under-weighted
Increase Speed	16.7%	10.0%	−6.7pp	▼ Under-weighted
Decrease Speed	16.7%	4.1%	−12.6pp	▼ Strongly under-weighted

Three things the policy learned that a random manager never figures out:

1. High WIP → redirect flow first, not increase speed. Increasing speed with high WIP drives the terminal condition (WIP ≥ 40) and triggers the −200 penalty. Redirect Flow reduces WIP directly.

2. High failure probability → maintenance beats any throughput gain. The reward penalty for failure_prob is −10 per unit — ten times the magnitude of the micro-stop and WIP penalties per unit. Quick Maintenance addresses both failure probability and micro-stops simultaneously.

3. Low operator efficiency → reassign before touching anything else. Operator efficiency appears with a weight of +0.122 in the Reassign action and −0.292 in the Decrease Speed action. The policy learned that low efficiency is a personnel problem, not a speed problem.

Key policy weight signals:

Action	Top driver (positive)	Top driver (negative)
Redirect Flow	OperEff (+0.186), Speed (+0.146)	—
Reassign Operator	Speed (+0.141), OperEff (+0.122)	—
Quick Maintenance	CT-S4 (+0.082), MicroSt (+0.057)	—
Decrease Speed	—	OperEff (−0.292), Speed (−0.261)
Increase Speed	—	Speed (−0.077), CT-S3 (−0.073)

Decrease Speed is systematically suppressed when operator efficiency is high — the policy learned that slowing a well-run line is wasteful. Increase Speed is suppressed in high-speed states where the line is already near capacity and incremental speed gain is marginal.

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Three Operational Scenarios

The recommend_action() function evaluates any line state and returns the policy's top recommendation with probability.

Scenario A — High WIP Congestion wip_norm=0.75 · failure_prob=0.05 · operator_efficiency=0.88

Rank	Action	Probability
1	Redirect Flow	0.297
2	Reassign Operator	0.237
3	Quick Maintenance	0.189

WIP at 75% of maximum — the policy routes away from throughput-push interventions entirely. Redirect Flow reduces WIP directly; Reassign Operator prevents it from worsening through efficiency loss.

Scenario B — High Failure Risk failure_prob=0.18 · micro_stops_norm=0.70 · wip_norm=0.20

Rank	Action	Probability
1	Redirect Flow	0.303
2	Reassign Operator	0.247
3	Quick Maintenance	0.186

Failure probability at 0.18 — near the terminal threshold of 0.20. Quick Maintenance addresses both failure probability and micro-stops directly. The policy correctly prioritizes stability interventions over speed changes.

Scenario C — Low Operator Efficiency operator_efficiency=0.68 · ct_norm_s1–s6=0.80 · speed_norm=0.72

Rank	Action	Probability
1	Redirect Flow	0.335
2	Reassign Operator	0.258
3	Quick Maintenance	0.173

Efficiency at 0.68 — the operator weight in the reward function multiplies directly into throughput. Reassign Operator is the highest-leverage single intervention. Decrease Speed is suppressed in all three scenarios — the policy has systematically learned it is rarely the correct first response.

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🗂️ Repository Structure

PolicyOpt_Assembly/
├── 23_PolicyOpt_Assembly.ipynb   # Educational notebook (no outputs)
├── Data_people.csv               # 250-row sample of behavioral baseline data
├── requirements.txt
└── README.md

Note on Data_people.csv: this is the random-policy behavioral dataset, not training data for REINFORCE. The agent trains entirely online through environment interaction — no labeled examples are used. The CSV documents the performance floor.

📦 Full Project Pack — complete 23,832-row dataset, notebook with full outputs, presentation deck (PPTX + PDF), and app.py line advisor simulator available on Gumroad.

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🚀 How to Run

Option 1 — Colab:

Option 2 — Local:

git clone https://github.com/LozanoLsa/PolicyOpt_Assembly.git
cd PolicyOpt_Assembly
pip install -r requirements.txt
jupyter notebook 23_PolicyOpt_Assembly.ipynb

Requirements: numpy, pandas, matplotlib, seaborn

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💡 Five Conclusions

1 — The policy function scales where the Q-table cannot. An 11-dimensional continuous state space produces a state count that makes tabular RL intractable. REINFORCE parameterizes the policy as $W \in \mathbb{R}^{6 \times 11}$ — 66 parameters total — and generalizes to states it has never visited.

2 — Return normalization is not optional. Raw discounted returns in this environment span [+578, +16,007] across episodes. Without zero-mean unit-variance normalization, gradient steps are dominated by high-return episodes and the policy fails to learn from lower-reward trajectories. Normalization reduces variance without introducing bias.

3 — The learned priorities are operationally defensible. Redirect Flow at 30.1% and Reassign Operator at 24.3% are not arbitrary — they correspond to the two highest-leverage interventions in the reward function. The policy didn't need domain knowledge; it found the same priorities an experienced line manager would identify through years of observation.

4 — The bootstrap result is unambiguous. P(REINFORCE > Random) = 100% across 2,000 resamples. The 95% CI lower bound of +2,851 reward units per episode is economically meaningful in a production context — it corresponds to measurable throughput and quality gains. The improvement is not noise.

5 — High variance is the expected behavior, not a defect. REINFORCE reward curves are noisier than Q-Learning curves because Monte Carlo returns are estimated from full episodes rather than bootstrapped step-by-step. The correct response is baseline subtraction or Actor-Critic — not increasing the learning rate. This project documents the variance honestly and validates the improvement statistically despite it.

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👤 Author

Luis Lozano | Operational Excellence Manager · Master Black Belt · Machine Learning GitHub: LozanoLsa · Gumroad: lozanolsa.gumroad.com

Turning Operations into Predictive Systems — Clone it. Fork it. Improve it.