9. Supervised Learning¶

9.1 What Supervised Learning Does In DDM¶

Intuition

Supervised learning predicts unknown quantities from data. In DDM, it usually supports the information model.

Examples:

predict travel time from time, route, weather, and traffic,
predict order probability by zone and time,
predict service duration from customer/job features,
predict cancellation probability.

Formal definition

Training data:

(features, outcome) = (z_i, y_i)

Learning goal:

learn f(z) approx y

Translation:

Use input features z to predict outcome y.

Properties

Supervised learning predicts; it does not directly decide.
Predictions become inputs to the decision model.
Accuracy matters, but decision impact matters more.

flowchart LR
    A["Historical data"] --> B["Train prediction model f"]
    B --> C["Forecast y_hat"]
    C --> D["Information model"]
    D --> E["Decision model"]
    E --> F["Decision x"]

9.2 Regression and Classification¶

Intuition

Regression predicts numbers. Classification predicts categories.

Formal definitions

Regression:

y = numerical outcome
f(z) = predicted number

Classification:

y = class label
f(z) = predicted class or probability

Worked examples

Regression:

predict travel time in minutes

Classification:

predict whether an order will be late: yes/no

Probability classification:

predict P(customer cancels | waiting time, zone, time)

9.3 Loss Functions and Evaluation¶

Intuition

A loss function measures prediction error.

Formal definitions

Squared error:

\[ \text{loss}=(\text{actual}-\text{predicted})^2 \]

Absolute error:

\[ \text{loss}=|\text{actual}-\text{predicted}| \]

Mean squared error:

\[ \operatorname{MSE} = \frac{1}{n}\sum_i \left(y_i-f(z_i)\right)^2 \]

Properties

Squared error heavily penalizes large mistakes.
Absolute error is easier to interpret.
A model with lower prediction error is not always better for decisions.

Worked example: travel-time prediction

Actual travel time:

30 minutes

Prediction A:

25 minutes
absolute error = 5
squared error = 25

Prediction B:

40 minutes
absolute error = 10
squared error = 100

Prediction A is more accurate.

9.4 From Prediction To Decision¶

Intuition

Good prediction is not the final goal. The final goal is better decisions.

Formal pipeline

\[ z \rightarrow f(z) \rightarrow S_k \rightarrow x\in X(S_k) \]

Properties

Prediction errors can create bad decisions.
The most important predictions are those that change decisions.
Sometimes a simple interpretable model is better than a complex model if it is easier to trust and maintain.

Worked example

Travel-time model predicts:

Route A = 20 minutes
Route B = 25 minutes

Decision:

choose Route A

If the model underestimates Route A during rain, the decision model repeatedly chooses the wrong route.

9.5 Supervised Learning vs ADP vs RL¶

Method	Learns what?	Used for
Supervised learning	prediction from labeled data	information model
ADP	approximate policies or values	decision model
RL	values/policies from interaction	decision learning

Exam phrase:

Supervised learning can estimate information models such as demand or travel-time predictions. ADP and RL-style methods use such information to choose decisions over time.

9.6 Decision-Focused Supervised Learning¶

Intuition

In business decision making, the best prediction model is not always the one with the lowest average prediction error. The best model is the one that improves decisions.

For example, a travel-time model that is usually accurate but badly underestimates Friday evening congestion can cause serious delivery failures.

flowchart LR
    A["Raw data<br/>orders, weather, traffic"]:::data --> B["Features z"]:::feature
    B --> C["Prediction model f(z)"]:::model
    C --> D["Forecast<br/>travel time / demand"]:::forecast
    D --> E["State S_k"]:::state
    E --> F["Decision x in X(S_k)"]:::decision
    F --> G["Business outcome"]:::outcome
    classDef data fill:#e0f2fe,stroke:#0284c7,stroke-width:2px,color:#0f172a;
    classDef feature fill:#fef9c3,stroke:#ca8a04,stroke-width:2px,color:#0f172a;
    classDef model fill:#ede9fe,stroke:#7c3aed,stroke-width:2px,color:#0f172a;
    classDef forecast fill:#dcfce7,stroke:#16a34a,stroke-width:2px,color:#0f172a;
    classDef state fill:#eff6ff,stroke:#2563eb,stroke-width:2px,color:#0f172a;
    classDef decision fill:#ffedd5,stroke:#ea580c,stroke-width:2px,color:#0f172a;
    classDef outcome fill:#f8fafc,stroke:#334155,stroke-width:2px,color:#0f172a;

Formal notation

Prediction:

\[ \hat y=f(z) \]

Decision use:

\[ \begin{aligned} S_k &\text{ includes } \hat{y},\\ x &= \pi(S_k). \end{aligned} \]

Translation:

The prediction becomes part of the state or information model; it is not the decision itself.

Worked example: travel-time prediction and routing

Two routes:

Route	Predicted time	Actual time in rain
highway	20	50
local road	30	32

If the model ignores rain, it chooses highway. If the model includes rain as a feature, it chooses local road.

Business lesson:

The feature "rain" matters because it changes the decision.

Approach comparison

Prediction model	Merit	Disadvantage	DDM use
simple average	easy and robust	ignores context	baseline information model
linear regression	interpretable	misses nonlinear patterns	travel/service time with clear drivers
tree/forest model	captures interactions	less transparent	demand by zone/time
neural network	flexible	data hungry and opaque	large-scale prediction tasks

9.8 Slide Link: Supervised Learning Builds The Information Model¶

Mental model

The overview slides place supervised learning on the information-model side of business analytics. In DDM, supervised learning is usually not the decision policy itself. It predicts quantities that the decision model needs.

Formal prediction model

Let \(z\) be features available before the decision, such as time, location, weather, or historical demand. Let \(y\) be the outcome to predict.

\[ \hat y=f_\theta(z). \]

Business translation: the model turns observed features into a forecast used in \(S_k\), \(\omega_{k+1}\), or transition probabilities.

Worked example: travel-time prediction

Feature	Example
Time	Monday 17:00
Location	downtown link
Weather	rain
Historical speed cluster	rush-hour pattern
Target \(y\)	travel time on the link

The prediction becomes part of the information model:

\[ S_k=(t_k,\text{vehicles},\text{orders},\hat\tau(t_k)). \]

Decision consequence

A better travel-time forecast can change the route selected by the decision model. But the forecast is still not the decision. The decision remains \(x\in X(S_k)\).

9.9 Validation For Decision Use¶

Intuition

A prediction model can look accurate statistically but still be weak for decisions. DDM cares whether prediction errors change the chosen decision or harm the objective.

Validation question	Business meaning
Is average error low?	forecasts are generally close
Are peak periods accurate?	rush-hour decisions are reliable
Are rare long delays captured?	service promises are protected
Does the decision improve?	model helps operations, not just metrics

Exam phrase

Supervised learning supports DDM by estimating uncertain quantities for the information model. The final decision still requires a decision model with feasible actions, costs/rewards, and an objective.

Chapter source note

Course basis: DDM information-modeling slides and supervised-learning lecture topic. Textbook enrichment: Powell on online learning, lookup tables, aggregation, and learning functions; Kochenderfer et al. on parameter learning and prediction as decision support. Supervised learning supports \(S_k\) and \(\omega_{k+1}\); it does not replace the decision model.