A simulation study modeling a tuition-dependent institution that uses contextual multi-armed bandits to learn the optimal institutional aid discount to offer admitted students.
The core tension
Higher discounts increase the probability a student enrolls — but reduce net tuition per enrolled student. So the revenue-maximizing discount is not the yield-maximizing discount, and the right answer differs by student segment. That makes aid packaging a genuine sequential optimization problem, not a fixed-rate policy.
What I modeled
I simulated 5,000 admitted students across three segments — High-Need, Merit-Focused, and Low-Need — each with its own logistic enrollment-response curve. The "arms" are discount rates from 20% to 60%; the reward for an offer is a Bernoulli enrollment draw times net tuition. I then pitted three bandit algorithms against each other in both contextual (per-segment) and non-contextual forms:
- ε-Greedy
- UCB1
- Thompson Sampling
What I found
- Thompson Sampling (contextual) achieved the lowest cumulative regret, converging most reliably to the per-segment optimal arm — its Bayesian posterior tunes its own exploration without manual hyperparameters. UCB1 was a close second; ε-Greedy lagged because it never stops exploring.
- Context matters more than algorithm choice. The gap between contextual and non-contextual versions of the same algorithm was larger than the gap between algorithms. Accurate segment identification yields more revenue than fine-tuning exploration parameters.
- Yield ≠ revenue. The 60% discount maximized enrollment for every segment but maximized revenue for none. Institutions chasing raw yield metrics will systematically over-discount.
- Early exploration has a real cost — roughly the first ~500 admits — but every contextual bandit recouped it comfortably by 5,000 admits versus a naive fixed-discount strategy.
Why it matters
This is the financial-aid optimization problem at the heart of enrollment management, made tractable. It also previews the optimization thesis behind Allocate, the higher-education platform I'm building through PraxisIQ: treat institutional aid as a portfolio-allocation problem and optimize across the student body within budget and compliance constraints, rather than applying static merit-and-need rules. The notebook is explicit about the assumptions a production system must revisit — i.i.d. arrivals, perfectly observed segments, no capacity constraints, and the ethics of differential pricing by inferred need.
The full simulation, enrollment-response model, and algorithm implementations are in the accompanying notebook.