Clever marketing:
- Cryptic billboard with 5 numbers in SF→ token IDs from OpenAI’s tokenizer, decoded to get
listenlabs.ai/puzzle
Problem:
- you are the bouncer at berghain. fill 1,000 spots from a stream of random arrivals while meeting specific quotas
- do not reject more than 20,000 people, and the less rejected the better
Challenges:
- constrained optimization, real-time resource allocation
- people arrive one by one, and have binary attributes. you must decide immediately whether to accept or reject.
- attributes are correlated - young people can also be well dressed → may overshoot quotas by accepting these early, but reject too many and you can’t meet your minimum
Solutions explored by the author
- greedy - accept anyone that contributes to a quota deficit, accept all remaining for open spots → 1200 rejections
- Gaussian-copula modeling and linear programming
- model the multivariate distribution of attributes, solve for optimal acceptance probabilities
- …
- 900 rejections, but very complex
- threshold-based algorithms
- dynamic risk threshold - be lenient earlier, stricter later
- prefer people satisfying multiple constraints - compute a coverage score
- threshold the decision with mild randomness
- 800 rejections
Solution from leaderboard #2
- dynamic programming with a DB table of 1 gb …
- for later scenarios, table too big
- “as number of people gets large, only the relative ratios between numbers matter” → differential equation representation , track relative ratios instead of absolute counts
Solution from leaderboard #1
- tuned parameters to use for each scenario instead of one universal algorithm