
The multi-armed bandit problem is a classic decision-making framework where you must choose between:
| Action | Description |
|---|---|
| Exploit | Use what you already know works best |
| Explore | Try something new to gain better knowledge |
Imagine a doctor choosing between a known treatment (reliable but maybe not optimal) vs. a new experimental drug (unknown outcome, but potentially better).
The PXT team faces this constantly:
Known Model (Exploit) ←——————→ New LLM Approach (Explore)
Safe, predictable Costly, uncertain, potentially superior
In standard bandit problems, exploration is free. In costly bandits, every observation or experiment has a real cost:
Cost of Knowledge = Time + Compute + Risk + Human Capital
Foundation Models (Claude, GPT) → API calls cost money per token
Fine-tuning → GPU hours on SageMaker
Deployment → Latency + infrastructure costs
You cannot learn everything. Every piece of knowledge has a price. The optimal algorithm decides WHEN the price is worth paying.
An algorithm is measured by regret — the difference between:
Regret = Σ (Best Possible Reward - Actual Reward)
over all decisions made
The article describes this through their evaluation frameworks:
Rigorous Evaluation = Measuring:
├── Model Performance (are predictions accurate?)
├── Bias Detection (are we fair across groups?)
├── Safety Metrics (are outputs harmful?)
└── Business Impact (does it actually help?)
Each metric answers: "Are we paying the right price for the right knowledge?"
Principle: When uncertain, assume the best possible outcome and try it.
In the article's context:
New LLM Approach:
├── Estimated Performance: 75%
├── Uncertainty Bonus: +15% (because we haven't tried it much)
└── UCB Score: 90% → TRY IT
How PXT applies this:
Principle: Maintain a probability distribution over what's best, sample from it, act on the sample.
Belief about Model A: [====|====] → 60% chance it's best
Belief about Model B: [===|=====] → 40% chance it's best
→ Randomly pick proportional to belief
→ Update belief after seeing result
→ Repeat
In the article's context: This maps to their Bayesian experimental design:
Principle: Don't just maximize reward. Maximize reward per unit of information cost.
Expected Reward Gain
IDS Score = ─────────────────────────
Information Cost of Action
This is the most sophisticated strategy and directly maps to the article's core mission:
PXT Decision Framework:
├── Option A: Fine-tune existing model
│ ├── Expected Gain: +5% accuracy
│ ├── Cost: 2 weeks + $50K compute
│ └── IDS Score: LOW
│
└── Option B: Prompt engineering on Claude
├── Expected Gain: +4% accuracy
├── Cost: 3 days + $500
└── IDS Score: HIGH → DO THIS FIRST
The article describes building a "talent intelligence layer" — this IS a costly bandit system at scale:
Talent Intelligence Layer
│
├── Natural Language Understanding
│ └── Which NLP model best understands job descriptions?
│ (Bandit: explore different models, exploit best one)
│
├── Network Science
│ └── Which collaboration signals predict performance?
│ (Bandit: costly to measure, must choose wisely)
│
└── Predictive Modeling
└── Which features matter for employee wellbeing?
(Bandit: each feature costs data collection effort)
Observe Employee Data
↓
Update Beliefs About What Works
↓
Choose Next Best Action (Optimal Algorithm)
↓
Pay the Cost of Learning
↓
Receive Signal (Did it help?)
↓
[Repeat — 1 million+ employees]
| Scale | Challenge | Optimal Response |
|---|---|---|
| 1 person | Simple A/B test | Any algorithm works |
| 1,000 people | Group differences emerge | Contextual bandits |
| 1,000,000 people | Heterogeneous needs | Hierarchical costly bandits |
Standard bandits ask: "What's the best action overall?"
Contextual bandits ask: "What's the best action given this specific context?"
Context = {
employee_level: "L5",
domain: "operations",
tenure: "2 years",
location: "fulfillment_center"
}
→ Optimal action for THIS person may differ from global optimum
This is why the article emphasizes:
THE COSTLY BANDIT FRAMEWORK
═══════════════════════════
PROBLEM: Make decisions under uncertainty when learning is expensive
MEASURE: Regret = Gap between actual and optimal outcomes
STRATEGIES:
UCB → Be optimistic, explore uncertain options
Thompson → Sample proportional to belief
IDS → Maximize reward per unit of information cost
SCALE UP:
Contextual → Personalize decisions to context
Hierarchical → Handle multiple levels simultaneously
APPLIED TO PXT:
┌─────────────────────────────────────────────┐
│ Which AI model helps which employee │
│ in which context at what cost │
│ to maximize wellbeing and productivity │
│ across 1M+ people continuously? │
└─────────────────────────────────────────────┘
The "price of knowledge" is not a problem to eliminate — it's a constraint to optimize around. The best algorithms don't try to learn everything; they learn exactly what's needed, when it's needed, at the lowest possible cost, while still achieving near-optimal outcomes.
This is the scientific foundation underlying everything described in the article — from prompt engineering experiments to mentoring junior scientists to building production ML systems.