Computer Science & Algorithms
Section 1
Core Idea
The Gittins index assigns a single number to each arm in a multi-armed bandit problem (with geometric discounting): it's the value of playing that arm optimally versus a fixed outside option. Choosing the arm with the highest index is optimal under the right formulation. Unlike UCB, the Gittins index is derived from the full dynamic programme; it accounts for the entire future stream of rewards and the cost of exploration. Computationally heavier than UCB, but it gives a principled, optimal policy for the discounted infinite-horizon bandit. Sub-entry under explore–exploit: when you need a rigorous rule for which option to try next, Gittins is the gold standard for the bandit setting.
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Section 2
How to See It
Deciding & Judging
You're seeing The Gittens Index when a system assigns a single score to each option (e.g. variant, channel, strategy) that encodes both estimated value and uncertainty, and chooses the highest-scoring option—the score is an "index" that optimally balances explore and exploit.
Section 3
How to Use It
In bandit problems with discounting, compute (or approximate) the Gittins index per arm and play the arm with the highest index. When exact computation is costly, use index-based heuristics (e.g. UCB, Thompson sampling) that mimic the same idea: one number per arm that combines mean and uncertainty. In product and growth: treat variants or channels as arms; use an index policy to allocate traffic and learn.
Decision filter
"Are we repeatedly choosing among options with uncertain payoffs and learning as we go? If yes, an index policy (Gittins when tractable, UCB or Thompson as approximations) gives a principled explore–exploit balance."
As a founder
Allocation across channels, features, or segments is a bandit: you learn as you go. The Gittins index is the optimal rule for the discounted bandit; in practice, UCB or Thompson sampling approximate it. Adopt index thinking: one score per option that combines reward and uncertainty, then choose the top.
Section 5
Founders & Leaders
Ed ThorpMathematician; author, Beat the Dealer; quantitative investor
Thorp used optimal stopping and dynamic programming in blackjack and investing—the same machinery behind the Gittins index. Optimal allocation under uncertainty with learning is the bandit problem; the index is the solution. Founders can adopt the mindset: score options by value and uncertainty, then allocate to the highest index; when exact Gittins is infeasible, use UCB or Thompson.
Section 7
Connected Models
Reinforces
Explore-exploit Tradeoff
The Gittins index is the optimal resolution of the explore–exploit tradeoff for the discounted bandit: one number per arm that encodes when to exploit (high mean) and when to explore (high uncertainty). Same tradeoff, solved exactly for that setting.
Tension
Upper Confidence Bound
UCB is a simple index (mean + confidence bound) that's easy to compute; Gittins is the optimal index but harder to compute. The tension: UCB approximates Gittins and works well in practice; use Gittins when you need the exact optimal policy and can afford the computation.
Leads-to
Kelly Criterion
Kelly optimises bet size given edge and odds; Gittins optimises which arm to play given beliefs. Both are optimal allocation under uncertainty—Kelly for capital, Gittins for attention across options.
Section 8
One Key Quote
— J.C. Gittins, Bandit Processes and Dynamic Allocation Indices (1979)"The optimal strategy is to choose at each stage the arm with the largest Gittins index." The index reduces the multi-armed bandit to a single number per arm; the policy is greedy in indices.
Section 11
Summary & Further Reading
The Gittins index gives the optimal policy for the discounted multi-armed bandit: assign an index to each arm, play the arm with the highest index. It optimally balances explore and exploit. When computation is costly, UCB or Thompson sampling approximate it.
01
Paper
Original derivation of the Gittins index and optimality.
02
Book
Comprehensive treatment of index policies and bandits.
03
Internal
The high-level tradeoff; Gittins and UCB are concrete policies that resolve it.