Cognitive Scaffold

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MENTAL MODEL · M13137

Gittins Index

Gittins Index
SystemsHigh supportAlgorithmic Decision Making
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Updated 2026-08-17

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INTRODUCTION

English translation pending.

CORE DEFINITION

The Gittins index is a dynamic allocation index introduced by John C. Gittins in a 1979 paper on bandit processes. For a discounted multi-armed bandit with independent arms, it assigns each arm a number representing the best reward rate achievable from that arm, given its current state, relative to a fixed retirement option. Gittins proved that the optimal policy is to play the arm with the highest index at every step, which reduces a problem whose state space grows exponentially into a set of separate one-dimensional calculations. The result depends on geometric discounting and independent arms, and it also holds for several related objective criteria.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Option scoring: Give each candidate project a single index instead of debating them pairwise. - Explore-exploit split: Read a high index as evidence for exploitation and a falling one as a signal to explore. - Portfolio review: Recompute every index after each result and reassign effort to the top scorer.

anchor

Anchor fast decisions

The index works because geometric discounting makes an arm's value separable: how long an arm has already been played and how it compares with the alternatives both collapse into one number that depends only on that arm's own state. Ranking arms then becomes valid at every step, since the best arm's index does not depend on what the other arms look like. This converts a sequential problem with a joint state space into independent calculations, which is why the policy stays optimal yet tractable.

MINIMUM ACTION

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Source support: Explicit

  • link
    github.comhttps://github.com/kcchien/model-thinkingZH · Explicit
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