Gittins Index

The Gittins Index does something that seems almost impossible: it compresses an entire future of uncertainty, learning, risk, and reward into a single number. Instead of calculating every possible sequence of decisions, an intelligent agent simply chooses the option with the highest index. Under the right conditions, this astonishingly simple rule is not an approximation—it is mathematically optimal. But its elegance depends on an unrealistic assumption: ignored opportunities must remain frozen. The moment the world continues changing without us, the perfect solution begins to collapse.