Function Approximation

the deadly triad

Sutton and Barto's name for the three ingredients that, when combined, can make value learning blow up. Each alone is fine; together they are dangerous. The three are: function approximation (sharing weights across states), bootstrapping (updating a guess toward another guess, as TD does), and off-policy training (learning about one policy from data generated by another).

With all three, an update at one state can change the bootstrapped targets at the very states you used to compute it, and the distribution mismatch from off-policy data means the usual contraction that guarantees convergence no longer holds. Errors can feed back and amplify, so the weights diverge to infinity even on tiny problems (Baird's counterexample is the classic demonstration).

Drop any one leg and stability returns: use Monte Carlo instead of bootstrapping, stay on-policy, or use a table instead of approximation. Modern deep RL keeps all three (that is where the power is) and instead leans on target networks, experience replay, and gradient-TD-style fixes to tame the instability.

Each leg is harmless alone; the instability is strictly an interaction effect of all three.

Also called
deadly triad