Finite-Time Analysis of the Natural Policy Gradient in Finite-Horizon Markov Decision Processes

What the math gives to ML

The paper gives a constructive step-size principle for exact natural policy updates in finite-horizon problems: geometrically increasing the step size can convert the usual O(H^2/t) behavior into a geometric error decrease. The transferable asset is not standard natural gradient itself, but horizon-aware compensation for shrinking effective advantages and visitation mass near the end of an episode. A practical adaptation is to apply this schedule to the policy-head natural-gradient or trust-region update while retaining clipping or a KL cap for neural-network stability. This is most promising for episodic PPO-style training with fixed horizons, where the schedule can be tested independently of the particular policy parameterization.