Standard policy gradients weight each sampled action by advantage alone, regardless of how likely that action was under the current policy. This creates two pathologies: within a single decision context (e.g. one image or prompt), a rare negative-advantage action can disproportionately distort the update direction; across many such contexts in a batch, the expected gradient over-allocates budget to contexts the policy already handles well. We introduce the \textit{Delightful Policy Gradient} (DG), which gates each term with a sigmoid of \emph{delight}, the product of advantage and action surprisal (negative log-probability). For $K$-armed bandits, DG provably improves directional accuracy in a single context and, across multiple contexts, shifts the expected gradient strictly closer to the supervised cross-entropy oracle. This second effect is not variance reduction: it persists even with infinite samples. Empirically, DG outperforms REINFORCE, PPO, and advantage-weighted baselines across MNIST, transformer sequence modeling, and continuous control, with larger gains on harder tasks.

In contrast, we use 10% of the training set9 for validation, and treat the validation set as apurely held-out test set (this also means that we train on less data).10 Wewillexplainthismoreclearly.30 both spheres are sufficiently tiny (i.e.

Optimal Transport (OT) + Fairness (R2, R4): Let us highlight two key differences between "Wasserstein Fair10 Classification" (Jiang et al.) and our work. Generally group fairness constraints31 are trying to reflect a certain independence between the prediction and the sensitive attribute.

ERM combines two well-understood techniques: mini-batch sampling and gradient-based optimization using backpropagation.

There are two more things to verify.