# Delightful Gradients Accelerate Corner Escape

arXiv: https://arxiv.org/abs/2605.11908 · HTML: https://mlsanity.com/paper/2605.11908/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 7 of 7)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization](https://mlsanity.com/paper/2007.06558/) (2020)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [Softmax Policy Gradient Methods Can Take Exponential Time to Converge](https://mlsanity.com/paper/2102.11270/) (2021)
- [Policy Mirror Descent Inherently Explores Action Space](https://mlsanity.com/paper/2303.04386/) (2023)

## Built on by (most cited first, 2 of 2)

- [Fine-Tuning on Self-Generated and Reward-Weighted Data: Learning Dynamics, Convergence Rates, and Benefits of Off-Policyness](https://mlsanity.com/paper/2609.36945/) (2026)
- [Training Language Models to Fail Gracefully](https://mlsanity.com/paper/2610.20401/) (2026)

## Abstract (arXiv)

Softmax policy gradient converges at O(1/t), but its transient behavior near sub-optimal corners of the simplex can be exponentially slow. The bottleneck is self-trapping: negative-advantage actions reinforce the corner policy and can initially push the optimal action backward. We study Delightful Policy Gradient (DG), which gates each policy-gradient term by the product of advantage and action surprisal. For K-armed bandits, we prove that the zero-temperature limit of DG removes this corner-trapping mechanism on a quantitative sector near any sub-optimal corner, yielding a first-exit escape bound logarithmic in the initial probability ratio. At every fixed temperature, the same local mechanism persists because harmful actions are polynomially suppressed as they become rare. A key structural insight is that every action better than the corner action is an ally: its contribution to escape is non-negative. Combining corner instability with a monotonic value improvement identity, we prove that DG converges globally to the optimal policy in both bandits and tabular MDPs at an asymptotic O(1/t) rate. We also show, via an exact counterexample, that this tabular mechanism can fail under shared function approximation. In MNIST contextual bandits with a shared-parameter neural network, DG nevertheless recovers from bad initializations faster than standard policy gradient, suggesting that the counterexample marks a boundary of the theory rather than a practical prohibition.