# Moments Matter:Stabilizing Policy Optimization using Return Distributions

arXiv: https://arxiv.org/abs/2601.01803 · HTML: https://mlsanity.com/paper/2601.01803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 5 references that are in the map.
- First posted on arXiv 5 Jan 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, 5 of 5)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Discovered Policy Optimisation](https://mlsanity.com/paper/2210.05639/) (2022)
- [Learning Risk-Aware Quadrupedal Locomotion using Distributional Reinforcement Learning](https://mlsanity.com/paper/2309.14246/) (2023)
- [Policy Optimization in a Noisy Neighborhood: On Return Landscapes in Continuous Control](https://mlsanity.com/paper/2309.14597/) (2023)

## Abstract (arXiv)

Deep Reinforcement Learning (RL) agents often learn policies that achieve the same episodic return yet behave very differently, due to a combination of environmental (random transitions, initial conditions, reward noise) and algorithmic (minibatch selection, exploration noise) factors. In continuous control tasks, even small parameter shifts can produce unstable gaits, complicating both algorithm comparison and real-world transfer. Previous work has shown that such instability arises when policy updates traverse noisy neighborhoods and that the spread of post-update return distribution R(θ), obtained by repeatedly sampling minibatches, updating θ, and measuring final returns, is a useful indicator of this noise. Although explicitly constraining the policy to maintain a narrow R(θ) can improve stability, directly estimating R(θ) is computationally expensive in high-dimensional settings. We propose an alternative that takes advantage of environmental stochasticity to mitigate update-induced variability. Specifically, we model state-action return distribution through a distributional critic and then bias the advantage function of PPO using higher-order moments (skewness and kurtosis) of this distribution. By penalizing extreme tail behaviors, our method discourages policies from entering parameter regimes prone to instability. We hypothesize that in environments where post-update critic values align poorly with post-update returns, standard PPO struggles to produce a narrow R(θ). In such cases, our moment-based correction narrows R(θ), improving stability by up to 75% in Walker2D, while preserving comparable evaluation returns.